The first digit is 3 and the second 4 so the original number is 34
What is an order of an equation?
The highest-order derivative that a differential equation has is used to define the equation's order. The highest-order derivative of a differential equation is defined as its degree, which is expressed as a power.
Here, We
Let the first digit be a
Let the second digit be b
a + b = 7....(1)
The first order value:
a is a counting in tens. So actual value is 10(a)
b is counting in units. So actual value is 1(b)
10a + b...(2)
The second order value:
b is a counting in tens. So the actual value is 10(b)
a is counting in units. So actual value is 1(a)
10b + a....(3)
Now, we subtract equation(3) from (2) and we get
= (10b + a) -(10a + b) = 9
= 9b - 9a = 9
= b - a = 1...(4)
From equation(1)
a = 7 - b
Now, we put the value of a in equation(4) and we get
= b - (7-b) = 1
= b - 7 + b = 1
= 2b = 8
b = 4
Now, substitute the value of b in equation (1) and we get
a = 3
Hence, The first digit is 3 and the second 4 so the original number is 34
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What is the equation of the line that passes through the point (- 3/8 and has a slope of 4?
The equation of line that passes through the point (-3, 8) and has a slope of 4 is y = 4x + 20.
In the given question, we have to find the equation of the line that passes through the point (-3, 8) and has a slope of 4.
From the given question, m = 4 and point (x(1), y(1)) = (-3, 8).
To find the equation of line we put the values in the equation:
y - y(1) = m(x - x(1))
Now putting the value
y - 8 = 4(x - (-3))
Now simplifying the bracket first
y - 8 = 4(x + 3)
Now solving the expression using the distributive property
y - 8 = 4x + 12
Add 8 on both side, we get
y = 4x + 20
Hence, the equation of the line that passes through the point (-3, 8) and has a slope of 4 is y = 4x + 20.
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The complete question is:
What is the equation of the line that passes through the point (-3, 8) and has a slope of 4?
rationalize the denominator of $\frac{5}{2-\sqrt{3}}$, and write your answer in the form $\displaystyle{\frac{a b\sqrt{3}}{c}}$ where the fraction is in lowest terms. what is $a b c$?
The value of a+b+c will be 16 if [tex]\frac{5}{2-\sqrt{3}}[/tex] rationalize as [tex]\displaystyle{\frac{a + b\sqrt{3}}{c}}[/tex].
Given,
y = [tex]\frac{5}{2-\sqrt{3}}[/tex]
To solve the given expression we multiply the numerator and denominator by the conjugate of the denominator
[tex]= \frac{5}{2-\sqrt{3}} \frac{2+\sqrt{3} }{2+\sqrt{3}}[/tex]
[tex]= \frac{10+5\sqrt{3} }{2^2 - \sqrt{3}^2 }[/tex]
[tex]= \frac{10+5\sqrt{3} }{4-3 }[/tex]
[tex]= \frac{10+5\sqrt{3} }{1 }[/tex] = [tex]\displaystyle{\frac{a + b\sqrt{3}}{c}}[/tex]
Now, by comparing the result we get
a = 10, b = 5, c = 1
hence, a+b+c = 10+5+1 = 16
Therefore, the value of a+b+c will be 16.
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In Circle O, which angle is equal to 90°?
The angle that is equal to 90° is ∠ABC.
What is an angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. Dihedral angles are these.
Here, we have
Given the following diagram and we have to determine that in circle O, which angle is equal to 90°.
We concluded that
If one side of a triangle inscribed in a circle is the diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is the right angle.
Hence, the angle that is equal to 90° is ∠ABC.
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Twice the difference of a number and 10 is greater than - 26.
Answer:
x<-3
Step-by-step explanation:
The unknown number we can write as x.
2(x-10) > -26
2x - 20 > - 26
2x > -6
x< -3 Divide by negative so reverse the sign
What is the equation of a line that passes through the point 2 3 and 4 7?
The equation of a line that passes through the point (2, 3) and (4, 7) is y = 2x - 1.
In the given question, we have to find the equation of a line that passes through the point (2, 3) and (4, 7).
The general equation of line that passes through point is:
y - y(1) = m(x - x(1))
To find the equation of line we have to first find the slope of line by using the formula:
m = [tex]\frac{y(2)-y(1)}{x(2)-x(1)}[/tex]
The given points:
(x(1), y(1)) = (2, 3), (x(2), y(2)) = (4, 7)
m = [tex]\frac{7-3}{4-2}[/tex]
m = [tex]\frac{4}{2}[/tex]
m = 2
Now finding the line of equation.
We can use any of the point of the given.
m = 2, (x(1), y(1)) = (2, 3)
y - 3 = 2(x - 2)
Solving the equation using distributive property
y - 3 = 2x - 4
Add 3 on both side, we get
y = 2x - 1
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The complete question is:
What is the equation of a line that passes through the point (2, 3) and (4, 7)?
Which ordered pair is in the solution set to the system of inequalities shown in the accompanying graph?
Answer: D. (3, 2).
Step-by-step explanation: The solution of the system is in the intersections of both of the inequalities, and (3, 2) is in the area of intersection.
Answer:
I have no clue but you should get the free trial so a expert can tutor you and you get all your questions right
write a story problem that will result in the problem 5+(-12)
find the values of x and y
Answer: x=86, y=81
Step-by-step explanation: opposite angles and are same on parallelograms and x+9=95
Triangle A B C. Angle C is 90 degrees. Hypotenuse side A B is c, C B is a, C A is b.
Solve the right triangle shown in the figure.
Side B C = 3.2 meters, angle B = 43.2 degrees, angle C = 90 degrees
a.
Angle A = 46.8 degrees, side A C = 1.9 meters, Side A B = 3.7 meters
c.
Angle A = 46.8 degrees, side A C = 5.3 meters, Side A B = 6.2 meters
b.
Angle A = 46.8 degrees, side A C = 5.3 meters, Side A B = 4.4 meters
d.
Angle A = 46.8 degrees, side A C = 3.0 meters, Side A B = 4.4 meters
Please select the best answer from the choices provided
see picture.......................
Option A. Angle A = 46.8 degrees, side A C = 1.9 meters, Side A B = 3.7 meters satisfies the conditions of the problem: angle C is 90 degrees, angle B is 43.2 degrees, and side B C is 3.2 meters.
What is a right triangle?A right triangle is a type of triangle in which one of the angles is a right angle (90 degrees). The side opposite the right angle is called the hypotenuse and is typically the longest side of the triangle.
The other two sides are called the legs and are typically shorter than the hypotenuse. The Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, applies to all right triangles
Therefore, the remaining options (b, c, and d) do not satisfy the conditions of the problem and therefore are not correct.
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Nora’s saving club changes an interest of 5.5% per annum on any amount borrowed by its members.If a members borrow $125000.00 how much does he pay often 1year
well, the charge for a year is just 5.5% of the amount so 5.5% of 125000
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5.5\% of 125000}}{\left( \cfrac{5.5}{100} \right)125000}\implies \text{\LARGE 6875}[/tex]
Edith and Rashida are shooting free throws. Complete the ratio tables. who has a better ratio of basket to shots
Edith has a better ratio of the basket to shots.
What is ratio?
The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, Edith and Rashida are shooting free throws.
For Edith
B 1 2 3 4 5
S 3 6 9 12 15
ratio = 3/1
the ratio of Edith's shots = 3
For Rashida
B 2 4 6 8 10
S 5 10 15 20 25
Ratio = 5/2
The ratio of Rashida's shots = 2.5
Therefore, Edith has the better ratio of the basket to shots
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Complete question:
2.86 + (-14.6,) is i need help
Answer: -11.74
Step-by-step explanation: The reason for this is if you minus 14.6 from 2.86 you get -11.74.
whats the answer I dont get it
Answer:
Step-by-step explanation:
Find the length of the third side. If necessary, write in simplest radical form.
For a right triangle, use the Pythagorean Theorem.
Which of the following measurements might represent the length of the third side?The length of a triangle’s third side must always be between (but not equal to) the sum and difference of its other two sides. Take, for example, the numbers 2, 6, and 7. As a result, the length of the third side must be larger than 4 but less than 8.
Use the Pythagorean Theorem to get the area of a right triangle. Use the area formula for an isosceles triangle to calculate the area of an isosceles triangle. Use the law of cosines or the law of sines if you know some of the angles and other side lengths.
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a crew of mechanics at the highway department garage repair vehicles that break down at an average of 3 vehicles every 12 minutes (approximately poisson in nature). the mechanic crew can service an average of 3 vehicles every 10 minutes with a repair time distribution that approximates an exponential distribution. the crew cost is approximately $150 per hour. the cost associated with lost productivity from the breakdown is estimated at $50 per hour. which is cheaper, the existing system with one service crew or a revised system with two service crews? note that the average waiting time for adding the second crew is 0.01.
Total cost in single service crew is greater than double service crew. So, double service crew is cheaper.
We have, a crew of mechanics at the highway department garage repair vehicles. In case of poisson distribution,
λ = 3 vehicles every 12 minutes
= 3×60/12 = 3× 5
λ = 15 vehicles per hour
When time distribution is approximates an exponential distribution,
The mechanic crew can service an average, μ = 3 vehicles every 10 minutes
μ = 3×60/10 = 18 vehicles per hour
Cost for one service crew =$150 per hour
Cost associated with lost productivity from the breakdown or wait cost
=$50 per hour
For single crew, number of vehicles out of cost, Lₛ = 15/(18 - 15) = 15/3 = 5
Single service crew cost = $150 per hour
wait cost = $5×50 = $250 per hour
Total cost = $400 per hour
For double service crew, Number of vehicles out of service cost = 15/(36 - 15)
= 15/21 = 0.7143
Double service crew cost = 2× $150
= $300
Wait cost = $0.7143×50 = $35.715
Total cost = $335.715 per hour
As we see, the double service crew is cheaper.
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Select the GCF of these numbers. 2^5 · 5· 11 and 2^3· 5^2 · 7
2 2 · 3
3 2
13 · 19 3 ·23 2
2 3 ·5
2· 11 2
The GCF of these numbers. 2^5 · 5· 11 and 2^3· 5^2 · 7 is D. 2³.5
What is GCF?The greatest common factor is the largest number that can divide evenly into two or more other numbers (GCF). The highest common factor is another name for this (HCF). A factor is a smaller number that could divide into a larger one evenly.
Before determining the greatest common factor, enumerate the prime factors of each integer. The greatest common factor of two or more integers is the biggest integer that is a factor of each.
In this case, 2 appears three times as the most frequent factor and 5 only once as the most frequent factor among the numbers.
Hence 2³.5 is the GCF of the given number.
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A salesmen earns a basic salary of sh 35000 a month. He is entitled to a commission of 10% of goods sold above Sh 300,000, and a further commission of 12% of goods sold above sh 500,000 in one month he earned a total 13900, from the sales of sh 139000 from the sales made Determine the sales made in that month.
Answer:
Step-by-step explanation:
We can begin to solve this problem using mathematics. Let's name the total sales for the month "S".
We know that the salesman receives a 10% commission on sales over $300,000 and a 12% commission on sales above 500,000. As a result, we may construct the following equation:
Commission = 0.10 (S - 300,000) + 0.12 (S - 500,000) = 0.10 (S - 30,000) + 0.12 (S - 60,000) = 0.22 (S - 90,000).
We also know that the salesman receives a total commission of $13,900. So we can plug that number into the equation:
13,900 = 0.22S - 90,000
To obtain the value of S, multiply both sides of the equation by 90,000:
13,900 + 90,000 = 0.22S
103,900 = 0.22S
Finally, we can obtain the value of S by dividing both sides of the equation by 0.22: S = 472,273.63
As a result, the total sales for the month were Sh 472,273.63.
Solve the quadratic equation numerically (using tables of x- and y- values). X squared + 5 x + 6 = 0.
The solution of the given quadratic equation [tex]x^{2} +5x+6[/tex] = 0 is x = -2 and -3
Now, According to the question:
What is quadratic equation?
A quadratic equation is a second-order polynomial equation in a single variable x ax2+bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The given quadratic equation is:
[tex]x^{2} +5x+6[/tex] = 0
To solve the equation:
Comparing the above equation with the standard form of quadratic equation:
[tex]ax^{2} +bx+c=0[/tex]
a =1 , b = 5 , c = 6
The roots of quadratic equation are given as follows:
x = (-b ± √ (b^2 - 4ac) )/2a.
x = (-5 ±√([tex]5^2[/tex]- 4(1)(6)) / 2 ×1
x = -5 ± 1/2
x = -2 , -3
Hence, The solution of the given quadratic equation [tex]x^{2} +5x+6[/tex] = 0 is x = -2 and -3
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The ratio of C:D is 5:3, the ratio of F:D is 6:1.
Find the ratio of C:D:F.
The ratio of C:D:F is 5:3:18.
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
here, we have,
given that,
The ratio of C:D is 5:3,
the ratio of F:D is 6:1.
i.e. F:D= 18:3
now,
C:D:F= 5:3:18.
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How to solve -5 -1 / -6 -9i?
The solution to the complex number (-5 - i)/(-6 - 9i) is (1 - i)/3
What is an equation?An equation shows the relationship between numbers and variables in an expression.
Complex numbers are in the form a + bi, where both a and b are real numbers and i = √(-1)
Given that:
[tex]\frac{-5-i}{-6-9i} \\\\To\ solve\ multiply\ numerator\ and\ denominator\ by\ conjugate:\\\\=\frac{-5-i}{-6-9i} *\frac{-6+9i}{-6+9i}\\ \\=\frac{30-45i+6i+9}{36+81}\\ \\=\frac{39-39i}{117} \\\\=\frac{1-i}{3}[/tex]
The solution is (1 - i)/3
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find the length (in cm) of an arc of a circle with radius 6 cm if the arc subtends a central angle of 60
The length (in cm) of an arc of a circle 5π
60°=π/3 radians
A unit circle's arc length is expressed in radians.
We may get the length of an arc using the following formula given an angle and a circle's diameter: ArcLength = (angle / 360) * (2 * pi * radius) Pi equals 22/7, diameter equals 2 * radius, and angle is in degrees.
If a unit circle's arc length is π/3,
(that is a circle with a radius of 1)
For a circle with a radius of 15, the arc length for the same angle would be
X15xπ/3
=5π
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find the sales price original=$5.50 markup=75%
Answer:
$ 9.625
Step-by-step explanation:
75% = 0.75
5.50 x 0.75 = $4.125
5.50 + 4.125 = $ 9.625
Marissa is selling paintings for $10 each and bracelets for $4 each. Her goal is to sell at least $600 in products, and she must sell at least 60 bracelets. Which of the following combinations will satisfy these constraints?
20 paintings and 60 bracelets
25 paintings and 80 bracelets
30 paintings and 70 bracelets
40 paintings and 60 bracelets
Answer:
40 paintings and 60 bracelets
Step-by-step explanation:
40 x 10$ = 400
60 x 4$ = 240
400 + 240 = 640
The only option that satisfies both constraints is Option 4: 40 paintings and 60 bracelets, which generates a total revenue of $640.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let's calculate the total revenue for each option and see which one satisfies the given constraints.
Option 1: 20 paintings and 60 bracelets
Total revenue = (20 x $10) + (60 x $4) = $200 + $240 = $440
Option 2: 25 paintings and 80 bracelets
Total revenue = (25 x $10) + (80 x $4) = $250 + $320 = $570
Option 3: 30 paintings and 70 bracelets
Total revenue = (30 x $10) + (70 x $4) = $300 + $280 = $580
Option 4: 40 paintings and 60 bracelets
Total revenue = (40 x $10) + (60 x $4) = $400 + $240 = $640
Therefore, the only option that satisfies both constraints is Option 4: 40 paintings and 60 bracelets, which generates a total revenue of $640.
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Solve
-4.5 x (-2) =
Selection :
-0.9
9
0.9
-9
The solution to -4.5 x (-2) is 9.
What is the arithmetic calculation?
Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
The reason for this is that when two negative numbers are multiplied together, the result is positive.
This is because the negative sign on a number is similar to a "minus" sign, indicating that the number is less than zero.
When you have two "minus" signs together (in this case, one on -4.5 and one on -2),
they cancel each other out, leaving the positive product of 4.5 and 2, which is 9.
-4.5 is a negative decimal number, and -2 is also a negative integer number. When multiplied, it results in a positive number, which is 9.
Hence, the solution to -4.5 x (-2) is 9.
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como convertir 17/3 en un número mixto
Answer:
5 2/3
Step-by-step explanation:
17 / 3 = 5 and 2/3
What is the inverse of 9?
Answer: -9
Step-by-step explanation:
Which function represents g(x), a reflection of f(x)
(10)' across the x-axis?
g(x) = -2 (10)
g(x) = - CE
g(x) = f (0)
g(x) = {(10)-x
The function that represent reflection of f(x) is given by g(x) = Negative two-fifths(10)x
Describe Reflection of a function:Similar to reflections regarding the y-axis, the x-axis reflections are fundamentally the same. The only distinction is that the points are mirrored from above the x-axis to below the x-axis, and vice versa, rather than along the y-axis.
Make sure you have studied how to perform basic vertical and horizontal translations before we move on to reflections across the y-axis.
The reflection across the co-ordinate axis which is x-axis is as follows;
Reflection about the x-axis
Pre-image point before reflection = (x, y)
Point of image after reflection = ((x, -y)
Therefore, the x coordinate remains the same while the y coordinate changes sign
For which given that f(x) = y = 2/5(10)x and g(x) = Reflection of f(x) across the x-axis, we have
Reflection about the x-axis
Pre-image point before reflection = (x, f(x))
cordinate of image after the reflection = (x, g(x))
Hence g(x) = -f(x) = -2/5(10)x.
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Complete question:
Which function represents g(x), a reflection of f(x) = Two-fifths (10)x across the x-axis? g(x) = Negative two-fifths(10)x g(x) = Negative two-fifths (one-tenth) Superscript x g(x) = Two-fifths (one-tenth) Superscript negative x g(x) = Two-fifths(10)-x
1. 60 ft; yd
2.100 meters; cm
4. 5 hr; min
5. 12 meters; ft
6. 16in; cm
7. 5 liters; qt
8. 2076 cm; yd
9.15 pounds; grams
show work please
Answer:
Step-by-step explanation:
1. 60 ft = 7.3 yd (60 ft * 0.3333 = 19.98 ft)
2. 100 meters = 10,000 cm (100 m * 100 = 10,000 cm)
3. 5 hr = 300 min (5 hr * 60 = 300 min)
4. 12 meters = 39.37 ft (12 m * 3.281 = 39.37 ft)
5. 16 in = 40.64 cm (16 in * 2.54 = 40.64 cm)
6. 5 liters = 1.32 qt (5 L * 0.2642 = 1.321 qt)
7. 2076 cm = 2.29 yd (2076 cm * 0.0109 = 22.7 yd)
8. 15 pounds = 6,803.86 grams (15 lb * 453.59 = 6,803.86 g)
Help, 50 points
Which of the following is equivalent to the statement “(–3, 0) is an x-intercept"?
1.–3 is a root.
2.–3 is a zero.
3.x + 3 is a factor.
4.All of the above are equivalent statements.
Answer: is, 4. All of the above are equivalent statements.
What is x-intercepts of quadratic function?The x-intercept is where the graph crosses the x-axis.
here, we have,
The x-intercept is the point at which a line crosses the x-axis.
now,
The roots of a function are the x-values of the x-intercepts.
Therefore, if (-3, 0) is an x-intercept, then -3 is a root.
The zeros of the function are the x-values when y = 0.
(-3, 0) means x = -3 when y = 0.
Therefore, -3 is a zero.
According to the factor theorem, if f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).
Given (-3, 0), then f(-3) = 0. Therefore, (x - (-3)) = (x + 3) is a factor.
Therefore, all given statements are equivalent statements.
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Use the drop-down menus to answer the questions. What do the numbers on the left, or y-axis, represent? how many students spent 2 or more hours studying? how many students spent fewer than 2 hours a night studying?.
The numbers on the left, or y-axis, represents the number of students studying for each time spent. 12 students spent 2 or more hours studying while ? students spent fewer than 2 hours a night studying.
A bar graph is a chart that uses bars to represent different values or quantities. The bars can be arranged horizontally or vertically, and they can be of different heights or lengths to indicate the size of the value or quantity they represent. Bar graphs are often used to compare data and to show trends over time. They are also called bar charts or column charts.
The bar graph shows the number of hours spent studying on the x-axis while the number of students on the y-axis.
Analyzing the bar graph, there are 12 students who spent 2 or more hours studying.
2-2:59 ⇒ 7
3-3:59 ⇒ 4
4-4:59 ⇒ 1
7 + 4 + 1 = 12
On the other hand, there are 8 students who spent fewer than 2 hours a night studying.
0-0:59 ⇒ 3
1-1:59 ⇒ 5
3 + 5 = 8
Hence, 12 students spent 2 or more hours studying while 8 students spent less than 2 hours.
The problem seems incomplete, it must be...
"A bar graph titled Time Students Spent Studying with hours on the x-axis and students on the y-axis. 3 students spent 0 to 59 minutes, 5 students spent 1 to 1 hour and 59 minutes, 7 students spent 2 to 2 hours and 59 minutes, 4 students spent 3 to 3 hours and 59 minutes, and 1 student spent 4 to 4 hours and 59 minutes.
Use the drop-down menus to answer the questions.
What do the numbers on the left, or y-axis, represent?
How many students spent 2 or more hours studying?
How many students spent fewer than 2 hours a night studying?"
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Answer:
Number of students
12
8
Step-by-step explanation: