Answer:
The correct option is D
f(x) = 5(0.8)
has y-intercept of 4
Explanation:
To know which of the given functions has a y-intercept of 4, we test them one after the other.
a. f(x) = 3(1 + 0.05)
f(x) = 3.15 WRONG
b. f(x) = 4(0.95)
f(x) = 3.8 WRONG
c. f(x) = 5(1.1)
f(x) = 5.5 WRONG
d. f(x) = 5(0.8)
f(x) = 4 CORRECT
Show that Polygon ZSCH
is a Scaled copy of
Polygon XJYN.
As ratio is not given, we cannot prove that they are scaled copy.
Define scaled copy.Corresponding portions, or parts that are at the same location in relation to the remainder of each figure, exist in both the original figure and its scaled copy. These components could be angles, points, or segments. Polygon 2, for instance, is a scaled-down version of Polygon 1. There is a point in Polygon 2 for each point in Polygon 1.
Given,
Polygon ZSCH is a Scaled copy of Polygon XJYN.
We simply calculate the ratio of the lengths of the two corresponding sides of two polygons to determine the scale factor. The scaling factor is known as such and the polygons are similar if the ratio is the same for all matching sides.
As ratio is not given, we cannot prove that they are scaled copy.
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8 O 6 4. N Which function is graphed? 2. 4 6 8 -8 -6 -4 -2 0 -2 -6 O A. Y- (x² + 4, x=2 1-x+4,452 (x² + 4, x2 OD. V- x + 4, x32 1-x+4,4
The given curve is parabola and its last point is on the x axis at x = 2
So, the equation of curve is :
[tex]x^2+4,x<2[/tex]In the equation of line,
The line start from x = 2 so, x ≥ 2
So, Equation of line is : -x + 4, x ≥ 2
Answer : B)
[tex]y=\begin{cases}x^2+4,x<2 \\ \square \\ -x+4,\text{ x}\ge2\end{cases}[/tex]Hayley's rectangular bedroom is 6 meters by 5 meters. What is the diagonal distance from one corner to the opposite corner? If necessary, round to the nearest tenth.
Hayley's rectangular bedroom is 6 meters by 5 meters. What is the diagonal distance from one corner to the opposite corner? If necessary, round to the nearest tenth.
Apply the Pythagorean Theorem
c^2=a^2+b^2
we have
a=6 m
b=5 m
c^2=6^2+5^2
c^2=36+25
c^2=61
square root c=7.8 m
answer is 7.8 metersgiven the residual plot below, which of the following statements is correct?
Let me explain this question with the following picture:
We can recognize a linear structure when all the points have a pattern that seems like a straight line as you can see above for example.
In the graph of your question, we can see that the points don't have a definited pattern and that's clearly not seemed like a straight line.
Therefore, the answer is option B:
There is not a pattern, so the data is not linear.
What are three ratios equivalent to 9/5?
The given ratio is 9/5
This ratio is already in the simplified form. To find equivalent ratios, we would multiply the numerator and denominator by constant numbers. We have
If we multiply by 2, it becomes
9 * 2/5 * 2 = 18/10
If we multiply by 3, it becomes
9 * 3/5 * 3 = 27/15
If we multiply by 4, it becomes
9 * 4/5 * 4 = 36/20
Thus, three equivalent ratios are
18/10, 27/15 and 36/20
160 is what percent of the sum of 100 and 120 and 160
42.105%
1) Let's first add thosse numbers up: 100 +120+160 =380
2) Now we can write out the following ratio, to find out what percentage is equivalent to 160 out of that 380:
[tex]\begin{gathered} 160----x \\ 380----100 \\ \frac{160}{380}=\frac{x}{100} \\ 380x=16000 \\ \frac{380x}{380}=\frac{16000}{380} \\ x=42.105\% \end{gathered}[/tex]Note that we had to cross multiply that.
3) Hence, the answer is 160 is approximately 42.105% of 380
Decide whether or not the number 46/45 Could represent the probability
Solution
- A probability, by definition, is a fraction that is less than or equal to 1.
- The number 46/45 is a number greater than 1.
- Thus, the number 46/45 CANNOT be a probability
Solve the following system algebraically. y= x2 - 9x + 18 y = x - 3
we have
y=x^2-9x+18 -----> equation A
y=x-3 ------> equation B
Solve the system of equations
substitute equation B in equation A
x^2-9x+18=x-3
x^2-9x+18-x+3=0
x^2-10x+21=0
Solve the quadratic equation using the formula
[tex]x=\frac{-b\pm\sqrt[\square]{b^2-4ac}}{2a}[/tex]we have
a=1
b=-10
c=21
substitute the given values
[tex]\begin{gathered} x=\frac{-(-10)\pm\sqrt[\square]{(-10)^2-4(1)(21)}}{2(1)} \\ \\ x=\frac{10\pm\sqrt[\square]{100-84}}{2} \\ \\ x=\frac{10\pm\sqrt[\square]{16}}{2} \\ \\ x=\frac{10\pm4}{2} \\ \\ x=7 \\ x=3 \end{gathered}[/tex]Find the value of y for x=7
y=x-3
y=7-3=4
the first solution is (7,4)
Find the value of y for x=3
y=3-3=0
the second solution is (3,0)
therefore
the answer is the first optionHello can you please help me with problem number 12
Turn the 48in to ft
[tex]\begin{gathered} 1ft=12in \\ \\ 48in\times\frac{1ft}{12in}=4ft \end{gathered}[/tex]Then, 48 inches is equal to 4ft.
Comparing the given quatities you get that:
48inches > (greater than) 3ftthe rate of change at which the water level rises is ___ centimeters per minutes. so, involving the equation ____ for y gives a y-value equal to___
We will have the following:
The rate at which the water rises is 13/4 cm per minute.
So, solvinng the equation:
[tex]\frac{13}{4}=\frac{y}{12}[/tex]For y gives a value for y equal to:
[tex]y=\frac{13\cdot12}{4}\Rightarrow y=39[/tex]Could you tell me the process of solving the problem?
Given:
[tex]Ln8=\frac{2\pi m\xi}{\sqrt{1-\xi^2}}[/tex]m=250
Required:
Find the value of
[tex]\xi[/tex]Explanation:
The value of ln8 is:
[tex]ln8=2.079[/tex][tex]\begin{gathered} 2.079=\frac{2\times3.14\times\xi}{\sqrt{1-\xi^2}} \\ 2.079(\sqrt{1-\xi^2})=6.28\xi^ \end{gathered}[/tex]Take the square on both sides.
[tex]\begin{gathered} 4.322(1-\xi^2)=39.44\xi^2 \\ \frac{1-\xi^2}{\xi^2}=\frac{39.4384}{4.322} \\ \frac{1}{\xi^2}-1=9.125 \\ \frac{1}{\xi^2}=9.125+1 \\ \frac{1}{\xi^2}=10.125 \end{gathered}[/tex]O EQUATIONS AND INEQUALITIESSolving a word problem with three unknowns using a linear...
Given:
The sum of three numbers is 81, The third number is 2 times the second, The first number us 9 moe than the second.
Required:
We need to find all the numbers
Explanation:
Assume that a, b and c are the first, second and third numbers respectively.
By given ststement
[tex]\begin{gathered} a+b+c=81\text{ .....\lparen i\rparen} \\ c=2b\text{ .....\lparen ii\rparen} \\ a=b+9\text{ .....\lparen iii\rparen} \end{gathered}[/tex]substitute c and a in equation (i)
[tex]\begin{gathered} b+9+b+2b=81 \\ 4b=72 \\ b=18 \end{gathered}[/tex]now put value of b in equation (ii) and (iii)
[tex]c=2*18=36[/tex]and
[tex]a=18+9=27[/tex]FInal answer:
first number a = 27
second number b = 18
third number c = 36
Michael wants to save $55,000.00 for a down payment on a home. How much will he need to invest in anaccount with 8.5% APR, compounding daily, in order to reach his goal in 3 years?
Step 1. The information that we have is:
The final amount that Michael wants to save is:
[tex]A=55,000[/tex]We will call that amount A.
The annual percentage rate of the investment, which we will label as r, is:
[tex]r=8.5[/tex]We will need this annual percentage rate represented as a decimal number, therefore, we divide it by 100:
[tex]\begin{gathered} r=8.5/100 \\ r=0.085 \end{gathered}[/tex]The time of the investment, t, is 3 years:
[tex]t=3[/tex]And it is compounded daily, let n be the number of times of compounding in a year:
[tex]n=365[/tex]Step 2. We need to find the initial amount of the investment, which will be called P or principal.
The formula we will use to find it is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Step 3. Substituting the known values:
[tex]55,000=P(1+\frac{0.085}{365})^{(365)(3)}[/tex]From this equation, we need to solve the operations and solve for P, the principal amount of the investment.
Step 4. Simplifying the equation:
[tex]55,000=P(1+0.0002328767)^{1095}[/tex]Continue simplifying:
[tex]\begin{gathered} 55,000=P(1.0002328767)^{1,095} \\ 55,000=P(1.2904233) \end{gathered}[/tex]Then, we solve for P:
[tex]\begin{gathered} \frac{55,000}{1.2904233}=P \\ 42,621.6726=P \end{gathered}[/tex]Rounding to the nearest cent (2 decimal places) The amount that he needs to invest is $42,621.67
Answer: $42,621.67
The elimination method is used in place over substitution when one equation is not easily solved for ______________ variable.A) a standardB) a dependentC) an independentD) a single
Given:
There are given the statement about the elimination method and substitution method.
Explanation:
According to the concept:
One equation cannot be easily solved for a single variable.
Final answer:
Hence, the correct option is D.
use your theorem from 2-37 about the angles in a triangle to find in the diagram below. show all work.
We have that, for any triangle, the sum of all its angles equals 180. In this case, we have the following:
[tex]96+2x+(x+12)=180[/tex]Now we solve for x to get the following:
[tex]\begin{gathered} 96+2x+x+12=180 \\ \Rightarrow2x+x=180-96-12 \\ \Rightarrow3x=72 \\ \Rightarrow x=\frac{72}{3}=24 \\ x=24 \end{gathered}[/tex]We have that x = 24, now to find the angles, we substitute this value on each expression:
[tex]\begin{gathered} 2x \\ x=24 \\ \Rightarrow2(24)=48 \\ x+12 \\ \Rightarrow24+12=36 \end{gathered}[/tex]therefore, the remaining angles are 48° and 36°
A line passes through the point (-6,1) and has a slope of -5/2
Write an equation in slope - intercept form for this line .
Answer: [tex]y=-\frac{5}{2}x+16[/tex]
Step-by-step explanation:
The equation in point-slope form is [tex]y-1=-\frac{5}{2}(x+6)[/tex]. To find the equation in slope-intercept form, isolate [tex]y[/tex].
[tex]y-1=-\frac{5}{2}(x-6)\\\\y-1=-\frac{5}{2}x+15\\\\y=-\frac{5}{2}x+16[/tex]
Solve the system withelimination.1-2x + y = 813x + y = -2([?],[?]
Now we substitute the value of x into the first equation to get the value of y
[tex]\begin{gathered} -2\cdot-2+y=8 \\ 4+y=8 \\ y=8-4=4 \end{gathered}[/tex]Finally the solution is (-2,4)
3x+5=8(x-2)+1
Solve the following equation for x
Answer: x=4
Step-by-step explanation:
1. 3x+5 = 8x-16+1
2. 3x+5 = 8x-15
3. 3x+20 = 8x
4. 20 = 5x
5. x = 4
Determine weather it is a function, and state it’s domain and range.
Find the inverse of:
[tex]f(x)=(3x-24)^2[/tex]The variable x can take any real value and the function f(x) exists. This means
the domain of f(x) is (-∞, +∞).
Now find the inverse function.
[tex]\begin{gathered} y=(3x-24)^2 \\ \pm\sqrt[]{y}=3x-24 \\ \pm\sqrt[]{y}+24=3x \\ x=\frac{\pm\sqrt[]{y}+24}{3} \\ x=\pm\frac{1}{3}\sqrt[]{y}+8 \end{gathered}[/tex]Swapping letters, we get the inverse function:
[tex]y=\pm\frac{1}{3}\sqrt[]{x}+8[/tex]For each value of x, we get two values of y, thus this is not a function.
The domain of the inverse is restricted to values of x that make the square root exist, thus the domain is x ≥ 0, or [0, +∞)
The range of the inverse is the domain of the original function, that is, (-∞, +∞)
Function: No
Domain: [0, +∞)
Range: (-∞, +∞)
The choice to select is shown below.
Question 13 (3 points)
Intel's microprocessors have a 1.8% chance of malfunctioning. Determine the
probability that a random selected microprocessor from Intel will not malfunction.
Write the answer as a decimal.
EXPLANATION
The probability that Event A happening is the following:
[tex]P(A)[/tex]
The probability of Event A not happening is the following:
[tex]100-P(A)[/tex]Therefore, we have:
[tex]P(Malfunctioning)+P(Non\text{ Malfunctioning\rparen=100\%}[/tex]Plugging in the terms into the expression:
1.8 + P(Not malfunctioning) = 100%
Subtracting -1.8 to both sides:
[tex]P(Not\text{ malfunctioning\rparen=100-1.8}[/tex]Subtracting numbers:
[tex]P(Not\text{ malfunctioning\rparen=98.2}[/tex]In conclusion, the probability of not malfunctioning is 0.982
For each of the following scenarios state the domain (starting set) show and state the mapping, and decide if it is a function. Be sure to label your set and indicate the direction of the relation.
Domain: Number of pages
Range:Number of books
Mapping: Number of pages to the number of books.
Explaination: The number of pages is the independent variable and the number of books is the dependent variable.
The given mapping is a function as total number of pages can not have more than two output (number of books).
The coordinates of triangle LMN are shown.YL(-1,4)XN (4, -1)M(-1, -3)What is the length of LM? Enter the answer in the box.unit(s)
Given data:
The given coordinate of L is (-1,4).
The given coordinate of M is(-1, -3).
The expression for LM length is,
[tex]\begin{gathered} LM=\sqrt[]{(-1-(-1))^2+(-3-4)^2} \\ =\sqrt[]{0+49} \\ =7 \end{gathered}[/tex]Thus, the LM length is 7 units.
Each year, a scientist measures the water level of a local lake. Negative numbers indicatethat the water level is below its historical average. Which list shows the water levels in orderfrom highest to lowest?0.7, 0.38, 0.09, – 0.41, – 0.60.7, 0.38, 0.09,-0.6,- 0.41-0.6, 0.38, – 0.41, 0.09, 0.70.38, 0.09, 0.7,– 0.6 – 0.410.38, 0.7, 0.09 – 0.41, -0.6
Answer:
-0.6, -0.41, 0.09, 0.39, 0.7
Step-by-step explanation:
Negative numbers: The higher the absolute number, the lower it is. For example, -2 is lower than -1.
Positive numbers: The lower the absolute number, the lower it is. For example, 1 is lower than 2.
In this question:
We have these following values:
0.7, 0.39, 0.09, -0.41, -0.6
Ranking from lowest to highest, it is:
-0.6, -0.41, 0.09, 0.39, 0.7
The line 3x + 4y - 7 = 0 is parallel to the line k . x + 12y + 3 = 0. What is the value of k?
The function is solved below
What is a function?
The function is instantly given a name, such as a, in functional notation, and its description is supplied by what it does to the input x, using a formula in terms of x. Instead of sine, put sine x. (x). Leonhard Euler invented functional notation in 1734. Some commonly used functions are represented with a symbol made up of many letters (usually two or three, generally an abbreviation of their name). In this scenario, a roman font is typically used, such as "sine" for the sine function, rather than an italic font for single-letter symbols. A function is also known as a map or a mapping, however some writers distinguish between "map" and "function."
The function can be written as
3x+4y-7 = 0
or, y = (-3/4)x + 7/4
so, slope = -3/4
and other function is
kx+12y+3 = 0
or, y = (-k/12)x - 1/4
so, slope = -x/12
Given the lines are parallel, so slopes are equal
i.e., -3/4 = -k/12
or, k = (3/4)12 = 9
Hence, the value of k is 9.
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B.
The scale of figure A to figure B is 1 to 2. If the area of figure A is 7 ft2, what is the area of figure B?
OA. 3.5 ft²
OB. 35 ft²
OC. 14 ft²
OD. 28 ft²
A data set is summarized in the frequency table below. Using the table, determine the number of values less than or equal to 6.ValueFrequency152332435463788397108113Give your answer as a single number. For example if you found the number of values was 14, you would enter 14.
The number of values less than or equal to 6 is 5 + 3 +2 +3 +4 +3 = 20
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?
ANSWER :
EXPLANATION :
Which factoring do we use and why and how to know the difference between factoring simple trinomial and perfect square
By definition, a perfect square trinomial is a trinomial that can be written as the square of a binomial. It is in the form:
[tex]a^2+2ab+b^2=(a+b)(a+b)[/tex]The simple trinomial is in the form:
[tex]ax^2+bx+c[/tex]Not all the simple trinomials can be written as the square of a binomial, then we need to check if the trinomial follows the structure of the perfect square trinomial. If it doesn't, then the factors won't be the same, and this is the main difference.
a. The given trinomial is:
[tex]x^2+5x+6[/tex]If it is a perfect square trinomial then:
[tex]\begin{gathered} a^2=x^2 \\ a=x \\ b^2=6 \\ b=\sqrt[]{6} \\ 2ab=5x \\ 2\cdot x\cdot\sqrt[]{6}\ne5x \\ \text{Then it is not a perfect square trinomial} \\ x^2+5x+6=(x+3)(x+2)\text{ It is a simple trinomial} \end{gathered}[/tex]b. The given trinomial is:
[tex]x^2+6x+9[/tex]Let's check if it is a perfect square trinomial:
[tex]\begin{gathered} a^2=x^2\to a=x \\ b^2=9\to b=\sqrt[]{9}=3 \\ 2ab=2\cdot x\cdot3=6x \\ \text{This is a perfect square trinomial, then } \\ x^2+6x+9=(x+3)(x+3)=(x+3)^2 \end{gathered}[/tex]What are the coordinates of the four vertices and the two foci?
This relation map is the musician to the instrument they play. is this relation a function?
