Given data:
The given table.
The standard expression for the exponential function is,
[tex]y=a(b)^x[/tex]Substitute o for x and 5 for y in the above expression.
[tex]\begin{gathered} 5=a(b)^0 \\ 5=a \end{gathered}[/tex]Substitute 1 for x, 15 for y, and 5 for a in the standard exponential expression.
[tex]\begin{gathered} 15=5(b)^1 \\ b=3 \end{gathered}[/tex]The exponential expression can be written as,
[tex]y=5(3)^x[/tex]Thus, the expression for the exponential function is y=5(3)^x.
use the diagram at the right name the following three points ray
From the geometric diagram below
(1) Three diagram
[tex]\text{ Points JQE is a 3 points}[/tex](2) A ray
[tex]RP\text{ is a ray}[/tex](3) Two intersecting lines but not perpendicular
[tex]\text{ line RF and line NI are the two intersecting lines but not perpendicular}[/tex]the perimeter of a square box is 12x + 32 drag number to complete an equivalent expression that shows the premier has four times the side length of the box
The perimeter of the box is given as
12x + 32
To write an equivalent expression that shows the premier has four times the side length of the box , we would factorise the expression. It becomes
4(12x/4 + 32/4)
= 4(3x + 8
2 points Bob flips a coin. He also spins the pointer on the spinner shown below. What is the probability that Bob flips the coin so that it lands tails up and spins the pointer so it stops on the letter R? * N E Your answer
Answer: 1/16 = 0.0625
Step by step solution:
The probability (P) of an event happening is
[tex]P=\frac{Numbe\text{r of ways it can happen}}{Total\text{ number of outcomes}}[/tex]When Bob flips the coin he has two options, head or tail. The probability that it lands tails up is:
[tex]P=\frac{1}{2}[/tex]The probability that the pointer stops on the letter R is:
[tex]P=\frac{1}{8}[/tex]Now, the probability of both events happening (tails up and pointer on R) is:
[tex]P=\frac{1}{2}\times\frac{1}{8}=\frac{1}{16}=0.0625[/tex]During a lab Jill made a solution that was 3% water. Rewrite this percent as a fraction in simplest form.
Answer each part. If necessary, round your answers to the nearest hundredth.(a) Abdul runs 3 miles in 17 minutes.How many miles does he run per minute?I miles per minute(b) It takes 37 pounds of seed to completely plant a 4-acre field.How many pounds of seed are needed per acre?pounds per acre
To determine the speed of Abdul, we can divide 3 miles by 17 minutes.
[tex]\frac{3mi}{17\min}=\frac{0.17647mi}{\min}\approx\frac{0.18mi}{\min }[/tex]Therefore, Abdul runs approximately 0.18 miles per minute.
change this standard form equation into slope intercept form 6x - 2y=-8
we have the equation
6x-2y=-8
Convert to slope-intercept form
y=mx+b
so
Isolate the variable y
step 1
Adds 2y both sides
6x-2y+2y=-8+2y
6x=-8+2y
step 2
Adds 8 both sides
6x+8=-8+2y+8
6x+8=2y
step 3
Divide by 2 both sides
3x+4=y
rewrite
y=3x+4Hello, I need some assistance with this homework question please for precalculusHW Q17
Solution:
Given the image;
Thus, there is a local maximum at;
[tex]x=-2[/tex]CORRECT OPTION: Yes
The local maximum is;
[tex]y=4[/tex]its asking for the approximate depth of the river. but I don't know how to determine that
From figure, trngles VWX and VYZ are similar.
So, the ratio of corresponding sides of triangles will be equal. Hence,
[tex]\begin{gathered} \frac{VW}{VY}=\frac{WX}{YZ} \\ \frac{3}{62}=\frac{5}{d} \\ d=\frac{5\times62}{3} \\ =103.3\text{ m} \end{gathered}[/tex]Therefore, the approximate depth of the river is d=103.3 m.
Harold and Harry both rented cars from Hurry Up Motors. Harold rented his car for 6 days andwas charged $194. Harry rented his car for 3 days and was charged $122. Choose theequation that represents y, the rental cost, in terms of x, the days of the rental.
Step 1:
Write the coordinates in terms of cost and number of days.
( cost , days )
Step 2
( 3 , 122 ) and ( 6, 194)
Step 3:
Find the slope
[tex]\begin{gathered} \text{Slope m = }\frac{y_2-y_1}{x_2-x_1} \\ x_1\text{ = 3} \\ y_1\text{ = 122} \\ x_2\text{ = 6} \\ y_2\text{ = 194} \\ m\text{ = }\frac{194\text{ - 122}}{6\text{ - 3}} \\ m\text{ = }\frac{72}{3} \\ m\text{ = 24} \end{gathered}[/tex]Step 4
Find the equation using the slope m and point 1
[tex]\begin{gathered} m\text{ = }\frac{y-y_1}{x-x_1} \\ 24\text{ = }\frac{y\text{ - 122}}{x\text{ - 3}} \\ \text{y - 122 = 24(x - 3)} \\ \text{y - 122 = 24x - 72} \\ y\text{ = 24x - 72 + 122} \\ y\text{ = 24x + 50} \end{gathered}[/tex]Final answer
The equation is y = 24x + 50
Find the equation of this line.(2,2) and (0,-4)
To find the equation;
x₁ = 2 y₁ = 2 x₂ = 0 y₂=-4
we will use the formula;
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x_{}-x_1)[/tex]substituting the values into the above;
[tex]y-2=\frac{-4-2}{0-2}(x-2)[/tex]Then, we will go ahead and evaluate;
[tex]y-2\text{ = }\frac{-6}{-2}(x-2)[/tex][tex]y-2\text{ =3(x-2)}[/tex]y - 2 = 3x - 6
add 2 to both-side of the equation
y = 3x -6+ 2
y = 3x -4
Consider parallelogram VWXY below using information given in the figure to find x, m angle zvw and m angle zwv
ANSWERS
• x = 5
,• m∠ZVW = 46°
,• m∠ZWV = 41°
EXPLANATION
The diagonals of a parallelogram bisect each other, so
[tex]11=5x+1[/tex]To find x subtract 1 from both sides of the equation,
[tex]\begin{gathered} 11-1=5x+1-1 \\ 10=5x \end{gathered}[/tex]And divide both sides by 5,
[tex]\begin{gathered} \frac{10}{5}=\frac{5x}{5} \\ 2=x \end{gathered}[/tex]Hence x = 5
By the SAS property, triangle VZW and XZY are congruent:
Therefore, corresponding angles are also congruent. Angle ZXY is the one formed by the blue half-diagonal and the third side of the triangle, therefore its corresponding angle for the other triangle is the one formed also by the blue half-diagonal and the third side of the triangle, which is angle ZVW,
[tex]\angle ZVW\cong\angle\text{ZXY}[/tex][tex]m\angle ZVW=46[/tex]It is a similar situation for angle ZWV. This angle is formed by the light blue half-diagonal and the third side of triangle VZW, so its corresponding angle in triangle XZY is the one also formed by the light blue half-diagonal and the third side of the triangle, which is angle ZYX,
[tex]\angle\text{ZWV}\cong\angle\text{ZYX}[/tex][tex]m\angle ZWV=41[/tex]The ages (in years) of the 6 employees at a particular computer store are the following.31, 41, 35, 22, 38, 31Assuming that these ages constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places.(If necessary, consult a list of formulas.)
The standard deviation of the population = 6.08
Explanations:The given ages of the employers are:
31, 41, 35, 22, 38, 31
Find the mean of the dataset:
[tex]\begin{gathered} \mu\text{ = }\frac{\sum ^{}_{}x_i}{N} \\ \mu\text{ = }\frac{31+41+35+22+38+31}{6} \\ \mu\text{ = }\frac{198}{6} \\ \mu\text{ = }33 \end{gathered}[/tex]Find the summation of the square of each deviation from the mean
[tex]\begin{gathered} \sum ^6_{i\mathop=0}(x_i-\mu)^2=(31-33)^2+(41-33)^2+(35-33)^2+(22-33)^2+(38-33)^2+(31-33)^2 \\ \sum ^6_{i\mathop{=}0}(x_i-\mu)^2=(-2)^2+(8)^2+(2)^2+(-11)^2+(5)^2+(-2)^2 \\ \sum ^6_{i\mathop{=}0}(x_i-\mu)^2=4+64+4+121+25+4 \\ \sum ^6_{i\mathop{=}0}(x_i-\mu)^2=222 \end{gathered}[/tex]The standard deviation is given by the formula:
[tex]\begin{gathered} \sigma\text{ = }\sqrt[]{\frac{\sum ^{}_{}(x_i-\mu)^2}{N}} \\ \sigma\text{ = }\sqrt[]{\frac{222}{6}} \\ \sigma\text{ = }\sqrt[]{37} \\ \sigma\text{ = }6.08 \end{gathered}[/tex]The standard deviation of the population = 6.08 (rounded to 2 decimal places)
What should you multiply the first equation (top equation) by in order to eliminate the variable y when the two equations are added together? {x+2y=5{3x-4y=8
2
Explanationgiven
[tex]\begin{gathered} x+2y\rightarrow equation(1) \\ 3x-4y=8\rightarrow equation(2) \end{gathered}[/tex]Step 1
a) to eliminate the y variable we have
[tex]\begin{gathered} 2y \\ -4y \end{gathered}[/tex]in order to be eliminated both terms must have the same value and different sign,in other words the addition must equla zero, so weed a number (a) that makes the term from teh first equation equals (4y)
so
[tex]\begin{gathered} (2y*a)-4y=0 \\ 2ay=4y \\ so \\ 2a=4 \\ divide\text{ both sides by 2} \\ \frac{2a}{2}=\frac{4}{2} \\ a=2 \end{gathered}[/tex]therefore, the first equation should be multiplied by 2
I hope this helps you
3. What is the domain of the relation described by the set of ordered pairs {(-2, 8), (-1, 1), (0, 0), (3, 5), (4, -2)}?{-2, -1, 0, 4,5){-2, 0, 1, 5, 8}{-2, -1,0,3,4}{-2, -1, 0, 1,5}
The domain is related to x axis coordinates. So, you have to take the x coordinate of each point
-2,-1,0,3,4
The local weather report states that there is 3/5 a chance of rain today, but it is more likely to rain tommorrow than today. What is a possible probability of rain for tommorrow? A.0.4 B. 0.5 I C. 0.6 D. 0.7
D. 0.7
Explanations:Probability is the chance (likelihood) that an event will take place
The probabilty that it will rain today = 3/5 = 0.6
There is more likelihood that it will rain tomorrow that today.
This means that the probabilty that it will rain tomorro is greater than the probability that it will rain today.
Therefore, the probability of rain tomorrow is more than 0.6
Only option D (0.7) is greater than 0.6, and it is the only correct choice
1. How is the orientation of the triangie affected by the translation?
Solution: The orientation is inverted
Explanation:
Given a triangle ABC if we reflect if along a straight line L we get the triangle A'C'B' and now we are going to draw it
Solve the following equation.
(√x -7) (√x -2)= -18
Answer:NO SOLUTION
Step-by-step explanation:
solve for tangent x= -1 in radians without a calculator
Answer:
[tex]x\text{ = }\frac{3}{4}\pi\text{ or }\frac{7}{4}\pi[/tex]Explanation:
Here, we want to calculate the value of x without using a calculator
We have to look for the quadrants where the tan is negative
These are the second and the fourth quadrant
On the second quadrant, we have the reference angles as:
[tex]180-x[/tex]Mathematically in degrees:
[tex]\begin{gathered} \text{if tan x = 1} \\ x\text{ = 45 deg} \end{gathered}[/tex]Now, on the second quadrant, we have it that:
[tex]180-45\text{ = 135 deg}[/tex]On the fourth quadrant, we have the reference angle calculated as:
[tex]\begin{gathered} 360-\theta \\ \theta\text{ = 360-45} \\ \theta\text{ = 315 deg} \end{gathered}[/tex]Lastly, we have to convert these angles to radians
Mathematically, 1 pi is 180 degrees:
[tex]\begin{gathered} 1\text{ }\pi=\text{ 180 deg} \\ x\text{ = 135 deg} \\ x\text{ = }\frac{135\pi}{180}\text{ = }\frac{3}{4}\pi \\ \\ \text{Lastly:} \\ 1\pi\text{ = 180 deg} \\ x\text{ = 315 deg } \\ \\ x\text{ = }\frac{315}{180}\pi\text{ = }\frac{7}{4}\pi \end{gathered}[/tex]translate and simplify subtract 18 from -11 .enter only the simplified results
Problem
translate and simplify subtract 18 from -11 .enter only the simplified results
Solution
For this case we can do the following:
-11- 18= -29
Final answer: -29
Solve the quadratic equations in questions 1 – 5 by factoring.1. x2 – 49 = 02. 3x3 – 12x = 03. 12x2 + 14x + 12 = 184. –x3 + 22x2 – 121x = 05. x2 – 4x = 5
Given:
There are given the equation:
[tex]-x^3+22x^2-121x=0[/tex]Explanation:
According to the question:
We need to find the value of x by using the factoring:
S0,
From the equation:
[tex]-x^{3}+22x^{2}-121x=0[/tex]Tthen,
[tex]\begin{gathered} -x^{3}+22x^{2}-121x=0 \\ -x(x^2-22x+121)=0 \end{gathered}[/tex]Then,
[tex]\begin{gathered} -x(x^2-22x+121)=0 \\ x(x-11)^2=0 \\ x=0; \\ x-11=0 \\ x=11 \end{gathered}[/tex]Final answer:
Hence, the value of x by using factor method is shown below:
[tex]x=0,11[/tex]Enter your answer, rounded to the nearest tenth, in the box.
ANSWER:
-11.4
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f\mleft(x\mright)=\frac{100}{-10+e^{-0.1x}}[/tex]We calculate the result when x = -2, just like this:
[tex]\begin{gathered} f(-2)=\frac{100}{-10+e^{-0.1\cdot-2}} \\ f(-2)=\frac{100}{-10+e^{0.2}} \\ f(-2)=\frac{100}{-10+1.22} \\ f(-2)=\frac{100}{-8.78} \\ f(-2)=-11.4 \end{gathered}[/tex]When x = -2, the value of the function is equal to -11.4
DONT IGNORE! PLEASE HELP ME! 50 POINTS!
Answer: The answer is C (or the third option)
Step-by-step explanation: The formula for finding the measure of interior hexagon angles is ( n − 2) × 180 °. This means that C is the correct answer
Use the spinner shown in the figure below to find the probability indicated.Landing on green or a consonant
Based on the spinner, there are a total of 8 possible outcomes.
2 of which are green and 4 are consonants, however, 1 outcome is both consonant and a green (F green).
Therefore, the probability of landing on a green or consonant is:
[tex]\begin{gathered} P(A\text{ or B)}=P(A)+P(B)-P(A\text{ and B)} \\ P(A\text{ or B)}=\frac{2}{8}+\frac{4}{8}-\frac{1}{8} \\ P(A\text{ or B)}=\frac{5}{8} \end{gathered}[/tex]The probability of landing on a green or consonant is 5/8 or 62.5%.
it says use the table to rewrite the expression you wrote for problem 2. rewrite that expression so that both terms are written with the same exponent number 4. says use the distributive property simplify the expression you wrote for problem 3.number 5. says write your expression as the product of a decimal times a power of 10.number 6 says write your solution in scientific notation and number 7. says Evaluate (7.4 x 10^15 -- (9.9 x 10^13number 8 says Evaluate (8.9 x 10^5) + (6.5) x 10^6
7)
Given data:
The given expresson is a=7.7x10^15-(9.9x10^13)
The given expression can be written as,
a=770x10^13-9.9x10^13
=(770-9.9)x10^13
=760.1x10^13.
8)
Given data:
The given expresson is b=8.9x10^5-(6.5)x10^6
The given expression can be written as,
b=8.9x10^5-65x10^5
=(8.9-65)x10^5
=-56.1x10^5
ABC High School is debating whether or not to write a policywhere all students musthave uniforms and wear them during school hours. In a survey,45% of the studentswanted uniforms, and 55% did not.Calculate the probability that a person selected at random fromABC High School will want the school to have uniforms or willnot want the school to have uniforms.
If 45% don't want uniforms, it means that 45 out of 100 students don't want them, so the probability is 45/100 = 9/20
And 55% want unifrms, so the probability = 55/100 = 11/20
Hello, I need help completing and showing appropriate steps for this problem. Thank you so much!
The first step is to factorise the quadratic expression on the right side of the equation. The expression is
x^2 + 9x + 20
We would find two terms such that their sum or difference is 9x and their product is 20x^2. The terms are 5x and 4x. Replacing 9x with 5x and 4x, it becomes
x^2 + 5x + 4x + 20
By factorising, it becomes
x(x + 5) + 4(x + 5)
Since x + 5 is common, it becomes
(x + 4)(x + 5)
Thus, the original expression becomes
x/(x + 4) + 3/(x + 5) = (x + 2)/(x + 4)(x + 5)
The lowest common multiple of the denominators on both sides of the equations is (x + 4)(x + 5). We would multiply each term in the equation by
(x + 4)(x + 5). It becomes
(x + 4)(x + 5)x/(x + 4) + 3(x + 4)(x + 5)/(x + 5) = (x + 2)(x + 4)(x + 5)/(x + 4)(x + 5)
By cancelling out common terms in the numerator and denominator, we have
x(x + 5) + 3(x + 4) = x + 2
We would expand the parentheses on both sides by multiplying the terms inside with the term outside. It becomes
x^2 + 5x + 3x + 12 = x + 2
By collecting like terms, we have
x^2 + 5x + 3x - x + 12 - 2 = 0
x^2 + 7x + 12 = 0
Again, We would find two terms such that their sum or difference is 7x and their product is 12x^2. The terms are 4x and 3x. Replacing 7x with 4x and 3x, it becomes
x^2 + 4x + 3x + 12 = 0
By factorising, it becomes
x(x + 4) + 3(x + 4) = 0
Since x + 4 is common, it becomes
(x + 3)(x + 4) = 0
x + 3 = 0 or x + 4 = 0
x = - 3 or x = - 4
The solutions are x = - 3 or x = - 4
At a sale this week,a suit is being sold for $364. This is a 35% discount from the original price. What is the original price?
Okay, here we have this:
Considering the provided information, we are going to calculate the requested original price, so we obtain the following:
So we have the following formula:
Discount Price=Original Price*(100%-Discount)
Clearing for "Original price":
Discount Price=Original Price*(100%-Discount)
Original Price=Discount Price/(100%-Discount)
Replacing with the given data:
Original Price=Discount Price/(100%-Discount)
Original Price=$364/(100%-35%)
Original Price=$364/(65%)
Original Price=$364/(0.65)
Original Price=$560
Finally we obtain that the original price is $560.
)Mr. Nacarrato and his family are going on a road trip that is
2457 miles long. They have already driven 128 53/100 miles
How much further do they have to drive?
They need to go further 2328.47 miles distance.
What is improper fraction and mixed fraction?
A mixed fraction is one that has both a correct fraction and a whole number portion, and whose value is consistently greater than 1. When the numerator is always higher than or equal to the denominator, the fraction is said to be inappropriate. 4/3, 7/3, 11/5, and other incorrect fractions are a few instances.
Here the road trip is 2457 miles long .
They already drive 128 [tex]\frac{53}{100}[/tex] miles.
That is in mixed fraction , we need to convert them in improper fraction , then,
=> 128 [tex]\frac{53}{100}[/tex] = [tex]\frac{128*100+53}{100}= \frac{12853}{100}[/tex]
Now we need to subtract them from total distance then ,
=> 2457 - [tex]\frac{12853}{100}[/tex]
=> [tex]\frac{2457*100-12853}{100}[/tex]
=> [tex]\frac{245700-12853}{100}[/tex]
=> 2328.47 miles.
They need to go further 2328.47 miles.
To learn more about improper fraction and mixed fraction
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Select all sets of triangles that can be provencongruent using Side-Angle-Side(SAS).
SOLUTION
We want to select all triangles from the image that can be proven by the side angle side theorem which states that
If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
Now looking at the triangles
We can see that triangles in number 1, 2, 3 follows this theorem.
4 does not because the equal angles are not present
5, the triangles are congruent, but do not follow the SAS theorem
6 follows as we can see the equal sides and angle
7 shows two equal angles only, but we need one equal angles and two equal sides.
Hence the answer is 1, 2, 3 and 6 only
A man is approaching a pole 75 feet high and walking at the rate of
3 miles/hour. At what rate is he approaching the top of the pole
when he is 100 feet away from the pole?
Answer:
375!
Step-by-step explanation:
3 x 100 = 300
Now he is at the pole. Now he has to get to the top of it
which your basically doing
3 x 100 = 300 + 75 = 375
( 375 - 75 = 300 300 ÷ 100 = 3 )