the tens digit of a two digit number is 5 greater the units digit. If you subtract double the reversed number from it, the result is a fourth of the original number. Find the original number.
Given:
The tens digit of a two digit number is 5 greater the units digit.
If you subtract double the reversed number from it, the result is a fourth of the original number.
To find:
The original number.
Solution:
Let n be the two digit number and x be the unit digit. Then tens digit is (x+5) and the original number is:
[tex]n=(x+5)\times 10+x\times 1[/tex]
[tex]n=10x+50+x[/tex]
[tex]n=11x+50[/tex]
Reversed number is:
[tex]x\times 10+(x+5)\times 1=10x+x+5[/tex]
[tex]x\times 10+(x+5)\times 1=11x+5[/tex]
If you subtract double the reversed number from it, the result is a fourth of the original number.
[tex]11x+50-2(11x+5)=\dfrac{1}{4}(11x+50)[/tex]
[tex]11x+50-22x-10=\dfrac{1}{4}(11x+50)[/tex]
[tex]40-11x=\dfrac{1}{4}(11x+50)[/tex]
Multiply both sides by 4.
[tex]160-44x=11x+50[/tex]
[tex]160-50=11x+44x[/tex]
[tex]110=55x[/tex]
Divide both sides by 55.
[tex]\dfrac{110}{55}=x[/tex]
[tex]2=x[/tex]
The unit digit is 2. So, the tens digit is [tex]2+5=7[/tex].
Therefore, the original number is 72.
How is the solution set of the sentence below described? X + 5 < 7
A. {All numbers less than 7/5}
B. {All numbers less than 2}
C. {All numbers less than 7}
D. {All numbers less than 12}
E. None of these
Answer:
B. {All numbers less than 2}
Step-by-step explanation:
X + 5 < 7
Subtract 5 from each side
X + 5-5 < 7-5
x<2
All numbers less than 2
Help this is due in 10 mins
Answer:
Only A is true
for sure
....................
need some help with this
Answer:
y=4x-7
Step-by-step explanation:
here,
the equation of straight line in slope intercept form is;
y=mx+c
( m= slope
c= y-intercept )
soo..
the question has asked for slope 4 i.e. m=4
and y- intercept -7 i.e. c= -7
now.
the required equation is
y= 4x-7
mark me brainliest and follow me ... please
Given that x= –1/2 and y = 4 , evaluate 3x²y + xy²
Answer:
-5
Step-by-step explanation:
3x²y + xy²
Let x = -1/2 and y = 4
3(-1/2)^2 (4) + (-1/2) (4)^2
Exponents first
3(1/4) (4) + (-1/2) 16
Multiply
3 - 8
Subtract
-5
Answer: [tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd\huge \boldsymbol {-5}[/tex]
Step-by-step explanation: simplify it [tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd \displaystyle\ \Large \boldsymbol{} 3x^2y+xy^2=xy(3x+y)[/tex] evalute [tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd \displaystyle\ \Large \boldsymbol{} -\frac{1}{2} \cdot 4 (-3\cdot \frac{1}{2}+4)=-2\!\!\!\!\diagup\cdot\frac{5}{2\!\!\!\!\diagup} =\boxed{-5}[/tex]
When AG = 16 ft, find the area of the region that is NOT shaded. Round to the nearest tenth.
Answer:
730.88
Step-by-step explanation:
Area of the entire circle = pi * r^2
r = 16
Area = 3.14 * 16^2
Area = 803.84
1/4 of the circle contains the shaded area. It's area = 1/4 * 803.84
Area of 1/4 circle =
200.96
the area of the triangle
Area = 1/2 AG * G?
AG and G? are equal
Area = 1/2 * 16^2
Area = 128
Area of 1/4 circle - area of the triangle = area of the shaded portion
shaded portion = 200.95 - 128
Shaded Portion = 72.96
So the area of the unshaded part
unshaded = 803.84 - 72.96
Unshaded = 730.88
Urgent i need help!!…….
Answer:
Step-by-step explanation:
These are similar triangles. We know that because we know that all right triangles are similar. The height of the red one is 8 and the height of the blue one is 4; that means that the red one is twice the size of the blue one; likewise, the blue one is half the size of the red one. That means that ALL the measurements of these triangles exist in that ratio...even the base of the blue one. If the base of the red one is 3, and the red one is twice the size of the blue one, then the base of the blue one is 3/2 or 1.5. I can't see your choices because they are too small.
Evaluate the following expression using the values given: (1 point)
Find 3x − y − 3z if x = −2, y = 1, and z = −2.
Jernel has to figure out the area of her square garage. She knows that one side of the garage is equal to the length of her rabbit pen. The dimensions of the rectangular rabbit pen are 13 by 10.
Answer:169
Step-by-step explanation:13 x 13 = 169
You would take the larger side of the pen (13) or else it wouldn’t fit if you chose 10.
A side of the triangle below has been extended to form an exterior angle of 148°. Find the value of x
Answer: 32
Step-by-step explanation:
total= 180
180-148=32
Use the parabola tool to graph the quadratic function f(x)=−x2+4. Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
Answer:
see below
Step-by-step explanation:
f(x) = -x^2 +4
The vertex form is
y = a(x-h)^2 +k
Rewriting
f(x) = -(x-0)^2 +4
The vertex is (0,4) and a = -1
Since a is negative we know the parabola opens downward
f(x) = -(x^2 -4)
We can find the zeros
0 = -(x^2 -2^2)
This is the difference of squares
0 = -(x-2)(x+2)
Using the zero product property
x-2 =0 x+2 =0
x=2 x=-2
(2,0) (-2,0) are the zeros of the parabola and 2 other points on the parabola
We have the maximum ( vertex) and the zeros and know that it opens downward, we can graph the parabola
Answer:
Your vertex is (4,0)
Step-by-step explanation:
If 4 over 7 ton of concrete covers 7 over 8 of a bridge, how many tons of concrete are required to cover the entire bridge?
Answer:
Your answer would be 32/49.
Step-by-step explanation:
4/7 tons = 7/8 x
4/7 / 7/8
32/49
The tons of concrete are required to cover the entire bridge is 32/49 tons.
What are fractions?A fraction is a non-integer that is made up of a numerator and a denominator. An example of a fraction is 4/7.
How many tons is needed to cover the whole bridge?To determine this value, divide 4/7 by 7/8
4/7 ÷ 7/8
4/7 x 8/7 = 32/49 tons
To learn more about the division of fractions, please check: https://brainly.com/question/25779356
If the outliers are not included what is the mean of the data set 76,79,80,82,50,78,79,81,82
Answer:
The answer is 80
Step-by-step explanation:
we know that
the outlier is 50, as it is not around the other numbers in the data set.
therefore
mean=[76+ 79 + 80 + 82+ 78 + 83 + 79 + 81 + 82]/9
mean=[720]/9
mean=80
Answer:
80
Step-by-step explanation:
mean=[76+ 79 + 80 + 82+ 78 + 83 + 79 + 81 + 82]/9
mean=[720]/9
mean=80
Karma was given some birthday money. She puts money in an account. Every month after that, she deposits the same amount of money. The equation that models this situation is y=75x+60, where y is the amount of money in the account and x is the number of deposits. What does the y-intercept mean in this situation
Answer:
y represents the amount in the bank account after 7 months.
Step-by-step explanation:
Let karma gets x money on his birthday.
He has 60 in his account initially
He deposits teh same money for the seven months
So, the money he has after the seven months is 7 x + 60
According to the question,
y =7 x + 60
It shows that the amount after seven months is y.
simplify -8/2 ÷ 6/-3
Answer: the answer is 2 or C
-8/2 x -3/6
*Always do the recipical*
(-8 x -3) / (2 x 6)
-8 x -3= +24
2 x 6= 12
24/12= 2
The solution of the given expression -8/2 x -3/6 is 2. The correct option is B.
What is an expression?In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.
Given that the expression is,
-8/2 x -3/6
The expression will be solved as below,
E = (-8 x -3) / (2 x 6)
The numerator will get reciprocal and multiplied to the denominator,
E = 24 / 12
Divide the number 24 by 12 and get the solution,
E = 2
Therefore, the solution of the expression will be 2. The correct option is B.
To know more about an expression follow
https://brainly.com/question/8158404
#SPJ5
What is the probability of rolling 2 standard dice which sum to 9?
solve
[tex]100 {5}^{2} - 500 {5}^{6} [/tex]
Please help before 9:00 pm
Three red balls, 5 green balls and a number of blue balls are put together in a sac. One ball is picked at random from the sac. If the probability of picking a red ball is 1|6, find the a) The number of blue balls in sac. B) the probability of picking a green ball
Answer:
total balls = 18 .... 3/x = 1/6
blue = 10 ... 18-(5+3) = 10
p of green = 5/18 = .277
Step-by-step explanation:
write an example of a monomial of degrees 5
Answer:
find the value of:Cos = 0.54
expand this question (x+5)(x-3)
Find the measure of 2
Answer:
92
Step-by-step explanation:
Angle 2 and 92 are corresponding angles and corresponding angles are equal when the lines are parallel
Answer:
[tex]\angle 2=92^{\circ}[/tex]
Step-by-step explanation:
When two parallel lines are cut by a traversal, their corresponding angles are always equal. Corresponding angles can be found if you took each point of intersection and aligned them up with each other.
In this case, we see that [tex]\angle 2[/tex] and the angle marked as 92 degrees correspond with each other. Since all corresponding angles are equal, we have:
[tex]\angle 2=\boxed{92^{\circ}}[/tex]
Find the length of side BC give your answer to three significant figures
Answer:
19.4 cm
Step-by-step explanation:
Hi there!
This is a right triangle. We're given an angle, the side adjacent to the angle and we're solving for the hypotenuse. Given this information, we can use the cosine ratio:
[tex]cos\theta=\frac{adj}{hyp}[/tex]
Plug in the given angle and side
[tex]cos71=\frac{6.3}{BC}\\BC=\frac{6.3}{cos71} \\BC=19.4[/tex]
Therefore, the length of BC is 19.4 cm when rounded to 3 significant figures.
I hope this helps!
a)out of 300 students In a class 60% of the students took physics and 35 students took chemistry and 20% of the students did not take any of this subject. how many students take both the subject
Answer:
25 students take both subjects.
Step-by-step explanation:
Solve for 60% of 300 students:
60/100 = x/300
Cross multiply:
60 × 300 = 100 × x
18000 = 100x
Divide both sides by 100:
180 = x
Solve for 20% of 300 students:
20/100 = x/300
20 × 300 = 100 × x
6000 = 100x
60 = x
Solve for the percentage of students in chemistry:
x/100 = 35/300
x × 300 = 100 × 35
300x = 3500
x = 11.66666...7
x = about 11.7%
Find the difference in percentages:
100 - 60 - 20 - 11.7
8.3
8.3% take both subjects
Solve for 8.3% of students:
8.3/100 = x/300
8.3 × 300 = 100 × x
2490 = 100x
24.9
About 25 students
Check your work by adding all the students together (to get to 300):
25 + 60 + 180 + 35
300 students total
This is correct!
2) Find the sum of the first 50 terms of the
following series, to the nearest integer.
6, 10, 14,...
Answer:
The sum of the first 50 is 5200
Step-by-step explanation:The given sequence is a linear sequence.
So, first we calculate the common difference
d=t2-t1
d=10-6=4
The sum of the first 50 terms is then calculated using: sorry it wont let me copy and paste my explo and im lazy
Answer:
5,200
Step-by-step explanation:
6, 10, 14, ...
Sum = [ number of terms(first term+last term) ] / 2
-we know there are 50 terms
-we now the first term is 6
-we need to find the last term
last term = first term + (n-1)* difference between first and second term
last term = 6 + (50-1) * (10-6)
last term = 6 + 49*4 = 202
Sum = [ number of terms(first term+last term) ] / 2
Sum = [ 50 ( 6 + 202) ] / 2 = 5,200
Use the given conditions to write an equations for the line in slope- intercept form. passing through (1,-8) and (-7,8)
Answer:
y = -2x - 6
Step-by-step explanation:
Going from the first point to the second, we see x decreasing by 8 from 1 to -7 (this is the 'run') and y increasing by 16 from -8 to +8 (this is the 'rise'). Thus, the slope of the line through these two points is m = rise/run = 16/(-8) = -2.
Using the point-slope formula y - k = m(x - h) and the point (1, -8), we get:
y + 8 = -2(x - 1), or
y = -8 - 2x + 2, or
y = -2x - 6 (in slope-intercept form)
find the cost of four score of plate at 50k each and three dozens of spoon at 20k each
help asap no wrong answers----------------------
Answer:
[tex]y=-2(sin(2x))-7[/tex]
Step-by-step explanation:
1. Approach
Given information:
The graph intersects the midline at (0, -7)The graph has a minimum point at ([tex]\frac{\pi}{4}[/tex], 9).What conclusions can be made about this function:
The graph is a sine function, as its y-intercept intersects the midlineThis graph has a negative coefficient, this is because after intersecting the midlines at the y-intercept, the function has a minimum.This graph does not appear to have undergone any horizontal shift, as it intercepts the midlines with its y-interceptTherefore, one has the following information figured out:
[tex]y=-n(sin(ax))+b[/tex]
Now one has to find the following information:
amplitudemidlineperiod2. Midline
The midlines can simply be defined as a line that goes through a sinusoidal function, cutting the function in half. This is represented by the constant (b). One is given that point (0, -7) is where the graph intersects the midline. The (y-coordinate) of this point is the midline. Therefore, the midline is the following:
y = -7
2. Amplitude
The amplitude is represented by the coefficient (n). It can simply be defined by the distance from the midline to point of maximum (the highest part of a sinusoidal function) or point of minimum (lowest point on the function). Since the function reaches a point of minimum after intercepting the (y-axis) at its midlines, the amplitude is a negative coefficient. One can find the absolute value of the amplitude by finding the difference of the (y-coordinate) of the point of minimum (or maximum) and the absolute value of the midline.
point of minimum: [tex](\frac{\pi}{4},9)[/tex]
midline: [tex]y=-7[/tex]
Amplitude: 9 - |-7| = 9 - 7 = 2
3. Period
The period of a sinusoidal function is the amount of time it takes to reach the same point on the wave. In essence, if one were to select any point on the sinusoidal function, and draw a line going to the right, how long would it take for that line to reach a point on the function that is identical to the point at which it started. This can be found by taking the difference of the (x- coordinate) of the intersection point of the midline, and the (x-coordinate) of the point of minimum, and multiplying it by (4).
point of minimum: [tex](\frac{\pi}{4},9)[/tex]
midline intersection: [tex](0, -7)[/tex]
Period: [tex]4(\frac{\pi}{4}-0)=4(\frac{\pi}{4})=\pi[/tex]
However, in order to input this into the function in place of the variable (a), one has to divide this number by ([tex]2\pi[/tex]).
[tex]a=\frac{2\pi}{\pi}=2[/tex]
4. Assemble the function
One now has the following solutions to the variables:
[tex]n =-16\\a=2\\b=-7\\[/tex]
Substitute these values into the function:
[tex]y=-2(sin(2x))-7[/tex]
25. A pizza shop offers 30% off the price of a large pizza every Tuesday
night. If the regular price is $25, what is the discounted price?
Answer:
25 -(.3*25)
25-7.50 = $17.50
Step-by-step explanation:
Answer:
17.50
Step-by-step explanation:
First find the amount of the discount
25 * 30%
25 * .3
7.5
Subtract this from the original amount
25 - 7.5
17.50
*Please Help!*
What is the volume of water, to the nearest tenth of a cubic metre, that would fill this spa tub?
First cylinder= 0.75m diameter, 0.80m height
Cylinder Underneath= 1.25m diameter, 0.70m height
Semi Sphere that holds both cylinders= 3m long
Answer:
The volume of water that will fill the spa tub is 5.9 cubic meters.
Step-by-step explanation:
Volume of water that would fill the spa tub = volume of semi sphere - (volume of the first cylinder + volume of the second cylinder)
i. volume of first cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h
where r is the radius and h is the height of the cylinder.
r = [tex]\frac{0.75}{2}[/tex] = [tex]\frac{3}{8}[/tex]
= 0.375 m
h = 0.80 m
volume of the first cylinder = [tex]\frac{22}{7}[/tex] x [tex](\frac{3}{8} )^{2}[/tex] x 0.8
= 0.3536 cubic meters
ii. volume of the cylinder underneath = [tex]\pi[/tex][tex]r^{2}[/tex]h
r = [tex]\frac{1.25}{2}[/tex] = [tex]\frac{5}{8}[/tex]
= 0.625
h = 0.70 m
volume of the cylinder underneath = [tex]\frac{22}{7}[/tex] x [tex](\frac{5}{8}) ^{2}[/tex] x 0.7
= 0.8594 cubic meters
iii. volume of the semi sphere = [tex]\frac{2}{3}[/tex] [tex]\pi[/tex][tex]r^{3}[/tex]
where r is the radius = 1.5 m
volume of the semi sphere = [tex]\frac{2}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex](1.5)^{3}[/tex]
= 7.0714 cubic meters
Thus,
volume of the water to fill the spa tub = 7.0714 - (0.3536 + 0.8594)
= 5.8584
The volume of water that will fill the spa tub is 5.9 cubic meters.
Use the ordered pairs to give a function rule. Give the rule in slope intercept form {(-12,1.5)(-1,-1.25),(5,-2.75),(8,-3.5)}
Answer:
[tex]y = -0.25x -1.5[/tex]
Step-by-step explanation:
Given
[tex](x,y) = \{(-12,1.5)(-1,-1.25),(5,-2.75),(8,-3.5)\}[/tex]
Required
The function rule (in slope intercept)
First, we calculate the slope (m) using:
[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
This gives:
[tex]m = \frac{-1.25 -1.5}{-1 - -12}[/tex]
[tex]m = \frac{-2.75}{11}[/tex]
[tex]m = -\frac{2.75}{11}[/tex]
[tex]m = -0.25[/tex]
The equation is then calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
This gives:
[tex]y = -0.25(x - -12) + 1.5[/tex]
[tex]y = -0.25(x +12) + 1.5[/tex]
Open bracket
[tex]y = -0.25x -3 + 1.5[/tex]
[tex]y = -0.25x -1.5[/tex]
