The history of integers begins with the natural numbers (1,2,3,...), which are also called the counting numbers. They arise naturally by the need of counting things. But there is a problem. "There is a missing number". If you have a number n of things and you subtract all of them, what remains? Intuitively, it must be a number, a number representing nothing (to have nothing). This is the origin of zero.
Now, as time passes, the man began to do trades and arose the money. This leads to a problem. Other numbers are missing now. How do you express how much money you owe someone? counting numbers are not useful here, for they mean "the money you have". Th
Can you do the graph please I left some notes on the yellow sticky notes
The equation is a linear one, therefore its graph will be a line on the plane.
To completely define a line we need two points.
We can use the information about the y-intercept and use it as one of the points we need. (0, -3)
As for the second point, we can get the x-intercept by setting y=0 and evaluating the function for x:
[tex]\begin{gathered} y=0 \\ \Rightarrow\frac{1}{2}x-3=0 \\ \Rightarrow\frac{1}{2}x=3 \\ \Rightarrow x=6 \\ \Rightarrow(6,0) \end{gathered}[/tex]Then, we have the points we need: (0, -3) and (6,0).
Now, we only need to mark those points on the plane and draw a line through both of them.
Since the plane in the image only reaches the point (5,0), we need to calculate another point to specifically draw the graph on that grid.
Let set y=-1, then:
[tex]\begin{gathered} y=-1 \\ \Rightarrow\frac{1}{2}x-3=-1 \\ \Rightarrow\frac{1}{2}x=2 \\ \Rightarrow x=4 \\ \Rightarrow(4,-1) \end{gathered}[/tex]Now, we will use the points (0,-3) and (4,-1)
1. AI = 400 ft2. Calculate the distance MI for the length of the zipline cable. 3. Calculate the angle at which our zipliners will be descending toward the island . Safety regulations state that the angle at which a zipline cable meets the launching point cannot be smaller than 68 degrees . Please determine if we are in compliance with these regulations
2. The Pythagorean theorem states:
[tex]c^2=a^2+b^2[/tex]where a and b are the legs and c is the hypotenuse of a right triangle.
Applying this theorem to triangle AMI (where AI and MA are the legs and MI is the hypotenuse), we get:
[tex]\begin{gathered} MI^2=AI^2+MA^2 \\ MI^2=400^2+100^2 \\ MI^2=160000+10000 \\ MI^2=170000 \\ MI=\sqrt[]{170000} \\ MI\approx412.31\text{ ft} \end{gathered}[/tex]3. By definition:
[tex]\tan (angle)=\frac{\text{opposite}}{\text{adjacent}}[/tex]Applying this definition to triangle AMI, considering the angle M, we get:
[tex]\begin{gathered} \tan (\angle M)=\frac{AI}{MA} \\ \tan (\angle M)=\frac{400}{100} \\ \tan (\angle M)=4 \\ \angle M=\arctan (4) \\ \angle M\approx76\text{ \degree} \end{gathered}[/tex]This angle is greater than 68°, then it satisfies the regulation.
The standard height from the floor to the bull's-eye at which a standard dartboard is hung is 5 feet 8 inches. A standard dartboard is 18 inches in diameter.
Suppose a standard dartboard is hung at standard height so that the bull's-eye is 12 feet from a wall to its left.
Brian throws a dart at the dartboard that lands at a point 11.5 feet from the left wall and 5 feet above the floor.
Does Brian's dart land on the dartboard?
The equation of the circle that represents the dartboard is (x - 12)² + (y - 17/3)² = 9/16, where the origin is the lower left corner of the room and the unit of the radius is feet.
The position of Brian's dart is represented by the coordinates (11.5, 5). Brian's dart does land on the dartboard.
What is the equation of a circle?Mathematically, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center.r represents the radius of a circle.From the question, we have the following information:
The height of this standard dartboard, k = 5 feet, 8 inches.
The diameter of this standard dartboard = 18 inches.
The bull's eye, h = 12 feet.
Next, we would convert the all of the units in inches to feet as follows:
Height, k = 5 + 8/12
Height, k = 5 + 2/3
Height, k = 17/3 feet.
For the diameter, we have:
Diameter = 18/12
Diameter = 3/2 feet.
Also, we would determine the radius as follows:
Radius, r = diameter/2
Radius, r = (3/2)/2
Radius, r = 3/4 feet.
Substituting the parameters into the standard equation, we have;
(x - 12)² + (y - 17/3)² = (3/4)²
(x - 12)² + (y - 17/3)² = 9/16
Next, we would determine whether Brian's dart land on the dartboard:
(x - 12)² + (y - 17/3)² < 9/16
(x - 12)² + (y - 17/3)² < 9/16
(11.5 - 12)² + (5.5 - 5.67)² < 0.5625
0.25 + 0.0289 < 0.5625
0.2789 < 0.5625 (Yes, it does land because it's within the circumference of this standard dartboard).
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The adult daily dosage for a certain medicine is 90 mg (milligrams) of medicine for every pounds of body weight.
At this rate, find the daily dose for a man who weighs 175 pounds.
A daily dose of 15750 mg is required of a certain medicine for a man weighing 175 pounds
An adult daily dose of a certain medicine = 90 mg for every pound of body weight
Daily dose: The adult daily dose specifies the amount of drug dose in mg that must be taken within 24 hours as per the body weight of the person. The body weight of the person determines how much dose is required for the medicine to be effective in the body.
Weight of the man = 175 pounds
The daily dose for a man is given:
Weight of man*Daily dose per pound of body weight
= 175*90
= 15750
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Instructions: Solve the system. Enter your answer as an ordered pair.
Given the system:
[tex]\begin{gathered} 3x-9y=12\text{ Eq. 1} \\ 3x+4y=-1\text{ Eq. 2} \end{gathered}[/tex]First, we solve for 3x on both equations, as follows:
[tex]\begin{gathered} 3x=12+9y \\ 3x=-1-4y \end{gathered}[/tex]Equating both equations:
[tex]\begin{gathered} 12+9y=-1-4y \\ 13=-4-9y \\ 13=-13y \\ y=-1 \end{gathered}[/tex]Substituting y on equation 2:
[tex]\begin{gathered} 3x+4y=-1\text{ Eq. 2.} \\ 3x+4\times(-1)=-1 \\ 3x=-1+4 \\ 3x=3 \\ x=1 \end{gathered}[/tex]ANSWER
(1, -1)
the volume of a cube is 125 cubic centimeters. How many centimeters long is each edge of the cube?
Answer:
Each edge of the cube is 5 cm
Explanation:
The volume of a cube can be calculated using the formula;
[tex]V=l^3[/tex]Where;
V = volume of the cube
l = length of each side (since all the sides are equal)
Making length l the subject of formula by cube rooting both sides of the formula;
[tex]\begin{gathered} \sqrt[3]{V}=\sqrt[3]{l^3} \\ \sqrt[3]{V}=l \\ l=\sqrt[3]{V} \end{gathered}[/tex]Next, let's substitute the value of volume given;
V = 125 cubic centimeters
[tex]\begin{gathered} l=\sqrt[3]{V} \\ l=\sqrt[3]{125} \\ l=5\text{ cm} \end{gathered}[/tex]Each edge of the cube is 5 cm
Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.
Evaluate the expression |2x – 5| for x = –3 and for x = 3.
Answer:
9 and 1 respectively
Step-by-step explanation:
|2(-3)-5| = |-9| = 9
|2(2)-5| = |1| = 1
the vertical lines represents absolute value, this just mean that any negative values are then turned into their positive counterparts.
Find the point-slope form of the equation given: g(5) = 10 and g(2) = 8
will give brainliest
Answer:
[tex]y -10=\cfrac{2}{3} (x -5 )[/tex]========================
Given Two points: (5, 10) and (2, 8)To findThe point-slope form of the equation representing this lineSolutionPoint-slope form is:
[tex]y -y_1=m(x - x_1)[/tex], where (x₁, y₁) is one of the points and m is the slopeFind the slope:
[tex]m=\cfrac{y_2-y_1}{x_2-x_1} =\cfrac{8-10}{2-5} =\cfrac{-2}{-3} =\cfrac{2}{3}[/tex]Use one of the points and the slope to determine the equation of the line:
[tex]y -y_1=m(x - x_1)[/tex], substitute the slope and [tex]y -10=\cfrac{2}{3} (x -5 )[/tex]Answer:
[tex]y-10=\frac{2}{3} (x-5)[/tex]
Step-by-step explanation:
Pre-SolvingWe are given: g(5)=10, and g(2)=8.
The value inside the parentheses is the x value, and the value that it (g(x)) is equal to is the y value.
So, as points, the values are (5, 10), and (2, 8).
The equation wants to be written in point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point.
Solving SlopeWe first want to find the slope of the line.
The slope (m) can be found with two points using the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points.
We can label the values of the points we were given.
[tex]x_1=5\\y_1=10\\x_2=2\\y_2=8[/tex]
Now, substitute these values into the formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{8-10}{2-5}[/tex]
Subtract.
[tex]m=\frac{-2}{-3}[/tex]
Simplify.
[tex]m=\frac{2}{3}[/tex]
The slope is 2/3.
Since we now have the value of the slope, as well as [tex](x_1, y_1)[/tex], we can plug these values into the formula for point-slope form.
Point-Slope FormRecall that [tex]x_1=5[/tex] and [tex]y_1=10[/tex]; plug these in for [tex]x_1[/tex] and [tex]y_1[/tex] respectively.
[tex]y-10=m(x-5)[/tex]
We also just found the slope, which is 2/3. Plug that in for m.
[tex]y-10=\frac{2}{3} (x-5)[/tex]
Topics: Point-slope form, functions
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What is the standard form for yt and factored form
Given:
The leading coefficient of a polynomial is 3.
And the roots of the polynomial is -1, 1, and 2.
Required:
To write g(t) in factored form and standard form.
Explanation:
From the given data, the factored form is given by
[tex]\begin{gathered} g(t)=3(x-(-1))(x-1)(x-2) \\ =3(x+1)(x-1)(x-2) \end{gathered}[/tex]The standard form is,
[tex]\begin{gathered} g(t)=3(x+1)(x^2-2x-x+2) \\ =3(x+1)(x^2-3x+2) \\ =3(x^3-3x^2+2x+x^2-3x+2) \\ =3(x^3-2x^2-x+2) \\ =3x^3-6x^2-3x+6 \end{gathered}[/tex]Final Answer:
The factored form:
[tex]g(t)=3(x+1)(x-1)(x-2)[/tex]The standard form:
[tex]g(t)=3x^3-6x^2-3x+6[/tex]
That's the value of x, but you need to evaluate the expression x + 26 for
X = 28.5.
The answer to the expression is 54.6
How to solve variable related problems?1. Switch the positions of the variables in the equation. Starting with "solving for x" (or any other variable) in one of the equations, this "substitution" approach begins. [2] Say your equations are, respectively, 4x + 2y = 8 and 5x + 3y = 9.
2. To "solve for x," divide both sides of the equation.
3. Reconnect this to the other equation. Don't use the equation you just employed; rather, return to the other one.
When a particular variable's value is given to you
we just have to substitute that value in the required equation.
For instance in this question
x= 28.5
And the given equation is x + 26
Therefore the answer is 28.5 + 26 = 54.6 .
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If the formular-(X-X|Y-Xwere used to find the r-value of the5x буfollowing data, what would be the value of x?XY8496101811912|13A. 8B. 10C. 6D. 4
The value of x⁻, is the mean of the x values of the table.
The mean of x is obtained by adding all values of x, and divided the result by the total number of data, which is 5.
Then, you have:
[tex]\bar{x}=\frac{8+9+10+11+12}{5}=\frac{50}{5}=10[/tex]Hence, the mean of x, which is used in the formula to calculate the r-value, is 10
Jaime's football has a mass of 0.435 kilograms. His football helmet has a mass of 2.57 kilograms. Estimate how much more the mass of the helmet is than the mass of the football. Explain your estimate. Show your work.
Mass of football = 0.435kg
Mass of football helmet = 2.57kg
To find how much more the mass of the helmet is than the mass of football, we have to find the difference
2.57kg - 0.435kg
Find the time (in years) for the investment to double. (Round your answer to two decimal places)
Solution
Step 1
Write the compound interest formula
[tex]\text{A = P\lparen1 + }\frac{r}{n})^{nt}[/tex]Step 2
n = 4 (quarterly)
[tex]\begin{gathered} \text{P = x} \\ \text{A = 2x} \\ r\text{ = 7}\frac{3}{4}\text{ = 7.75\% = 0.0775} \end{gathered}[/tex]Step 3:
Substitute in the formula to find t.
[tex]\begin{gathered} 2x\text{ = x\lparen 1 + }\frac{0.0775}{4})^{4t} \\ \text{2 = \lparen1 + 0.019375\rparen}^4t \\ \text{2 = 1.019375}^{4t} \\ Take\text{ natural logarithm of both sides} \\ In(2)\text{ = 4t In\lparen1.019375\rparen} \\ 4t\text{ = }\frac{ln(2)}{ln(1.019375)} \\ 4t\text{ = 36.12080351} \\ t\text{ = }\frac{36.12080351}{4} \\ t\text{ = 9.03 years} \end{gathered}[/tex]Final answer
t = 9.03
Find the average rate of change of
refer to the image please
The average rate of change of the function f(x) = -2x² - 2 from x = 2 to x = 6 is -16
How to solve an equationAn equation shows the relationship between two or more numbers and variables.
The average rate of change of a function f(x) over the interval x = a to x = b is given by:
A(x) = [f(b) - f(a)]/[b - a]
Given that function f(x) = -2x² - 2 from x = 2 to x = 6, hence:
f(2) = -2(2)² - 2 = -10
f(6) = -2(6)² - 2 = -74
The average rate of change is:
A = [f(b) - f(a)]/[b - a]
Substituting:
A = [-74 - (-10)] / [6 - 2] = -16
The average rate of change is -16
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On August 31, 2024, Shocker borrows $57,000 from a local bank. A note is signed with principal and 9% interest to be paid on August 31, 2025. Record the adjusting entry for interest for Shocker at its year-end of December 31.
(a)Dr Unearned Revenue $1,400
Cr Service Revenue $1,400
(b)Dr Advertising Expense $880
Cr Prepaid Advertising $880
(c)Dr Salaries Expense $7,800
Cr Salaries Payable $7,800
(d)Dr Interest Expense $1,360
Interest Payable $1,360
Journal entry preparation
(a) According to the information provided, Shocker gets a $4,200 payment from a client for services done over the following three months, which implies the journal entry will be:
Unearned Dr. $1,400 in revenue
($4,200 x 1/3)
$1,400 in Cr Service Revenue
(a) Based on the information provided, we were told that the firm pays a local radio station $2,640 for radio advertisements throughout the months of December, January, and February, which implies that the Journal entry would be entered as:
Dr. Advertising Cost $880
($2,640 x 1/3)
$880 in Cr Prepaid Advertising
(c) According to the information provided, the corporation Employee salaries for the month of December were $7,800, which will be paid on January 7, 2022, implying that the Journal entry would be:
Dr Salaries Cost $7,800
$7,800 in Cr Salaries
(d) According to the facts provided, Shocker borrows $68,000 from a local bank, which implies the Journal entry will be:
$1,360 in Dr. Interest Expense
($68,000 x 6% x 4/12)
$1,360 in payable interest
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Cuál es la cantidad de divisores en 2121?
Answer:
2121 tiene 8 divisores respuesta B
A 4 1/2 bag of raisians must be divided equally into 1/4 bag portions
Answer:
18 portions
Step-by-step explanation:
1/4 x 4 1/2 = 18
The price p and the quantity x sold of a small flat-screen television set obeys the demand equation below.
a) Express the revenue R as a function of x. Use the formula R=px
b) How much should be charged for the television set if there are 70 television sets in stock?
c) How much should be charged for the television set if there are 1250 television sets in stock?
d) What is the revenue when there are 1250 sets in stock?
p= .14x +350
a. The revenue R as a function of x will be R = px.
b. The amount that charged for the television set if there are 70 television sets in stock is R / 70.
c. The amount that charged for the television set if there are 1250 television sets in stock is R / 1250
d. The revenue when there are 1250 sets in stock is 1250p
How to illustrate the information?1. From the information, the price p and the quantity x sold of a small flat-screen television is.
given. The revenue will be:
= Price × Quantity
= p × x.
= px
b. The amount that charged for the television set if there are 70 television sets in stock will be:
R = px
R = 70p
p = R / 70
c. The amount that should be charged for the television set if there are 1250 television sets in stock will be:
R = px
R = 1250p
p = R / 1250
d. The revenue when there are 1250 sets in stock will be:
= Price × Quantity
= p × 1250
= 1250p
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Shona is bundling magazines to recycle he notices at 6 magazines weigh 5/8 pound in all and that the magazines all weigh the same amount. What is the unit rate for pounds per magazine?I don't understand this at all
Given data:
The given weight of 6 magazines is 5/8 pound.
The given expression is,
6M=5/8 pounds
6M=0.625 pounds
1M=0.1041667 pounds
The weight of one magzine is 0.104167 pounds.
Two bicyclists, 44 miles apart, begin riding toward each other on a long straight avenue. One cyclist
travels 16 miles per hour and the other 17 miles per hour. At the same time, Spot (a greyhound), starting
at one cyclist, runs back and forth between the two cyclists as they approach each other. If Spot runs 39
miles per hour and turns around instantly at each cyclist, how far has he run when the cyclists meet?
The Greyhound has run to a distance equal to 50.7 miles.
This question can be solved using the distance, speed and time relation. The Distance, Speed and time are related to each other by the relation
Speed = Distance/Time, Let the time travelled be equal to t.
Distance travelled by first bicyclist is equal to 16t and Distance travelled by second bicyclist is equal to 17t. The total distance is equal to 44 miles. So, we get
44 = 17t + 16t
44 = 33t
=> t = 44/33
=> t = 1.3 hours
At this time a greyhound starts running back and forth around each cyclist. The speed of Greyhound is equal to 39 miles per hour. Distance will be given by
Distance = Speed × Time
Distance = 39 × 1.3
Distance = 50.7 miles
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What is the area of the triangle shown below?131310units2
SOLUTION
We want to find the area of the triangle in the image.
To do this, we will make use of the Heroes formula which states
[tex]\begin{gathered} A=\sqrt{s(s-a)(s-b)(s-c)} \\ where\text{ s =}\frac{a+b+c}{2} \\ a,b\text{ and c are the sides of the triangle } \end{gathered}[/tex]applying this, we have
[tex]\begin{gathered} s=\frac{13+13+10}{2} \\ s=\frac{36}{2} \\ s=18 \end{gathered}[/tex]The area A becomes
[tex]\begin{gathered} A=\sqrt{18(18-13)(18-13)(18-10)} \\ =\sqrt{18\times5\times5\times8} \\ =\sqrt{3,600} \\ =60\text{ units}^2 \end{gathered}[/tex]Hence the answer is 60 square units
Which property is shown -2x1/-2=1
Answer:
Multiplicative inverse
Step-by-step explanation:
How much solute is in each Percent Solution below
How many grams of KOH are in a 25% w/w solution?
25% w/w solution has 25 grams of solute.
The expression w/w stands for weight by weight. This expression indicates the amount of solute present in solution. Concerning this, 25 gram of KOH or potassium hydroxide is present in 100 gram of solution.
Further elaborating, the amount of solvent will be calculated by the formula -
Amount of solution = amount of solute + amount of solvent
Amount of solvent = 100 - 25
Performing subtraction to find the amount of solvent
Amount of solvent = 75 grams
Thus, the 100 gram of solution has 25 grams solute and 75 grams of solvent.
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Poland Spring Hotel is a 500-room property that offers only rooms, no F&B service. You are in the process of evaluating the business as an investment. Calculate the breakeven sales and rooms using the information below
Answer: GAS
Step-by-step explanation:
how the absolute value is never negative
Answer:
absolute value is a distance from 0; distance cannot be negative
Step-by-step explanation:
the def of absolute value is a numbers distance from 0
distances cannot be negative no matter what you are talking about
Answer: The point of absolute value is to find the distance from a number to 0, which can never be less than 0.
Step-by-step explanation:
The point of absolute value is to find the distance from a number to 0.
For example, if a number line has a -3 point on it, how far away will it be to 0.
<=====o=======o======>
-3 0
The answer is 3! Just like the absolute value
|-3| = ?
3 = ?
Compute the horizontal force P required to prevent the block from sliding down the plane for the 100 lb block shown. Assume the coefficient of static friction to be 0.65.
canThe first First step we need to do is to make the decomposition of the vectors W and P.
Both will have a component perpendicular and parallel to the plane. The perpendicular will be used to calculate the maximum static friction force, and the horizontal will be used to find the P required to prevent the block from sliding.
From the sketch, we are able to define both, parallel and perpendicular components of P, as it follows:
[tex]\begin{gathered} P_{\text{//}}=P\cos (30\degree)=\frac{P\sqrt[]{3}}{2} \\ P_{perp}=P\sin (30\degree)=\frac{P}{2} \end{gathered}[/tex]Now, we can do the same for W.
And for W we also can provide the two components as follows:
[tex]\begin{gathered} W_{//}=W\sin (30\degree)=\frac{W}{2} \\ W_{\text{perp}}=W\cos (30\degree)=\frac{W\sqrt[]{3}}{2} \end{gathered}[/tex]Now, we can elaborate on both equations: one for the perpendicular direction and the other for parallel. In the perpendicular direction, we have a component of W, one component of P, and the normal force N. Because the block is going to move, or change its movement along this direction, the sum of the forces pointing upwards must be equal to the sum of the forces pointing downwards. From this, we can write the following:
[tex]\begin{gathered} N=P_{\text{perp}}+W_{\text{perp}} \\ N=\frac{P}{2}+\frac{W\sqrt[]{3}}{2}=\frac{P+W\sqrt[]{3}}{2} \end{gathered}[/tex]Now, for the horizontal, we have the P component to the right and the W component to the left. If we imagine the block is almost sliding. We can write the following equation, from the premise the forces will cancel each other just like the perpendicular case:
[tex]\begin{gathered} P_{//}+F_{\mu}=W_{//} \\ \frac{P\sqrt[]{3}}{2}+N\times\mu_{static}=\frac{W}{2} \end{gathered}[/tex]Here it is used the fact that the friction force is equal to the multiplication of the coefficient of static friction by the normal force. Here we assumed also that the friction is maximum because the block is on the verge of motion downwards, and for this reason, the Friction is upwards, with the P component.
Now, substituting N and the coefficient, we find:
[tex]\begin{gathered} \frac{P\sqrt[]{3}}{2}+\frac{P+100\sqrt[]{3}}{2}0.65=\frac{100}{2}=50 \\ \frac{P(\sqrt[]{3}+0.65)+65\sqrt[]{3}}{2}=50 \\ P(\sqrt[]{3}+0.65)+65\sqrt[]{3}=100 \\ P(\sqrt[]{3}+0.65)=100-65\sqrt[]{3} \\ P=\frac{100-65\sqrt[]{3}}{\sqrt[]{3}+0.65}\cong\frac{100-65\times1.732}{1.732+0.65}=\frac{100-112.58}{2.382} \\ P=-\frac{12.58}{2.382}\cong-5.275\text{lbf} \end{gathered}[/tex]From this, we can see that the force P made to the left with an intensity equal to -5.275 lbf will bring the block on the verge of motion downwards. If we consider that P is strong enough to make it almost move upwards, it is, the Normal Force will be downwards, we can remake the calculation as it follows:
[tex]\begin{gathered} P_{//}=W_{//}+F_{\mu} \\ \frac{P\sqrt[]{3}}{2}=\frac{W}{2}+N\times\mu_{static} \end{gathered}[/tex]And substituting values, we have:
[tex]\begin{gathered} \frac{P\sqrt[]{3}}{2}=50+\frac{P+100\sqrt[]{3}}{2}0.65 \\ \frac{P(\sqrt[]{3}-0.65)}{2}=50+50\sqrt[]{3}\times0.65 \\ P=\frac{2}{\sqrt[]{3}-0.65}\times50(1+\sqrt[]{3}\times0.65)\cong196.46 \end{gathered}[/tex]From this, we know that the max value for P, where the block will not slide is going to be 196.46 lbf to the right.
A security keypad uses five digits (0 to 9) in a specific order. How many different
keypad patterns are possible if the first three digits must be even and the last digit
cannot be zero?
The different keypad patterns that are possible if the first three digits must be even and the last digit cannot be zero is 17500 ways.
How to calculate the value?It should be noted that the security keypad uses five digits (0 to 9) in a specific order. On this case, the numbers from 0 to 9 make up 10 numbers.
In this case, there are 5 even numbers.
The total number of possible codes will be:
= 5 × 5 × 10 × 10 × 7
= 17500
There are 17500 ways.
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1. There is a two digit number where the difference in the units digit and the tens digit is 5. If the digits are reversed, the
new number is the sum of twice the original number and seven. Find the number.
Answer:
38
Step-by-step explanation:
Let x = the ones digit, and let y = the tens digit.
The number looks like yx.
The value of the original number is
10y + x
"the difference in the units digit and the tens digit is 5."
x - y = 5 Equation 1
When you reverse the digits, you have xy.
The value of the new number is
10x + y
"If the digits are reversed, the new number is the sum of twice the original number and seven."
10x + y = 2(10y + x) + 7 Equation 2
We have a system of 2 equations.
x - y = 5
10x + y = 2(10y + x) + 7
Simplify the second equation.
10x + y = 2(10y + x) + 7
10x + y = 20y + 2x + 7
8x - 19y = 7
x - y = 5
8x - 19y = 7
Solve the first equation for x. Substitute that value for x in the second equation.
x = 5 + y
8(5 + y) - 19y = 7
40 + 8y - 19y = 7
-11y = -33
y = 3
x = 5 + y
x = 5 + 3
x = 8
The digits are:
ones digit: 8
tens digit: 3
The number is 38.
please hellppp!!!!!!!!!
Answer:
C
Step-by-step explanation: