To find the distance between the homes of Tom and Jimmy, it is assumed
that the distances from their home to the café are equal.
The distance between Tom and Jimmy's home is [tex]\underline{1,617.\overline 7 \ meters}[/tex]Reasons:
The direction in which Tom and Jimmy walks = Towards each other
The speed at which Tom walks = 52 meters per minute
The speed with which Jimmy walks = 70 meters per minute
The time at which Tom leaves = 4 minutes earlier than Jimmy
The point at which they meet = The café
The rate of their speed = Constant
Required:
The distance between Tom and Jimmy home.
Solution:
Tom and Jimmy had a plan to walk at the same speed and meet up at the café.
We have;
The café is equal distance from Tom and Jimmy's houses.
Which gives the following simultaneous equation.
52 × (4 + t) = The distance of Tom's house from the café
70 × t = The distance of Jimmy's house from the café
52 × (4 + t) = 70 × t52 × 4 = 70 × t - 52 × t = 18 × t
[tex]\displaystyle t = \frac{52 \times 4}{18} = \frac{104}{9} = 11.\overline{6}[/tex]
The time it take Jimmy to reach the café, t = [tex]\mathbf{11.\overline6}[/tex] minutes
The distance between their homes, d = 52 × (4 + t) + 70 × t
∴ d = 52 × (4 + [tex]11.\overline6[/tex]) + 70 × [tex]11.\overline6[/tex] = 1,617.[tex]\mathbf{\overline 7}[/tex]
The distance between Tom and Jimmy's home = 1,617.[tex]\overline 7[/tex] metersLearn more about simultaneous equations here:
https://brainly.com/question/12413726
Solve the equation for x.
2(2) + x = 4
[tex]2(2) +x =4\\\\\implies 4 +x =4\\\\\implies 4 +x -4 = 4-4\\\\\implies x = 0[/tex]
Answer:
x = 0
Solve solution:
Question:
2(2) + x = 4
Multiply:
2 x 2 + x 4
Cancel equal terms:
4 + x = 4
Answer: x = 0
Write an expression that represents 42 is the product of 6 and y
No explanation needed, just tell me the answer :)
Answer:
[tex]6y = 42\\y = 7[/tex]
Step-by-step explanation:
A function is defined as k(x)=2x^2 - 5x + 3 The value of k(-3) is
Answer:
36
Step-by-step explanation:
k(-3) = 2(-3)² - 5(-3) + 3
= 18 - (-15) + 3
= 33 + 3
= 36
Josh went to a restaurant for dinner. The cost of the
meal was $24 with a discount of $2. If the total bill includes
an 8% sales tax and a 14% tip, what is the discount
percent? What was the total bill including the tax and the
tip?
Answer:
17.41 Dollars
Step-by-step explanation:
First, you take the discount, which is 2 dollars, so now the cost without any additional costs is 22 dollars. Next, find 8 percent of 22 by multipling 22*0.08 and then you get 1.76. Subtract that from 22 and 20.24. Then take 14 percent of 20.24 by multiplying it by 0.14, which you get 2.8336. Round that down and you get 2.83. Subtract that from that and you get 17.41.
a class is 20% boys and 80% girls of the boys 30% wear glasses of the girls 40% wear glasses what percent of the class wears glasses??????
Answer:
38%
Step-by-step explanation:
20%-30%, 100%-30%, 20%-6%
80%-40%, 100%-40%, 5%-2%, 80%-32%
32+6=38%
Help!!
Question in picture!!
Step-by-step explanation:
A. monomial
B. polonomial
hope it helps.
stay safe healthy and happy.
Answer:
A= monomial
B= trinomial
Will Give Brainliest
Answer:
x = 19
Step-by-step explanation:
3x - 3 = 6(x - 10)
3x - 3 = 6x - 60 Use dist property
Subtract 3x from both sides
-3 = 3x - 60
Add 60 to both sides
57 = 3x
Divide both sides by 3
19 = x
What is the range of this graph?
The range is the y value of where the dots are located.
Answer: (3,4,5,6)
The conditional relative frequency table was calculated by row using data from a survey of one station’s television programming. The survey compared the target audience with the type of show, either live or recorded, over a 24-hour time period. A 4-column table with 3 rows titled television programming. The first column has no label with entries adult, children, total. The second column is labeled live with entries 0. 625, 0. 5, nearly equal to 0. 583. The third column is labeled recorded with entries 0. 375, 0. 5, nearly equal to 0. 417. The fourth column is labeled total with entries 1. 0, 1. 0, 1. 0. Which is the best description of the value 0. 375 in the table? Given that the program was targeted at adults, there is a 37. 5% chance that it was recorded. Given that the program was recorded, there is a 37. 5% chance that it was targeted at adults. 37. 5% of the programs are targeted at adults. 37. 5% of the programs are recorded.
The conditional relative frequency presents the result of the survey that conveys information about the programming and the audience.
The best description of the value 0.357 in the table is; Given that the program was targeted at adults, there is a 37.5% chance that it was recorded.Reasons:
The table is presented as follows;
[tex]\begin{tabular}{|c|c|c|c|}&Live&Recorded&Total\\Adult&0.625&0.375&1.0\\Children&0.5&0.5&1.0\\Total&\approx 0.583&\approx 0.417&1.0\end{array}\right][/tex]
Based on the given table, we have that the programs are categorized based on the intended audience.
Therefore, the 0.375, indicates that 37.5% of the program targeted at adults are recorded.
Therefore, the correct option is;
Given that the program was targeted at adults, there is a 37.5% chance that it was recorded.
Learn more about relative frequency table here:
https://brainly.com/question/8470699
https://brainly.com/question/3712144
Answer:
A
Step-by-step explanation:
its a
37. Briefly explain how the use of credit helped increase the average
American's standard of living in the 20th century.
Answer: If a person has a better credit, they have better chances of getting the job they had applied for. Getting the job means they get a stable income. Having a stable income helps a person to buy all essential needs.
Step-by-step explanation:
what is the equation
Answer:
y = -2x+9
Step-by-step explanation:
To figure out equations of tile patterns simply count the initial value and the rate of change, then convert it into (slope intercept form) which is
y = mx+b
In this case the rate of change is -2x because each figure loses 2 blocks as it goes.
You can also see the the initial figure 1 has 9 blocks so this is our constant
With this information we can create the equation y = -2x+9
m = -2
x = x
b = 9
If more aid is needed a simple search of (Visual Pattern - Writing an Equation and Creating a Table) will help you with a video easily.
I’ll give 100 points
Answer:
2055 is the answer.
Step-by-step explanation:
If x represents the number of minutes and y represents the hiker elevation in feet.
y = 8.19x + 663
y = 8.19(170) + 663
y = 1392.3 + 663
y = 2055.3
Hope it helps:)
Answer:
:)
Step-by-step explanation:
if each quadrilateral below is a rectangle, find the missing measures.
Answer:
Recall each angle in a rectangle is 90 degrees. So to find the other portion, subtract the given angle from the 90 degrees.
Step-by-step explanation:
The missing measures of the angles are as follows:
m∠BCD = 90°
m∠ABD = 16°
m∠CBE = 74°
m∠ADE = 74°
m∠AEB = 148°
m∠DEA = 32°
What is a rectangle?A rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal; or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square.
here, we have,
to determine the measures of the angles:
The figure that completes the question is added as an attachment
From the figure of the rectangle, we have:
m∠BDC = 16°
A rectangle has four (4) interior angles that are 90 degrees each.
This means that
m∠ADE = 90 - 16
m∠ADE = 74°
Also, we have:
m∠ABD = m∠BDC = 16° by the alternate interior angles
By the complementary angle, we have:
m∠CBE = 90 - 16 = 74°
By the alternate interior angles, we have
m∠ADE = m∠CBE = 74°
Solving further, we have the following equations:
m∠AEB = 180 - 2(16)
m∠AEB = 148°
m∠DEA = 180 - m∠AEB
m∠DEA = 180 - 148
m∠DEA = 32°
Hence, the measure of the angle DEA is 32 degrees
m∠BCD = 90°
m∠ABD = 16°
m∠CBE = 74°
m∠ADE = 74°
m∠AEB = 148°
m∠DEA = 32°
Read more about rectangles at:
brainly.com/question/2500701
#SPJ2
If there are 30 boys and 12 girls in a room, fill out all of the possible ratios of boys to girls that could be made
Answer:
30:12
Step-by-step explanation:
A shopkeeper orders a special brand of coffee powder to be delivered to
him. A packet of this coffee powder cost $2. These packets are packed into
containers which cost $3 each. Each container can hold 30 packets. A van
delivers 60 containers of this coffee powder to the shop and charges $20 for
transport, How much does the shopkeeper pay altogether?
Answer:
$3800
Step-by-step explanation:
30 x 2 = 60
60 + 3 = one container
60 containers = 63 x 60
3780 + 20
3800
Solve the system of equations
{y= 15x+9
{y= 1/2x–20
What is the solution to the system?
[tex]y = 15x +9~~~~.....(i)\\\\y = \dfrac 12 x -20~~~ ....(ii)\\\\\\\text{Substitute equation (i) in equation (ii):}\\\\15x +9 = \dfrac 12 x -20\\\\\ \implies 9 +20 = \dfrac x2 - 15 x\\\\\implies 29 = -\dfrac{29 x}2\\\\\ \implies 1 = -\dfrac x 2\\\\\implies x= -2\\\\\text{Substitute}~ x=-2~ \text{in equation (i):}\\\\y = 15(-2) +9 = -30 +9 = -21\\\\\text{Hence}~ (x,y) = (-2,-21)[/tex]
Solve the set of simultaneous equations graphically. Use a scale of 1cm = 1 unit on both axes.
y=4+x
y=1+3x ; 0≤x≤6
Graphs attached
(x,y)=(1.5,5.5)3
5
+
2
3
=
whats the answer
Answer:
19/15 is the answer
solve one step equation
5x = -15
Answer:
x=-3
Step-by-step explanation:
This is a one step solution all you do is divide 5 into -15
-15/5 = -3
so -3 = x
What is?..
1. 8 4/7 divided by 15?
2. How many 1/4-pound hamburgers can you make from 3 1/2 pounds of ground beef ?(In simplest form)
3. 3 divided by 1 1/5 plus 1/3? (Evaluate the expression. Write the answer in simplest form.)
4. 2/5 plus 2 1/6 divided by 5/6? (Evaluate the expression. Write the answer in simplest form.)
5. 6 1/2 - 7/8 divided by 5 11/16? (Evaluate the expression. Write the answer in simplest form.)
HURRYYYYYY PLEASEEEE.
Answers:
1. 4/7
2. DIVIDE – 3 ½ ÷ ¼ = 14 hamburgers
3. 2 5/6
4. 3
5. 6 9/26
HELP 15 PNTS.
IF CORRECT, WILL MARK BRILLIANT
Answer:
2nd question 4y is a coefficient
Step-by-step explanation:
4y^2 - 18y + 2
4 is the coefficient 18 is also a coefficient, because of the y, 2 is the constant. when a number has a variable, or a letter, it is a coefficient. 4y^2 is a term, 18y is a term, and 7 is a term. 3 terms with a coefficient of 4. i hope you get it right
1. The price of one share of a stock fell 4 dollars each day for 8 days. How
much value did one share of the stock lose after 8 days?
2. A credit card company charges a late fee of 25 dollars each time a customer
fails to pay on time. A customer missed the payment 4 times last year. At
the customer's request and out of courtesy, the credit card company
decides to cancel all late fees for that year. Write a numerical expression to
show how much money was return.
Step-by-step explanation:
1.
$4 for 8 days. that means $4 on each and every day, 8 times.
so, in total that is 4 × 8 = $32
that is how multiplications work.
m×n means that m is added n times (or vice versa and n is added m times).
2.
similar here.
$25 each time the customer missed a payment. and he missed 4 times that year.
the bank returned the fees for all 4 occasions. so,
returned money = 25 × 4 = $100
When r= 1 , h=2.4 find r in terms of h
Answer:
r= 5/12 h
Step-by-step explanation:
r/h = 1/2.4
r =[tex]\frac{10}{24}[/tex]h
r=[tex]\frac{5}{12}[/tex]h
expand and simplify (m+7) (m+3)
Answer:
m^2+10m+21
Step-by-step explanation:
Distribute:
m times m is m^2
m times 3 is 3m
7 times m is 7m
7 times 3 is 21
=> m^2+3m+7m+21
Add 3m and 7m
=> m^2+10m+21
Thus the equation is
m^2+10m+21
Hope this helps!
(m + 7)(m + 3)
= m(m + 3) + 7(m + 3)
= m² + 3m + 7m + 21
= m² + 10m + 21
____
Hope it helps ⚜
please i beg for help !!!!!!!!!!! will mark brainlist
Answer:
[tex]x=-10[/tex]
Step-by-step explanation:
This deals with negative exponents.
[tex]x^{-2}=\frac{1}{x^2}[/tex]
27 and 9 are both powers of 3, so we need to find a way to make both of these into a base 3.
9 is easy, thats just:
[tex]9=3\times3=3^2[/tex]
1/27 is a little more difficult. Start with 27:
[tex]27=9\times3=3\times3\times3=3^3[/tex]
and because its a 1/27, that exponent has to be negative.
[tex]3^3=27\\3^-^3=\frac{1}{27}[/tex]
Now we can get both of them to base 3, so do that in the given equation:
[tex]3^{(-3)\times(4-x)}=3^{(2)\times(2x-1)}[/tex]
Same as last time, the bases can be canceled out as the exponents have to be equal for this equation to be true.
[tex]3^{(-3)\times(4-x)}=3^{(2)\times(2x-1)}\\(-3)\times(4-x)=(2)\times(2x-1)[/tex]
Finally, solve for x:
[tex]-3(4-x)=2(2x-1)\\-12+3x=4x-2\\-10+3x=4x\\x=-10[/tex]
A rock is thrown into a pool 72 inches deep. The rock sinks at a rate of 4 inches per
second (s). The rock's height (h) above the bottom of the pool is given by the
equation: h = 72 – 4s. After how many seconds will the rock be half way to the
bottom?
Half of 72 is 36. If you divided 36 by 4, you would get 9. So, s = 9 and means that it takes 9 seconds for the rock to be sunk half way.
What is the slope and y-Intercept of the equation 3(y – 2) + 6(x + 1) - 2 = 0?
A. Slope = -2, y-intercept = 2/3
B Slope = 2, y-intercept =2/3
C Slope = -2, y intercept = -2/3
D Slope = 2, y intercept= -2/3
E Slope = -2, y intercept = 3/2
Answer:
A. Slope = -2, y-intercept = 2/3Step-by-step explanation:
Convert the given equation into slope-intercept form:
3(y - 2) + 6(x + 1) - 2 = 03y - 6 + 6x + 6 - 2 = 03y + 6x - 2 = 03y = - 6x + 2y = - 2x + 2/3The slope is -2, the y-intercept is 2/3
Correct choice is A
⇒ 3(y - 2) + 6(x + 1) - 2 = 0
⇒ 3y - 6 + 6x + 6 - 2 = 0
⇒ 3y = -6x + 2
⇒ y = (-6x + 2)/3
⇒ y = -2x + ⅔
FINAL ANSWER :Slope = -2
Y - intercept = +⅔
Answer :Option (a) is the correct answer .
Use the graph of △ABC with midsegments DE, EF and DF. Show that EF is parallel to AC and that EF=1/2 AC
According to the midsegment theorem, the midsegments are parallel to
and half the length of the opposite side.
The completed statement are as follows;
Because the slopes of [tex]\overline{EF}[/tex] and [tex]\overline{AC}[/tex] are both -4, [tex]\overline{EF}[/tex] ║ [tex]\overline{AC}[/tex]EF = [tex]\underline{\sqrt{17}}[/tex] and AC = [tex]\underline{2 \cdot \sqrt{17} }[/tex]Because [tex]\underline{\sqrt{17} }[/tex] = [tex]\underline{\frac{1}{2} \cdot 2 \cdot \sqrt{17} }[/tex], [tex]EF = \frac{1}{2} \cdot AC[/tex]Reasons:
From the given graph of ΔABC, we have;
Coordinates of the points A, B, and C are; A(-5, 2), B(1, -2), and C(-3, -6)
The coordinates of the point D and E on [tex]\mathbf{\overline{DE}}[/tex] are; D(-4, -2), and E(-2, 0)
The coordinates of the point F is; F(-1, -4)
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]\displaystyle Slope \ of \ line \ \overline{AC} = \mathbf{\frac{(-6) - 2}{-3 - (-5)} = \frac{-8}{2}} = -4[/tex]
[tex]\displaystyle Slope \ of \ line \ \overline{EF} = \frac{0 - (-4)}{-2 - (-1)} = \frac{4}{-1} = -4[/tex]
[tex]Length \ of \ segment,\ l = \sqrt{\left (x_{2}-x_{1} \right )^{2}+\left (y_{2}-y_{1} \right )^{2}}[/tex]Length of EF = √((-1 - (-2))² + (-4 - 0)²) = √(17)
Length of AC = √((-3 - (-5))² + (-6 - 2)²) = √(4 × 17) = 2·√(17)
Therefore, we have;
Because the slope of [tex]\mathbf{\overline {EF}}[/tex] and [tex]\mathbf{\overline {AC}}[/tex] are both , -4, [tex]\overline {EF}[/tex] ║ [tex]\overline {AC}[/tex]. EF = [tex]\underline{\sqrt{17}}[/tex], and AC
= [tex]\underline{\frac{1}{2} \cdot 2 \cdot \sqrt{17}}[/tex],. Because [tex]\underline{\sqrt{17}}[/tex] = [tex]\underline{\frac{1}{2} \cdot 2 \cdot \sqrt{17}}[/tex], [tex]EF =\mathbf{ \frac{1}{2} AC}[/tex]
Learn more about midsegment theorem of a triangle here:
https://brainly.com/question/7423948
Answer plz answer !!!
Answer:
B
Step-by-step explanation:
1/4 yard long, area is 1/3 and we have to find the width so:
1/3(area) divided by 1/49(length) would get you your width
What number comes in the blank?
20 x 47 x 5 = ____ x 100
Answer:
47
Step-by-step explanation:
20*47= 940
940*5=4,700
47*100=4,700