How many area codes of the form (XYZ) are possible if the digit 'X' and 'Y' can be any number ( through 9 but they can't repeat and the digit 7 can be any number 1 through 9?
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Start to see the possible options
[tex]XYZ=-\cdot-\cdot-_{}[/tex]The first digit will have 10 possible numbers to choose from 0 to 9, however in the second digit since it cannot repeat there will be only 9 possible to choose from. As for ther third number 0 is not an option meaning that there are 9 to choose as well.
[tex]\begin{gathered} XYZ=10\cdot9\cdot9 \\ XYZ=810 \end{gathered}[/tex]
Related Questions
Help meeeee4) Consider the equation z(x)=(x-5,x s101-x+8, x > 10Note that for this problem, you do not actually have to evaluate the results. Just make sure that youexplain your choices.a. If you are trying to evaluate Z(3), which equation would you choose, and why?b. If you are trying to evaluate Z(11), which equation would you choose, and why?c. If you are trying to evaluate Z(10), which equation would you choose, and why?
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4). a. If you are trying to evaluate Z(3) in order to know which equation would you choose we would have to make the following calcuations:
So, if Z(3), then:
substitute the x with the number 3
[tex]z\left(3\right)=3-5=-2,3\leq10,\text{ 1-3=-2, 3}>10[/tex]Therefore, the equation to choose if Z(3) would be x>10, because by substitute the x with the number 3 would be the largest function with a positive number and sign.
Which of the following shows the division problem down below
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Question:
Solution:
Synthetic division is a quick method of dividing polynomials; it can be used when the divisor is of the form x-c. In synthetic division, we write only the essential parts of the long division. Notice that the long division of the given problem is written as:
thus, the synthetic division of the given problem would be:
Writing 6 instead of -6 allows us to add instead of subtracting. We can conclude that the correct answer is:
A.
Part I: Domain and Range-identify the domain and range of each graph. Problem / Work Answe 2+ 6+ 2+ 1. Week 15 Homework Packet pdf 2003
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Domain is the set of input values,
In the graph x axis show the domain
Where the x values is lies at -2,-1,0,1,2
Sothe domain will be :
[tex]\text{Domain =-2}\leq x\leq2[/tex]Range is the set of output values,
In the graph the value of function at y axis is : 0,2,4,6,8-2,-4.....
So, the range will be :
[tex]\text{Range = -}\infty\leq y\leq\infty[/tex]In a film, a character is criticized for marrying a woman when he is three times her age. He wittily replies, "Ah, but in 21 years time I shall only be twice her age." How old are the man and the
woman?
Write a linear function that models the total monthly costs for each option for x hours of court rental time.
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The age of man is 63 years and the age of women is 21 years.
Given that, a character is criticized for marrying a woman when he is three times her age.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Let age of man be x and the age of women be y.
Now, x=3y ---------(1)
In 21 years time man will be twice her age.
x+21=2(y+21)
⇒ x+21=2y+42
⇒ x-2y=21 ---------(2)
Substitute equation (1) in (2), we get
3y-2y=21
⇒ y = 21
So, x=3y=63
Therefore, the age of man is 63 years and the age of women is 21 years.
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Graph the inequality on a plane. Shade a region below or above. Y < - 1
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In order to graph the inequality on the coordinate plane, we first need to find it's border, which is delimited by the line below:
[tex]y=-1[/tex]This line is a straight line parallel to the x-axis and that passes through the y-axis at the point (0, -1). Since the original inequality has a "less" sign, we need to make this boundary line into dashes.
Now we can analyze the inequality:
[tex]y<-1[/tex]Since the signal is "<", we need to shade all the region of the coordinate plane for which y is below -1, this means that we have to paint the region below the line. The result is shown below:
Complete each equation so that it has infinitely many solutions. 12x - x + 8 + 3x = __x + __ (__ are blanks)
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A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
What are a definition and an example of a linear equation?Linear formula first-degree algebraic equation with the variables y = 4x + 3 or similar (that is, raised only to the first power). Such an equation has a straight line for its graph.
-12-x=8-3x
Add what is to the right of the equal sign to both sides of the equation, then rewrite the equation as follows:-12-x-(8-3*x)=0
Take like variables away:-20 + 2x = 2 • (x - 10)
Solve: 2 = 0There is no answer to this equation.A constant that is not zero can never equal zero.x-10 = 0
On both sides of the equation, add 10:x = 10.
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The high school soccer booster club sells tickets to the varsity matches for $4 for students and $8
for adults. The booster club hopes to earn $200 at each match.
what does the slope mean in terms of the situation?
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8y= -4x +200
y= -1/2x +25
Slope = -1/2
Blackgrass black graph is the of y=f(x) chose the equation for the red graph
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The Solution:
The correct answer is [option A]
Given:
Required:
To determine the equation of the red graph if the black graph function is y = f(x).
The correctb
i need help solving this with the statements and reasons
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Given that:
[tex]\bar{AB}\mleft\Vert \mright?\bar{DC}[/tex]To prove that:
[tex]\Delta ABE\cong\Delta\text{CDE}[/tex]We know that congruent parts of congruent triangles are congruent
[tex]\angle\text{AEB }\cong\angle CDE\text{ (vertically opposite angles)}[/tex]Given that E is the midpoint of AC, therefore,
[tex]\begin{gathered} EA=EC\text{ } \\ EB=ED \end{gathered}[/tex]By the SAS congruency theorem as illustrated above, it is sufficient to prove that the triangles are congruent
Write an equation for the description.Two-thirds a number x plus 6 is 10.
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We have the next description:
- Two-thirds a number x plus 6 is 10.
To represent the description we can use the next equation:
[tex]\frac{2}{3}x+6=10[/tex]In 1990, the cost of tuition at a large Midwestern university was $104 per credit hour. In 1998, tuition had risen to $184 per credit hour.
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We have to find the linear relationship for the cost of tuition in function of the year after 1990.
The cost in 1990 was $104, so we can represent this as the point (0, 104).
The cost in 1998 was $184, so the point is (8, 184).
We then can calculate the slope as:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{184-104}{8-0} \\ m=\frac{80}{8} \\ m=10 \end{gathered}[/tex]We can write the equation in slope-point form using the slope m = 10 and the point (0,104):
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-104=10(x-0) \\ y=10x+104 \end{gathered}[/tex]We can then write the cost c as:
[tex]c=10x+104[/tex]We then can estimate the cost for year 2002 by calculating c(x) for x = 12, because 2002 is 12 years after 1990.
We can calculate it as:
[tex]\begin{gathered} c=10(12)+104 \\ c=120+104 \\ c=224 \end{gathered}[/tex]Now we have to calculate in which year the tuition cost will be c = 254. We can find x as:
[tex]\begin{gathered} c=254 \\ 10x+104=254 \\ 10x=254-104 \\ 10x=150 \\ x=\frac{150}{10} \\ x=15 \end{gathered}[/tex]As x = 15, it correspond to year 1990+15 = 2005.
Answer:
a) c = 10x + 104
b) $224
c) year 2005.
Solve for x. Write the reasons next to each step.Submit723x+10
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x = 26/3
Explanation:We would apply the mid-segment theorem:
The base of the smaller triangle = 1/2 (the base of the bigger triangle)
The base of the smaller triangle = 3x + 10
the base of the bigger triangle = 72
3x + 10 = 1/2(72)
Reason: Mid segment is parallel to the base of the large triangle. And it is equal to half the length of the base of the large triangle
simplifying:
3x + 10 = 72/2
3x + 10= 36
subtract 10 from both sides:
3x + 10 - 10 = 36 - 10
3x = 26
DIvide both sides by 3:
3x/3 = 26/3
x = 26/3
or x = 8 2/3
Determine whether 17y = 3x − 19 is quadratic or not. Explain.No; there is no x2 term, so a = 0.No; there is no x-term, so b = 0.No; there is no constant term, so c = 0.Yes; it can rewritten in the form y = ax2 + bx + c.
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The standard form of quadratic equation is given as,
[tex]ax^2+bx\text{ + c = 0 where a }\ne\text{ 0}[/tex]The equation is given as,
[tex]17y\text{ = 3x - 19}[/tex]Therefore,
[tex]\text{From the given equation x}^2\text{ is not present and also a = 0.}[/tex]Thus the given equation is not a quadratic equation.
Erin is buying produce at a store. She buys c cucumbers at $0.89 each and a apples at $0.99 each. What does the expression 0.89c + 0.99a represent? The expression represents the
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One cucumber costs $0.89, so with Erin buys "c" cucumbers, the price he will pay for the cucumbers is the unitary price (0.89) times the number of cucumbers ("c"), so the price is 0.89c.
One apple costs $0.99, so with Erin buys "a" apples, the price he will pay for the apples is the unitary price (0.99) times the number of apples ("a"), so the price is 0.99a.
Then, to find the final price Erin will pay, we just need to sum both prices: all the cucumbers and all the apples:
Final price = 0.89c + 0.99a
So the expression represents the final price (or cost) Erin will pay for all products.
4-10x = 3+5x subtract 4 from both sides
Answers
S={1/15}
1) Solving that expression
4-10x = 3+5x Subtract 4 from both sides
4-4-10x=3-4+5x
-10x =-1+5x Subtract 5x from both sides, to isolate x on the left side
-10x -5x = -1 +5x -5x
-15x=-1 Divide both sides by -15 to get the value of x, not -15x
x=1/15
S={1/15}
8. Factor ()=63−252++60 completely given that x=3 is a zero of p(x). Use only the techniques from the lecture on 3.3 (synthetic division). Other methods will receive a score of zero. Be sure to show all your work (including the synthetic division).
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Factor the polynomial
[tex]\begin{gathered} p(x)=6x^3-25x^2+x+60 \\ \text{Given that, }x=3\text{ is a zero} \end{gathered}[/tex]Using the synthetic division method to factorize the polynomial completely,
The resulting coefficients from the table are 6, -7, -20, 0
Thus the quotient is
[tex]6x^2-7x-20[/tex]Factorizing the quotient completely,
[tex]\begin{gathered} 6x^2-7x-20 \\ =6x^2-15x+8x-20 \\ =3x(2x-5)+4(2x-5) \\ =(3x+4)(2x-5) \end{gathered}[/tex]Therefore, the other two zeros of the polynomial are:
[tex]\begin{gathered} (3x+4)(2x-5)=0 \\ 3x+4=0 \\ x=-\frac{4}{3} \\ 2x-5=0 \\ x=\frac{5}{2} \\ \\ Therefore,t\text{he factors of the polynomial are:} \\ (x-3)(3x+4)(2x-5) \end{gathered}[/tex]Liam's monthly bank statement showed the following deposits and withdrawals.If Liam's balance in the account was $62.45 at the beginning of the month, what was the account balance at the end of the month?
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First, let's take the inital balance and add all the deposits:
[tex]62.45+32.35+63.09+98.79=256.68[/tex]Then, we'll take this amount and substract all the withdrawals:
[tex]256.68-114.95-79.41=62.32[/tex]This way, we can conclude that the account balance at the end of the month was $62.32
Find the surface area of the cylinderA). 188.4 ft^2B). 226.08 ft^2C). 244.92 ft^2D). 282.6 ft^2
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To solve this problem, we will use the following formula for the surface area of a cylinder:
[tex]A=2\pi rh+2\pi r^2,[/tex]where r is the radius of the base, and h is the height of the cylinder.
Substituting h= 10 ft, and r = 3 ft in the above formula, we get:
[tex]A=2\pi(3ft)(10ft)+2\pi(3ft)^2.[/tex]Simplifying, we get:
[tex]A=244.92ft^2.[/tex]Answer: Option C.
I need help with a question
Answers
8c + 3 = 5c + 12
5c is adding on the right, then it will subtract on the left
3 is adding on the left, then it will subtract on the right
8c - 5c = 12 - 3
3c = 9
3 is multiplying on the left, then it will divide on the right
c = 9/3
c = 3
please help ………………. …………. ………… i already have the answer for part A but im having trouble with Parts B and C
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In part B we must perform the following operation:
[tex](5a^3+4a^2-3a+2)+(a^3-3a^2+3a-9)[/tex]The key here is to group the terms according to the power of a they have:
[tex](5a^3+4a^2-3a+2)+(a^3-3a^2+3a-9)=(5a^3+a^3)+(4a^2-3a^2)+(-3a+3a)+(2-9)[/tex]Then, we can use the distributive property of the multiplication but in reverse:
[tex]b\cdot a+c\cdot a=(b+c)\cdot a[/tex]If we do this in each of the terms between parenthesis we get:
[tex]\begin{gathered} (5a^3+a^3)+(4a^2-3a^2)+(-3a+3a)+(2-9)= \\ =(5+1)a^3+(4-3)a^2+(-3+3)a-7 \\ (5+1)a^3+(4-3)a^2+(-3+3)a-7=6a^3+a^2-7 \end{gathered}[/tex]Then the answer for part B is:
[tex]6a^3+a^2-7[/tex]In part C we must simplify:
[tex](4y^3-2y+9)-(2y^3-3y^2+4y+7)[/tex]Here is important to remember that a negative sign before a parenthesis means that you have to change the sign of all the terms inside it. Then we have:
[tex](4y^3-2y+9)-(2y^3-3y^2+4y+7)=4y^3-2y+9-2y^3+3y^2-4y-7[/tex]Now we can do the same thing we did in part B, we group the terms according to the powers of y:
[tex]4y^3-2y+9-2y^3+3y^2-4y-7=(4y^3-2y^3)+3y^2+(-2y-4y)+(9-7)[/tex]Then we apply the distributive property in reverse:
[tex]\begin{gathered} (4y^3-2y^3)+3y^2+(-2y-4y)+(9-7)=(4-2)y^3+3y^2+(-2-4)y+2 \\ (4-2)y^3+3y^2+(-2-4)y+2=2y^3+3y^2-6y+2 \end{gathered}[/tex]Then the answer for part C is:
[tex]2y^3+3y^2-6y+2[/tex]While reviewing the previous day’s arrest report, a police sergeant that seven suspects were arrested, all of whom had either one or two previous arrests. Including yesterday arrests, there were 16 total among them. How many suspects had had less than two prior arrests?
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ANSWER :
EXPLANATION :
I wanted to know if this is the right answer
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Notice that angles 6 and 4 are alternate exterior angles, therefore:
[tex]m\measuredangle4=m\measuredangle6.[/tex]Answer: m<4=66.
A cannery needs to know the volume-to-surface-area ratio of a can to find the size that will create the greatest profit. Find the volume-to-surface-area ratio of a can.Hint : For a cylinder, S = 2πr2 + 2πrh and V = πr2h.a. 1/2b. 2(r+h) / rhc. πr(2r + 2h − rh)d. rh / 2(r+h)
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SOLUTION
[tex]Volume\text{ }of\text{ }can=\pi r^2h[/tex][tex]Surface\text{ }area\text{ }of\text{ }can=2\pi r^2+2\pi rh[/tex]The ratio can be established as shown below
[tex]\begin{gathered} \frac{\pi r^2h}{2\pi r^2+2\pi rh} \\ \frac{\pi r^2h}{2\pi r(r+h)} \\ \frac{rh}{2(r+h)} \end{gathered}[/tex]The correct answer is OPTION D
Go on the head 120 eggs delivered to her bakery she used to 98 eggs to bake cakes which equation can she use find the number of eggs r she has left
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Yolanda has 120 eggs, but she used 98 eggs
r represents the equation for the number of eggs that she left:
To find this, subtract the total of eggs by the eggs used
Then, r = 120 - 98
Brett colors 25% of the total shapes on his paper. He colors 14 shapes. How many total shapes are there on Brett’s paper?
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Answer:
56 i think because if 25% = 1/4 and 14 is 25% you would need to multiply 14 by 4 to get 100% or 4/4
Use the give right triangle to find ratios. In reduced form, for sin A, cos A, and tan A
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From the figure given, if theta = A
opposite = 28 and hypotenuse =53
substitute the values into the formula
[tex]\sin A=\frac{28}{53}[/tex][tex]\cos A=\frac{adjacent}{\text{hypotenuse}}[/tex][tex]\cos A=\frac{45}{53}[/tex][tex]\tan \theta=\frac{opposite}{adjacent}[/tex][tex]\tan A=\frac{28}{45}[/tex]Monica did an experiment to compare two methods of warming an object. The results are shown in thetable below. Which statement best describes her results?
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The correct answer is,
The temperature using method 2 changed exponentially.
State the rational number represented by each letter on the number line as a decimal.
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The rational number represented by the letter D is -43/100 and by the letter R is -46/100.
What is rational number?
A rational number is one that can be written as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively.
Here the number line is divided into 10 division with equal distance.
Each division is of the distance 0.01
So, the decimal number represented by letter D is -0.43 and by the letter R is -0.46.
To convert decimal number into rational number,
-0.43 = -43/100
-0.46 = -46/100
Therefore, the rational number represented by each letter on the number line as a decimal are D = -43/100 and R = -46/100.
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determine the number of real solutions for the following quadratic equation using the discriminate
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Given equation:
[tex]y=x^2-3x-4[/tex][tex]a=1,b=-3,c=-4[/tex]Discriminant:
[tex]\begin{gathered} b^2-4ac \\ (-3)^2-4(1)(-4) \\ =9+16 \\ =25 \end{gathered}[/tex]Number of real solutions:
Since the discriminant is > 0 (that is ,it is a positive value)
Determine the solution to the given equation.4 + 3y = 6y – 5
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Answer:
[tex]y=3[/tex]Explanation:
Step 1. The expression we have is:
[tex]4+3y=6y-5[/tex]And we are required to find the solution; the value of y.
Step 2. To find the value of y, we need to have all of the terms that contain the variable on the same side of the equation. For this, we subtract 6y to both sides:
[tex]4+3y-6y=-5[/tex]Step 3. Also, we need all of the numbers on the opposite side that the variables are, so we subtract 4 to both sides:
[tex]3y-6y=-5-4[/tex]Step 4. Combine the like terms.
We combine the terms that contain y on the left side of the equation, and the numbers on the right side of the equation:
[tex]-3y=-9[/tex]Step 5. The last step will be to divide both sides of the equation by -3 in order to have only ''y'' on the left side:
[tex]\begin{gathered} \frac{-3y}{-3}=\frac{-9}{-3} \\ \downarrow\downarrow \\ y=3 \end{gathered}[/tex]The value of y is 3.
Answer:
[tex]y=3[/tex]