Then, it has just 1 solution, and it should be placed in the second column.
[tex]\begin{gathered} 2^x-1=4^x+3. \\ \text{This has no solution} \end{gathered}[/tex][tex]\begin{gathered} 3x-2=3^x+1 \\ \text{This has no solution.} \end{gathered}[/tex]Next;
[tex]\begin{gathered} \frac{1}{2}x+3=3^x-1 \\ \text{This has no solution. It should be in the first column} \end{gathered}[/tex][tex]\begin{gathered} 2x+1=2^x \\ \text{Let x=0,} \\ 2(0)+1=2^0=1 \end{gathered}[/tex]This has one solution, and it should be placed in the second column.
How many roots does x^2-6x+9 have ? It may help to graph the equation.
The roots are those values that make a function or polynomial take a zero value. The roots are also the intersection points with the x-axis. In the case of a quadratic equation you can use the quadratic formula to find its roots:
[tex]\begin{gathered} ax^2+bx+c=y\Rightarrow\text{ Quadratic equation in standard form} \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\Rightarrow\text{ Quadratic formula} \end{gathered}[/tex]So, in this case, you have
[tex]\begin{gathered} y=x^2-6x+9 \\ a=1 \\ b=-6 \\ c=9 \end{gathered}[/tex][tex]\begin{gathered} x=\frac{-(-6)\pm\sqrt[]{(-6)^2-4(1)(9)}}{2(1)} \\ x=\frac{6\pm\sqrt[]{36-36}}{2} \\ x=\frac{6\pm0}{2} \\ x=\frac{6}{2} \\ x=3 \end{gathered}[/tex]As you can see, this function only has one root, at x = 3.
You can see this in the graph of the function:
5 6 7 8. One times a number equals 4 1
hello
to solve this problem, we need to find the property of equality
let the unknown number be represented by x
[tex]4=1\times x[/tex]to solve for x, divide both sides of the equation by 1
[tex]\begin{gathered} 4=1x \\ \frac{4}{1}=\frac{1x}{1} \\ x=4 \end{gathered}[/tex]the number here is 4
the property used to get the answer is division property of equality
6. Point A is located at (7, -3) and point M is located at (-9,5). If M is themidpoint of segment AP, what are the coordinates of point P?"A) (-25, 13)B) (-1,1)C) (8,-4)OD) (25, -13)7 Name the ray that is opposite to ray CD."
Answer:
The coordinates of P is;
[tex](-25,13)[/tex]Explanation:
Given that;
Point A is located at (7, -3) and point M is located at (-9,5).
And;
M is the midpoint of segment AP.
The coordinate of P will be represented by;
[tex]P=(x_2,y_2)[/tex]Using the formula for calculating midpoint;
[tex]\begin{gathered} x=\frac{x_1+x_2}{2} \\ y=\frac{y_1+y_2}{2} \end{gathered}[/tex]Making x2 and y2 the subject of formula;
[tex]\begin{gathered} x_2=2x-x_1 \\ y_2=2y-y_1 \end{gathered}[/tex]So, substituting the given coordinates;
[tex]\begin{gathered} M=(x,y)=(-9,5) \\ A=(x_1,y_1)=(7,-3) \end{gathered}[/tex]So, we have;
[tex]\begin{gathered} x_2=2x-x_1 \\ x_2=2(-9)-7 \\ x_2=-25 \end{gathered}[/tex]And;
[tex]\begin{gathered} y_2=2y-y_1 \\ y_2=2(5)-(-3)=10+3 \\ y_2=13 \end{gathered}[/tex]Therefore, the coordinates of P is;
[tex](-25,13)[/tex]1. Find all real solutions to each equation. (a) x(2x − 5) = 1
Use the distributive property to expand the parenthesis:
[tex]x(2x-5)=2x^2-5x[/tex]Then:
[tex]undefined[/tex]PLEASE DO IT ASAP
What is the value of the expression?
0.3(1/4 - 1) + 0.35
-0.575
-0.125
0.125
1.4
1.925
The value of the expression 0.3(1/4 - 1) + 0.35 is 0.125
The expression is
0.3(1/4 - 1) + 0.35
The expression is defined as the sentence with a minimum of two variables and at least one math operation.
Here the expression is
0.3 (1/4 - 1) + 0.35
First do the arithmetic operation in the bracket
0.3(1/4 - 1) + 0.35 = 0.3 × -0.75 + 0.35
In next step do the multiplication
0.3 × -0.75 + 0.35 = -0.225 + 0.35
Do the addition of the numbers
-0.225 + 0.35 = 0.125
Hence, the value of the expression 0.3(1/4 - 1) + 0.35 is 0.125
Learn more about arithmetic operation here
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I'm not sure if you can exactly give me the answers, but I need help solving these types of questions, I will attach them below. they are about tangent lines.
Question 1
Explanation
To solve these types of questions, we will use the Tangent radius theorem
Tangent to a Circle Theorem
The tangent theorem states that a line is a tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency.
The figure below helps give a pictorial view
The principle to be used here for question 1 will be
[tex]x^2+8^2=17^2[/tex]Simplifying further
[tex]\begin{gathered} x^2+64=289 \\ x^2=289-64 \\ x^2=225 \\ x=\sqrt{225} \\ x=15 \end{gathered}[/tex]Thus, the value of x is 15 units
a teacher bought 4 folders and 9 books for $33.75. on another day, she bought 3 folders and 12 books at the same prices for $34.50. how much did she pay for each folder and each book?
The teacher made two different purchases:
First purchase:
4 folders and 9 books for $33.75
Second purchase
3 folders and 12 books for $34.50
Let "f" represent the cost of each folder and "b" represent the cost of each book. You can express the total cost of each purchase as equations:
[tex]\begin{gathered} 1)4f+9b=33.75 \\ 2)3f+12b=34.50 \end{gathered}[/tex]Now we have established a system of equations, to solve it, the first step is to write one of the equations in terms of one of the variables.
For example, I will write the first equation in terms if "f"
[tex]\begin{gathered} 4f+9b=33.75 \\ 4f=33.75-9b \\ \frac{4f}{4}=\frac{33.75-9b}{4} \\ f=\frac{135}{16}-\frac{9}{4}b \end{gathered}[/tex]The second step is to replace the expression obtained for "f" in the second equation:
[tex]\begin{gathered} 3f+12b=34.50 \\ 3(\frac{135}{16}-\frac{9}{4}b)+12b=34.50 \end{gathered}[/tex]Distribute the multiplication on the parentheses term
[tex]\begin{gathered} 3\cdot\frac{135}{16}-3\cdot\frac{9}{4}b+12b=34.50 \\ \frac{405}{16}-\frac{27}{4}b+12b=34.50 \\ \frac{405}{16}+\frac{21}{4}b=34.50 \end{gathered}[/tex]Pass the number to the right side of the equal sign by applying the opposite operation to both sides of it
[tex]\begin{gathered} \frac{405}{16}-\frac{405}{16}+\frac{21}{4}b=34.50-\frac{405}{16} \\ \frac{21}{4}b=\frac{147}{16} \end{gathered}[/tex]Now divide b by 21/4 to cancel the multiplication and to keep the equality valid, you have to divide both sides of the expression, so divide 147/16 by 21/4 too, or multiply them by its reciprocal fraction, 4/21, is the same.
[tex]\begin{gathered} (\frac{21}{4}\cdot\frac{4}{21})b=(\frac{4}{21}\cdot\frac{147}{16}) \\ b=\frac{7}{4}\approx1.75 \end{gathered}[/tex]Each book costs $1.75
Now that we have determined how much does each book cost, we can determine the cost of each folder by replacing the value of "b" in the expression obtained for "f"
[tex]\begin{gathered} f=\frac{135}{16}-\frac{9}{4}b \\ f=\frac{135}{16}-\frac{9}{4}\cdot\frac{7}{4} \\ f=\frac{9}{2}\approx4.5 \end{gathered}[/tex]Each folder costs $4.50
Which function, A or B, has a greater rate of change? Be sure to include the values for the rates of change in your answer. Explain your answer.
The function B has a greater rate of change
Explanation:Function A is represented by the table:
Selecting the points (1, 5) and (2, 7)
The rate of change of function A:
[tex]\begin{gathered} m_A=\frac{7-5}{2-1} \\ \\ m_A=2 \end{gathered}[/tex]The rate of change of the function A = 2
Function B is represented by the graph:
(1, 1) and (2, 4)
[tex]\begin{gathered} m_B=\frac{4-1}{2-1} \\ \\ m_B=3 \end{gathered}[/tex]The rate of change of the function B = 3
The function B has a greater rate of change
How much would you need to deposit in an account now in order to have $20,000 in the account in 4 years? Assume the account earns 5% interest.I want answer and explanation.
The rule of the simple interest is
[tex]\begin{gathered} I=PRT \\ A=P+I \end{gathered}[/tex]I is the amount of interest
P is the initial amount
R is the interest rate in decimal
T is the time
We need to find the initial amount if the new amount is $20,000, the interest rate is 5% for 4 years, then
A = 20000
R = 5/100 = 0.05
T = 4
Substitute them in the rules above
[tex]\begin{gathered} I=P(0.05)(4) \\ I=0.2P \\ 20000=P+0.2P \\ 20000=1.2P \\ \frac{20000}{1.2}=\frac{1.2P}{1.2} \\ 16666.67=P \end{gathered}[/tex]You need to deposit $16,666.67
The rule of the compounded interest
[tex]A=P(1+r)^t[/tex]A is the new amount
P is the initial amount
r is the interest rate in decimal
t is the time
A = 20000
r = 0.05
t = 4
Substitute them in the rule above
[tex]\begin{gathered} 20000=P(1+0.05)^4 \\ 20000=P(1.05)^4 \\ \frac{20000}{(1.05)^4}=\frac{P(1.05)^4}{(1.05)^4} \\ 16454.05=P \end{gathered}[/tex]You need to deposit $16,454.05
find the other binomial p squared -13 p +36 =(p-9)
To find the other factor of the polynomial
[tex]p^2-13p+36[/tex]We need to find two integers which multiplication gives 36 and addition is -13.
This integers would be -9 and -4, then we have
[tex]p^2-13p+36=p^2-9p-4p+36[/tex]now we factor the right term using common factors:
[tex]\begin{gathered} p^2-9p-4p+36=p(p-9)-4(p-9) \\ =(p-9)(p-4) \end{gathered}[/tex]Hence:
[tex]p^2-9p-4p=(p-9)(p-4)[/tex]Therefore, the other binomial we are looking for is (p-4).
The students of a school were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard.Each penholder was to be radius of 3cm and height 10.5 cm. The school was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be brought for the competition. Assume: pi = 22/7
Recall the surface area for the following figures.
[tex]\begin{gathered} \text{Cylinder}=2\pi rh+2\pi r^2 \\ \\ \text{The term }2\pi r^2\text{ includes a cover both the top and bottom of the cylinder} \\ \text{Since we will be using only the bottom modify the formula such that it only} \\ \text{includes the bottom part} \\ \\ \text{Pen Holder Surface Area}=2\pi rh+\pi r^2 \end{gathered}[/tex]Given that
height = h = 10.5 cm
radius = r = 3 cm
π = 22/7
Substitute the following given and we have the surface area for the pen holder
[tex]\begin{gathered} \text{Pen Holder Surface Area}=2\pi rh+\pi r^2 \\ \text{Pen Holder Surface Area}=2(\frac{22}{7})(3\operatorname{cm})(10.5\operatorname{cm})+(\frac{22}{7})(3\operatorname{cm})^2 \\ \text{Pen Holder Surface Area}=198\operatorname{cm}+(\frac{22}{7})(9\operatorname{cm}) \\ \text{Pen Holder Surface Area}=198\operatorname{cm}+\frac{198}{7}\operatorname{cm} \\ \text{Pen Holder Surface Area}=\frac{1584}{7}\operatorname{cm}^2 \end{gathered}[/tex]Now that we have the surface area, multiply it by 35 since there are 35 competitors in the competition
[tex]undefined[/tex]Hello! By the way when answering the question just don’t mind my work shown or my answer I know for a fact I am wrong.
We have to calculate the height of the stack of hay bales.
We can start by calculating the volume as the number of bales times the volume of one hay:
[tex]\begin{gathered} V=n*V_0=8*(10+\frac{2}{3}) \\ V=8*10+8*\frac{2}{3} \\ V=80+\frac{16}{3} \\ V=80+\frac{15}{3}+\frac{1}{3} \\ V=80+5+\frac{1}{3} \\ V=85+\frac{1}{3} \end{gathered}[/tex]Now, we know that this volume will be the area of the base times the height.
The area of the base can be calculated as the product of the length and the width:
[tex]\begin{gathered} A_b=L*W \\ A_b=4*(1+\frac{1}{3}) \\ A_b=4+\frac{4}{3} \\ A_b=\frac{4*3+4}{3} \\ A_b=\frac{12+4}{3} \\ A_b=\frac{16}{3} \end{gathered}[/tex]We then can calculate the height as the volume divided by the base area:
[tex]\begin{gathered} h=\frac{V}{A} \\ h=\frac{85+\frac{1}{3}}{\frac{16}{3}} \\ h=\frac{85*3+1}{3}*\frac{3}{16} \\ h=\frac{256}{3}*\frac{3}{16} \\ h=\frac{256}{16} \\ h=16 \end{gathered}[/tex]Answer the height is 16 feet.
Ary is writing thank you cards to everyone who came to her wedding. It takes her of an hour to write one thank you card. If it took her 8 hours to finish writing all of the cards, how many thank you cards did she write? 48 thank you cards 36 thank you cards 46 thank you cards 40 thank you cards
The question doesn't specify which fraction of an hour it takes Ary to write a thank you card.
Let's imagine that it takes her 1/4 of an hour to write a thank you card.
In such case, in one hour she will be able to write 4 thank you cards.
and therefore in 8 hours, ishe will be able to write 32 thank you cards (8 times 4 cards).
If it takes her 1/6 of an hour to write a thank you card, then in hone hour she will write a total of 6 thank you cards, and therefore, in 8 hours she will be able to write 8 times 6 thank you cards: 8 x 6 = 48 thank you cards.
If it takes her 1/5 of an hour to write a thank you card, then in hone hour she will write a total of 5 thank you cards, and therefore, in 8 hours she will be able to write 8 times 5 thank you cards: 8 x 5 = 40 thank you cards.
You just use this type of criteria to solve the problem whatever the fraction of the hour it takes to write one card as they specify in the question.
Sophia is in the business of manufacturing phones. She must pay a daily fixed cost of $200 to rent the building and equipment, and also pays a cost of $100 per phone produced for materials and labor. Make a table of values and then write an equation for C,C, in terms of p,p, representing total cost, in dollars, of producing pp phones in a given day.
I need the equation
Answer:
C = 100p + 200
Step-by-step explanation:
Because C is the total cost per day, 200 is the y-intercept because it's paid daily. The 100 is the slope since "he pays a cost of $100 per phone produced
Hello I need help with this question as fast as possible please , I am on my last few questions and I have been studying all day for my final exam tomorrow. It is past my bed time and I am exhausted . Thank you so much for understanding:))
Solution:
Given the inequality below
[tex]2\left(4+2x\right)\ge \:5x+5[/tex]Solving the inequality to find the value of x
[tex]\begin{gathered} 2\left(4+2x\right)\ge \:5x+5 \\ Expand\text{ the brackets} \\ 8+4x\ge \:5x+5 \\ Collect\text{ like terms} \\ 4x-5x\ge5-8 \\ -x\ge\:-3 \\ x\le \:3 \end{gathered}[/tex]Hence, the answer is
[tex]x\le \:3[/tex]a 14-member board used for admitted
Using the Borda's method, when one person is ranked as 1st, he/she gets 3 points, if he/she is ranked 2nd, get 2 points, also, if he/she is ranked as 3rd get 1 point, and finally, 0 points if she/he is ranked as 4th
so, let's detemine how many points got each one
Cardona: Was selected 1st by 6 people, 2nd by 2 people, 3rd by 4 people and 4th by 2 people
[tex]C=3*6+2*2+1*4=26[/tex]So, that's a total of 26 points
Pitts-Jones: Was selected as: #1 by 4 people, #2 by 3 people, #3 by 6 people and 4th by 1 person
[tex]P=3*4+2*3+1*6=24[/tex]So, that's 24 points for Pitts-Jones,
De Plata: Was ranked #1 by 2 people, #2 by 8 people, #3 by 1 person and #4 by 3 people
[tex]D=3*2+2*8+1*1=23[/tex]That's 23 points for De Plata
Vincent: Was ranked as #1 by 2 people, #2 by 1 person, #3 by 3 people and #4 by 8 people
[tex]V=3*2+2*1+1*3=11[/tex]that's 11 points for Vincent,
Answer: From the above, we can conclude that the winner using Borda's method is Cardona
12. Suppose you buy 20 gallons of gasoline in a city that collects excisetax of .16 per gallon. If you pay $1.25 per gallon, what percent of theprice is city excise tax?a.b.c.13.4%13.2%12.8%
We can calculate the percent of the price that is excise tax by dividing the amount of tax per gallon by the final price of the gallon.
If the tax is 0.16 per gallon and the final price is 1.25 per gallon, the percentage can be calculated as:
[tex]p=\frac{0.16}{1.25}\cdot100\text{ \%}=0.128\cdot100\text{ \%}=12.8\text{ \%}[/tex]The percentage that is city excise tax is 12.8% of the final price of the gasoline.
The cargo of the truck weighs at most 2,800 pounds. Use w to represent the weight (in pounds) of the cargo.To get the 10% discount, a shopper must spend no less than $100. Use d to represent the spending (in dollars) of a shopper who gets the discount
We can write this inequalities as:
If the cargo W has to be 2,800 pounds at most, then:
[tex]W\le2,800[/tex]The shopper has to spend $100 or more to get a discount, so the spending d to get a discount can be written as:
[tex]d\ge100[/tex]A certain orange colour requires mixing 5 parts of red paint with 7 parts of yellow paint.Roderick mixed 15 parts of red paint with 21 parts of yellow paint. Did he create the correct orange colour?
Answer:
Roderick has created the correct orange color.
Explanation:
The orange color required mixing 5 parts of red paint with 7 parts of yellow paint. The ratio is given below:
[tex]\operatorname{Re}d\colon\text{Yellow}=5\colon7[/tex]Roderick mixed 15 parts of red paint with 21 parts of yellow paint. This is expressed in ratio as:
[tex]\begin{gathered} \operatorname{Re}d\colon\text{Yellow}=15\colon21 \\ \text{Divide both sides by 3} \\ \frac{15}{3}\colon\frac{21}{3}=5\colon7 \end{gathered}[/tex]Since the two ratios reduces to the same value, they are equivalent, thus Roderick has created the correct orange color.
Select the sequence of transformations that will carry rectangle A onto rectangle A'. A) reflect over y-axis, rotate 90° clockwise, then reflect over x-axis B) rotate 180° clockwise, reflect over y-axis, then translate 3 units left C) rotate 180° clockwise, reflect over x-axis, then translate 2 units left D) rotate 90° clockwise, reflect over y axis, then translate 3 units left
Let:
[tex]\begin{gathered} A=(3,4) \\ B=(4,2) \\ C=(1,-1) \end{gathered}[/tex]and:
[tex]\begin{gathered} A^{\prime}=(-3,1) \\ B^{\prime}=(-4,-1) \\ C^{\prime}=(-1,-4) \end{gathered}[/tex]After a reflection over the y-axis:
[tex]\begin{gathered} A\to(-x,y)\to A_1=(-3,4) \\ B\to(-x,y)\to B_1=(-4,2) \\ C\to(-x,y)\to C_1=(-1,-1) \end{gathered}[/tex]After a translation 3 units down:
[tex]\begin{gathered} A_1\to(x,y-3)\to A_2=(-3,1) \\ B_1\to(x,y-3)\to B_2=(-4,-1) \\ C_1\to(x,y-3)\to C_2=(-1,-4) \end{gathered}[/tex]Since:
[tex]\begin{gathered} A_2=A^{\prime} \\ B_2=B^{\prime} \\ C_2=C^{\prime} \end{gathered}[/tex]The answer is the option K.
Need to graph and then mark length of stay (in days) on the bottom of the graph. Need 4 points on graph and 4 number on bottom of graph
given the data
13,9,5,11,6,3,12,10,11,7,3,2,2,2,10,10,12,12,12,8,8
sort data
s= 2, 2, 2, 3, 3, 5, 6, 7, 8, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13
then we have
2 ---- 3
3 ----- 2
5----- 1
6 ---- 1
7 -----1
8------2
9 ------1
10-----3
11-------2
12------4
13-------1
A certain drug dosage calls for 330 mg per kg per day and is divided into four doses (1 every 6 hours). If a person weighs 210 pounds, how many milligrams of the drug should he receive every 6 hours?Round your answer to the nearest milligram. Do not include units with your answer.
First, we convert the 210 pounds to kilograms as the dose is given in mg per kg.
Recall that:
[tex]1pound=0.453592\text{ kilograms.}[/tex]Therefore:
[tex]210\text{ pounds=95.2544 kilograms.}[/tex]The dose call for 330 mg per kg, therefore, to get the dose for 95.2544 kg, we multiply by 95.2544:
[tex]330*95.2544\text{ mg=31433.952mg.}[/tex]Finally, dividing by 4 we get the dose the person should receive every 6 hours:
[tex]7858.488mg\approx7858mg.[/tex]Answer: [tex]7858.[/tex]Amanda and Jamie are standing 25 feet apart and spot a bird in the sky between them. The angle of elevation from Amanda to the bird is 55, and from Jamie to the bird is 63. How far away is the bird from Amanda?
We have to find how far is the bird from Amanda.
With the information given, we can draw:
We can start by finding the third angle.
The sum of the angles have to be equal to 180°, so we can find it as:
[tex]\begin{gathered} \alpha+55\degree+63\degree=180\degree \\ \alpha=180-55-63 \\ \alpha=62\degree \end{gathered}[/tex]Now, we can apply the Law of Sines to find the distance between Amanda (A) and the bird (B):
[tex]\frac{AB}{\sin J}=\frac{AJ}{\sin B}[/tex]where AJ is the distance between Amanda and Jamie and AB is the distance between the bird and Amanda.
We then can solve for AB as:
[tex]\begin{gathered} AB=AJ\cdot\frac{\sin J}{\sin B} \\ AB=25\cdot\frac{\sin63\degree}{\sin62\degree} \\ AB\approx25\cdot\frac{0.891}{0.883} \\ AB\approx25.23 \end{gathered}[/tex]Answer: 25.23 [Option A]
Let's find2. 1+5 3First write the addition with a common denominator.Then add.12— +51-4-13Х5
The given addition exercise is:
[tex]\frac{2}{5}+\frac{1}{3}[/tex]The LCM of the denominator (5 and 3) = 15
Multiply 2/5 by 3/3
[tex]\frac{2}{5}=\frac{2\times3}{5\times3}=\frac{6}{15}[/tex]Multiply 1/3 by 5/5
[tex]\frac{1}{3}=\frac{1\times5}{3\times5}=\frac{5}{15}[/tex]The addition becomes
[tex]\frac{6}{15}+\frac{5}{15}=\frac{11}{15}[/tex]Therefore, we can fill in the vacant boxes as shown below:
[tex]\frac{2}{5}+\frac{1}{3}=\frac{6}{15}+\frac{5}{15}=\frac{11}{15}[/tex]What is an equation of the points given? And is parallel to the line 4x-5y=5?
We know that two lines are parallel if they have the same slope. So we first find the slope of the given line. One way to do this is to rewrite the equation in its slope-intercept form, solving for y:
[tex]\begin{gathered} y=mx+b \\ \text{ Where} \\ m\text{ is the slope and} \\ b\text{ is the y-intercept} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} 4x-5y=5 \\ \text{ Subtract 4x from both sides of the equation} \\ 4x-5y-4x=5-4x \\ -5y=5-4x \\ \text{ Divide by -5 from both sides} \\ \frac{-5y}{-5}=\frac{5-4x}{-5} \\ y=\frac{5}{-5}-\frac{4x}{-5} \\ y=-1+\frac{4x}{5} \\ y=\frac{4x}{5}-1 \\ y=\frac{4}{5}x-1 \end{gathered}[/tex]Now, we have the slope and a point through which the line passes:
[tex]\begin{gathered} m=\frac{4}{5} \\ (x_1,y_1)=(-5,2) \end{gathered}[/tex]Then, we can use the point-slope formula:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-2=\frac{4}{5}(x-(-5)_{}) \\ y-2=\frac{4}{5}(x+5_{}) \end{gathered}[/tex]The above equation is the equation of the line in its point-slope form. However, we can also rewrite the equation of the line in its standard form by solving for the constant:
[tex]ax+by=c\Rightarrow\text{ Standard form}[/tex][tex]\begin{gathered} y-2=\frac{4}{5}(x+5_{}) \\ \text{ Multiply by 5 from both sides of the equation} \\ 5(y-2)=5\cdot\frac{4}{5}(x+5_{}) \\ 5(y-2)=4(x+5_{}) \\ \text{ Apply the distributive property} \\ 5\cdot y-5\cdot2=4\cdot x+4\cdot5 \\ 5y-10=4x+20 \\ \text{ Subtract 5y from both sides} \\ 5y-10-5y=4x+20-5y \\ -10=4x+20-5y \\ \text{Subtract 20 from both sides } \\ -10-20=4x+20-5y-20 \\ -30=4x-5y \end{gathered}[/tex]Therefore, an equation of the line that passes through the point (-5,2) and is parallel to the line 4x - 5y = 5 is
[tex]\boldsymbol{4x-5y=-30}[/tex]3, -10, 16, -36, 68, ___-3, 12, -33, 102, -303, ___Identify a pattern in each list of numbers. Then use this pattern to find the next number.
As for the sequence 3,-10,16,-36,68,..., notice that
[tex]\begin{gathered} 3-13=-10 \\ -10+26=-10+2(13)=-10+2^1(13)=16 \\ 16-52=16-4(13)=16-2^2(13)=-36 \\ -36+104=-36+8(13)=-36+2^3(13)=68 \end{gathered}[/tex]Therefore, the next term is
[tex]68-2^4(13)=68-16(13)=-140[/tex]The answer is -140.
Regarding the second pattern, notice that
[tex]\begin{gathered} -3+15=12 \\ 12-45=12-3(15)=12-3^1(15)=-33 \\ -33+135=-33+9(15)=-33+3^2(15)=102 \\ 102-405=102-27(15)=102-3^3(15)=-303 \end{gathered}[/tex]Then, the next term of the sequence is
[tex]-303+3^4(15)=912[/tex]The answer is 912
Function g can be thought of as a translated (shifted) version of f(x) = x?Y Y6+5+432f7 6 5 4 3 21 2 3 4 5 6 7-2--3+-6-7Write the equation for g(x).
Answer:
g(x) = (x + 5)²
Explanation:
g is the same function f shifted 5 units to the left.
Then, if we have a function h(x) =f(x+c), h(x) is f(x) shifted c units to the left.
So, to translate f 5 units to the left, we need to replace x by (x + 5), to get:
[tex]\begin{gathered} f(x)=x^2 \\ g(x)=f(x+5) \\ g(x)=(x+5)^2 \end{gathered}[/tex]So, the equation for g(x) is:
g(x) = (x + 5)²
2. Jim is 8 years old, and his Uncle Bill is 512 times older than he his. What is his Uncle Bill's age?
Answer:
Uncle Bill has ignored the laws of nature and the known universe and reached a stunning 4096 years old
Step-by-step explanation:
Just multiply 8 * 512
500 * 8 = 4000, 12 * 8 = 96, 4000 + 96 = 4096
Answer:44
Step-by-step explanation:
A model of a dinosaur skeleton was made using a scale of 1 in : 15 in in a museum. If the size of the dinosaur’s tail in the model is 8 in, then find the actual length of dinosaur’s tail.
The length of the real dinosaur's tail is 120 inches.
How to find the actual length of the tail?We know that the scale of the model is 1in : 15in, this means that each inch in the model represents 15 inches of the actual dinosaur.
So, if the tail of the model has a length of 8 inches, the length of the real tail will have 15 times that, so the length is given by the product:
8in*15 = 120in
Learn more about scale models.
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Find the measure of Zx in the figure.
The measure of Zx isº.
57°
X
90°
...
Please help me with this