Answer:
Step-by-step explanation:
First both the rational numbers should have same denominators. So, find least common denominator
Least common denominator is 10
[tex]\frac{-1}{5}=\frac{-1*2}{5*2}=\frac{-2}{10}\\\\\\\frac{1}{2}=\frac{1*5}{2*5}=\frac{5}{10}\\\\\\[/tex]
Now multiply the numerator and denominators of the both the numbers by 10.
[tex]\frac{-2*10}{10*10}= \frac{-20}{100} \ and \ \frac{5*10}{10*10}=\frac{50}{100}\\\\\\Now\ 10 \ rational \ numbers \ between\frac{-20}{10} \ and \ \frac{50}{100} \ is \\\\\\\frac{-19}{100},\frac{-18}{100},\frac{-17}{100},\frac{-16}{100}.\frac{-15}{100},\frac{-14}{100},\frac{-13}{100},\frac{-12}{100},\frac{-11}{100};\frac{-10}{100}[/tex]
find the x-intercept and y-intercept from the following linear equation: -7x+4y=56
Answer:
x-intercept = (-8,0) y-intercept = (0,14)
Step-by-step explanation:
-7x + 4y = 56
4y = 7x + 56
y = 7/4x + 14
y-intercept = 14
0 = 7/4x + 14
-7/4x = 14
x = -8
. If R1 = {(x, y)| y = 2x + 7, where x∈ R and -5 ≤ x ≤ 5} is a relation. Then find the domain and range of R1.
Answer:
Domain is [-5, 5]
Range is [-3, 17]
Step-by-step explanation:
R1 = {(x, y)| y = 2x + 7, where x∈ R and -5 ≤ x ≤ 5}
The domain is given by the all possible input values of x . Here the function is defined for -5 ≤ x ≤ 5, so the domain is [ - 5, 5].
The range is given by the output values of he function.
When x = - 5
f (- 5) = 2 (-5 ) + 7 = - 3
When x = 5
f (5) = 2 (5) + 7 = 17
So, the range is [ -3 , 17].
Let f(x) = -2x - 7 and g(x) = -4x + 6. Find (gof)(-5).
Answer:
(g ￮ f )(- 5) = - 6
Step-by-step explanation:
Evaluate f(- 5), then substitute the value obtained into g(x)
f(- 5) = - 2(- 5) - 7 = 10 - 7 = 3 , then
g(3) = - 4(3) + 6 = - 12 + 6 = - 6
Answer:
[tex](gof)(-5)=-6[/tex]
Step-by-step explanation:
One is given the following information;
[tex]f(x)=-2x-7\\g(x)=-4x+6[/tex]
One is asked to find the following,
[tex](g o f)(-5)[/tex]
The expression ([tex]gof[/tex]) is another way to denote ([tex]g(f(x))[/tex]), in essence, substitute function (f) into function (g) in place of parameter (x). The simplify to find the resulting function;
[tex]g(f(x))\\=-4(-2x-7)+6\\=(-4)(-2x)+(-4)(-7)+6\\=8x+28+6\\=8x+34[/tex]
One is asked to evaluate the function ([tex]gof[/tex]) for (-5). Substitute (-5) into the function and simplify to evaluate;
[tex](gof)(-5)=8x+34\\=8(-5)+34\\=-40+34\\=-6[/tex]
Find the lowest common multiple of 180 and 140.
Hello,
In prime decomposition:
180=2²*3²*5
140=2²*5*7
lcm(180,140)=2²*3²*5*7=1260
Proof: 1260/180=7 and 1260/140=9
A fire extinguisher releases 27/4  liters of carbon dioxide in 9/16 minutes what is the speed in terms of liters per minute
Answer:
12 liters per min
Step-by-step explanation:
Math
27/4 = x
9/16 1
27/4=(9/16)x
Divide both sides by 9/16
12=x
find 3 rational numbers between (-3-4) and (3/4)
Answer:
The three Rational between 3 and 4
A rational number between 3 and 4 is 1/2 (3 + 4) = 7/2. Hence, 13/4, 7/2 and 15/4 are the three rational numbers lying between 3 and 4.
Step-by-step explanation:
Using Euler's formula, how
many edges does a polyhedron
with 5 faces and 5 vertices have?
[?] edges
Euler's Formula: F + V = E + 2
Answer:
8 edges
Step-by-step explanation:
Form the formula F+V=E+2
U make E the subject by moving everything thing else to the left hand side
F+V-2=E
this implies 5+5-2=E
10-2=E
therefore Edges = 8
The polyhedron with 5 faces and 5 vertices has 8 edges.
To determine the number of edges in a polyhedron with 5 faces and 5 vertices using Euler's formula (F + V = E + 2).
we need to substitute the given values into the equation.
Given:
Number of faces (F) = 5
Number of vertices (V) = 5
Substituting these values into Euler's formula, we have:
5 + 5 = E + 2
Simplifying the equation:
10 = E + 2
Subtracting 2 from both sides:
E = 10 - 2
E = 8
Therefore, the polyhedron with 5 faces and 5 vertices has 8 edges.
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Johan published a monthly poetry magazine. In March he printed 1400 copies of magazine. In April he increased his print run by 15%
Answer:
1610
Step-by-step explanation:
Answer:
1610
Step-by-step explanation:
you can easily get the solution without a calculator:
1400
+ 140 (+10%)
+ 70 (+5%)
= 1400 + 210
Alexandra finished 3/5th of her work. What percentage of work did she complete?
60 percent
Step-by-step explanation:
Covert 3/5th into percentage so the answer will be 60.
#CarryOnLearningThe year of Average 11, 15, 17, X+1, 19, X-2, 3 is 14. Find median.
Answer:
median of given data is 18
Please help!!! ASAP!
Answer:
so what we have to do first is multiply 9*10
which is 90 now we divide by two to get 45
now we multiply 45 by 20 to get
900
Hope This Helps!!!
I have this math problem I can't solve.
"Evelyn and Meredith decided to kayak 1 mile up and then back in the Humboldt channel.
The rate of the water flowing in the channel was 2 miles per hour. The total time it took them to kayak up and back was 3 hours and 40 minutes. Assuming they were padding their double kayak at a fairly consistent rate, find the rate Evelyn and Meredith were paddling.
Step 2 - Draw a picture to model the problem.
Step 3 - Label variables and create a table.
Step 4 - Write an equation to model the problem.
Step 5 - Solve the equation. Provide supporting work and detail.
Step 6 - Explain the results."
If you can help please do.
Evelyn and Meredith were paddling at a rate of [tex]\frac{3+\sqrt{493}}{11}mph[/tex] which is equivalent to 2.29mph approximately.
Step 2: See attached picture
Step 3: In this case we only have different variables, there is the rate at which Evelyn and Meredith were paddling, the rate at which they moved when rowing upstream, the rate at which they moved when rowing downstream, the time it took them to paddle upstream and the time it took them to paddle downstream.
v = rate at which Evelyn and Meredith were paddling.
[tex]v_{up}[/tex]= velocity at which they were moving when paddling upstream.
[tex]v_{down}[/tex]= velocity at which they were moving when paddling downstreamstream.
[tex]t_{up}[/tex]= time it took them paddling upstream.
[tex]t_{down}[/tex]= time it took them paddling downstream
Se attached picture for the table.
Step 4: Building this equation will require us to combine different equations into a single one. Let's start with the equation for the final rate at which they paddled when rowing upstream.
[tex]v-2=v_{up}[/tex]
When rowing upstream, the current will drag the kayak, so we subtract it from the rate at which they were rowing.
Let's find the final rat at which they moved when rowing downstream.
[tex]v+2=v{down}[/tex]
next, the problem tells us it took them 3 hours and 40 minutes to row up and down the channel so we can convert it into just hours like this:
[tex]40min*\frac{1hr}{60min}=\frac{2}{3}hr[/tex]
[tex]3hr+\frac{2}{3}hr=\frac{11}{3}hr[/tex]
so now we can build our equation for time.
[tex]t_{up}+t_{down}=\frac{11}{3}[/tex]
We also know that the rate is built by dividing the distance over the time it took them to travel the distance, so:
[tex]v_{up}=\frac{1}{t_{up}}[/tex]
[tex]v_{down}=\frac{1}{t_{down}}[/tex]
If we solved each of those equations for their respective times, we would end up with the following:
[tex]t_{up}=\frac{1}{v_{up}}[/tex]
[tex]t_{down}=\frac{1}{v_{down}}[/tex]
so we can now combine all the equations together so we get:
[tex]t_{up}+t_{down}=\frac{11}{3}[/tex]
[tex]\frac{1}{v_{up}}+\frac{1}{v_{down}}=\frac{11}{3}[/tex]
[tex]\frac{1}{v-2}+\frac{1}{v+2}=\frac{11}{3}[/tex]
So this equation models the problem.
Step 5: We can solve this equation by multiplying everything by the LCD
In this case the LCD is:
3(v-2)(v+2)
so, when doing the respective multiplications we end up with:
[tex]\frac{3(v-2)(v+2)}{v-2}+\frac{3(v-2)(v+2)}{v+2}=\frac{11(3)(v-2)(v+2)}{3}[/tex]
We can now simplify to get:
3(v+2)+3(v-2)=11(v+2)(v-2)
We can now do the respective multiplications to get:
[tex]3v+6+3v-6=11(v^{2}-4)[/tex]
and we can further simplify:
[tex]6v=11v^{2}-44[/tex]
Step 5: So we can now solve it by using the quadratic formula, first, we need to rewrite the equation in standard form:
[tex]11v^{2}-6v-44=0[/tex]
So we can now use the quadratic formula:
[tex]v=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}[/tex]
we substitute:
[tex]v=\frac{-(-6) \pm \sqrt{(-6)^{2}-4(11)(-44)}}{2(11)}[/tex]
and simplify:
[tex]v=\frac{6 \pm \sqrt{36+1936}}{22}[/tex]
[tex]v=\frac{6 \pm \sqrt{1972}}{22}[/tex]
[tex]v=\frac{6 \pm \sqrt{4(493)}}{22}[/tex]
[tex]v=\frac{6 \pm 2\sqrt{493}}{22}[/tex]
[tex]v=\frac{3 \pm \sqrt{493}}{11}[/tex]
this gives us two possible results:
[tex]v=\frac{3 + \sqrt{493}}{11}[/tex] and [tex]v=\frac{3 - \sqrt{493}}{11}[/tex]
Step 6: We only pick the first result since it's the positive result. We don't take the second one because a negative result represents the kayak moving in the opposite direction which is not how the situation was modeled.
For further information, take a look at the following link:
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The farmer wants the ratio of horses to cows to equal 5 to 3. He keeps his 45 horses and buys more cows. Workout the number of cows he must buy
you have $9 and earn $0.50 for each cup of orange juice you sell. Write an equation that represents the total amount A (in dollars) you have after selling j cups of orange juice
Answer:
Hello there ,
The answer to this equation would be:
A=.50j+9
Step-by-step explanation:
this answer should be correct because he started with 9,
and he is selling each cup (j) for 0.50
Let me show you an example:
Ok lets say he sold 10 (j) cups:
you would replace the (j) with the 10
A=0.50(10)+6
A=5+6
A=11 and he would have $11
but that just an example so the real answer to your question is:
A=.50j+9
Hope this help. If correct please give brainliest.
Thank you,
Have a good day !!!!!
which equation is represented by the table
Answer:
B. b = 3a + 2
Step-by-step explanation:
We can write the equation in slope-intercept form as b = ma + c, where,
m = slope/rate of change
c = y-intercept/initial value
✔️Find m using any two given pair of values, say (2, 8) and (4, 14):
Rate of change (m) = change in b/change in a
m = (14 - 8)/(4 - 2)
m = 6/2
m = 3
✔️Find c by substituting (a, b) = (2, 8) and m = 3 into b = ma + c. Thus:
8 = 3(2) + c
8 = 6 + c
8 - 6 = c
2 = c
c = 2
✔️Write the equation by substituting m = 3 and c = 2 into b = ma + c. Thus:
b = 3a + 2
someone help me please with this algebra problem
Answer:
4
Step-by-step explanation:
3r = 10 + 5s
r = 10
3(10) = 10 + 5s
30 = 10 + 5r
20 = 5r
r = 4
(-9g5+ 9) + (4g5- 5)
The midpoint, M , of segment AB has coordinates (2,−1) . If endpoint A of the segment has coordinates (−3,5) , what are the coordinates of endpoint B ?
The coordinates of endpoint B are?
the coordinates of endpoint B are (7,7)
Answer:
Solution given:
M(x,y)=(2,-1)
A[tex](x_{1},y_{1})=(-3,5)[/tex]
Let
B[tex](x_{2},y_{2})=(a,b)[/tex]
now
by using mid point formula
x=[tex]\frac{x_{1}+x_{2}}{2}[/tex]
$ubstituting value
2*2=-3+a
a=4+3
a=7
again
y=[tex]\frac{y_{1}+y_{2}}{2}[/tex]
$ubstituting value
-1*2=5-b
b=5+2
b=7
the coordinates of endpoint B are (7,7)
A nursery sells English, tea, and miniature rosebushes in red, pink, yellow, and white. How many
different types of rosebushes could you buy?
is this year 3 math? Its 4
Someone pls help me ill give out brainliest pls don’t answer if you don’t know
Answer:
Rectangle shaped cross section is formed by intersection of plane and prism.
Step-by-step explanation:
Given: A rectangular Prism.
To find: Shape of Cross Section when a plane intersect the prism diagonally
A plane intersect the Rectangular prism .i.e, Cuboid diagonally which means plane passes from top edge of cuboid to edge on bottom on opposite side.
Figure is attached.
In this way we get a Rectangular shaped Cross section which includes edges of cuboid and diagonals of the side faces.
Therefore, Rectangle shaped cross section is formed by intersection of plane and prism.
Sarah borrows £500 for 2 years at a rate of 15% to buy a
new laptop.
Calculate the simple interest she will pay on this loan.
Answer: 150 pounds
Step-by-step explanation:
A lighthouse casts a 128-ft shadow. A nearby lamppost that measures 5
feet casts an 8-foot shadow. What is the height of the light house, rounded
to the nearest foot? *
Answer:
80 ft
Step-by-step explanation:
Let the height of the light house be x feet.
[tex] \therefore \: \frac{128}{8} = \frac{x}{5} \\ \\ x = \frac{128 \times 5}{8} \\ \\ x = \frac{640}{8} \\ \\ x = 80 \: feet[/tex]
Does this graph show a function? Explain how you know.
• A. No; there are yvalues that have more than one x-value.
O B. No; the graph fails the vertical line test.
O C. Yes; there are no yvalues that have more than one x-value.
O D. Yes; the graph passes the vertical line test.
HELP PLSS
Which of the following equations represents the graph shown?
Answer:
ok from looking at this equation we can we that every it goes 1 up and on over so
-x+2
Hope This Helps!!!
What 23.5 x 10 to the power of two in scientific notation explain please
Answer:
2.35 x 10^3
Step by Step:
Rewrite the number in scientific notation.2.35 x 10^3
C.P 0f 16 oranges is equal to the Sip of 22
oranges. find profit
percent
or LOSS
Step-by-step explanation:
Given that :C.P of 16 oranges is equal to the SP of 22 oranges.To calculate :Profit or loss %.Calculations :LCM of 16 and 22 is 176.
Let the CP of 16 oranges be Rs. 176 and also let the SP of 22 oranges be Rs. 176.
So,
➝ CP of 16 oranges = Rs. 176
➝ CP of 1 orange = Rs. 176 ÷ 16
➝ CP of 1 orange = Rs. 11
And,
➝ SP of 22 oranges = Rs. 176
➝ SP of 1 orange = Rs. 176 ÷ 22
➝ SP of 1 orange = Rs. 8
______________
Here, CP is greater than SP. So, here is loss.
➝ Loss = CP ― SP
➝ Loss = Rs.(11 ― 8)
➝ Loss = Rs. 3
______________
Finding the loss%,
★ Loss % = {(Loss/CP) × 100} %
➝ Loss % = {3/11 × 100} %
➝ Loss % = 27.27 %
Therefore, loss% is 27.27%.
four tens + four nines
Answer:
[tex]76[/tex]
Step-by-step explanation:
Write the question in equation form
[tex]4(10)+4(9)[/tex]
Multiply
[tex]40+36[/tex]
Add
[tex]76[/tex]
Squares of Binomials
Please Help
What is the common ratio of the geometric sequence 6,4,8/3,16/9,...
r = 2
r = 2/3
r = -2
r = 3/2
The common ratio of the geometric sequence is: B. r = 2/3.
How to Find the Common Ratio of a Geometric Sequence?The common ratio of a geometric sequence is determined by taking the last term and divide by the preceding term.
Given the geometric sequence, 6,4,8/3,16/9,..., the common ratio is calculated as follows:
16/9 ÷ 8/3 = 16/9 × 3/8 = 2/3 × 1/1 = 2/3
Or
8/3 ÷ 4 = 8/3 × 1/4 = 2/3
Or
4/6 = 2/3
Therefore, the common ratio of the geometric sequence is: B. r = 2/3.
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In the picture shown below, what proportion would NOT give the correct value of x?
Answer: (c)
Step-by-step explanation:
In the given figure, two triangles are similar namely [tex]\triangle ABC[/tex] and [tex]\triangle ADB[/tex]
For similar triangles, the ratio of the corresponding sides are equal.
For option (a), Hypotenuse to Perpendicular ratio is given, that is correct
Similarly for option (b), Perpendicular to hypotenuse ratio is given
Both option (a) and (b) gives the same value of [tex]x[/tex] that is,
[tex]\Rightarrow x=\sqrt{81\times 45}\\\Rightarrow x=60.37[/tex]
Option (c) does not give the correct value of [tex]x[/tex]
Answer:
C
Step-by-step explanation:
In the given figure, two triangles are similar namely and
For similar triangles, the ratio of the corresponding sides are equal.
For option (a), Hypotenuse to Perpendicular ratio is given, that is correct
Similarly for option (b), Perpendicular to hypotenuse ratio is given
Both option (a) and (b) gives the same value of that is,
Option (c) does not give the correct value of
