[tex]f(x)=x^2-2x-8;\ g(x)=\dfrac{1}{4}x-1\\\\f(x)=g(x)\iff x^2-2x-8=\dfrac{1}{4}x-1\qquad\text{multiply both sides by 4}\\\\4x^2-8x-32=x-4\qquad\text{subtract x from both sides}\\\\4x^2-9x-32=-4\qquad\text{add 4 to both sides}\\\\4x^2-9x-28=0\\\\4x^2-16x+7x-28=0\\\\4x(x-4)+7(x-4)=0\\\\(x-4)(4x+7)=0\iff x-4=0\ \vee\ 4x+7=0\\\\x=4\ \vee\ 4x=-7\\\\\boxed{x=4\ \vee\ x=-\dfrac{7}{4}}[/tex]
2−1/2n=3n+16
n=3n+16
Answer:
The answer is
n=5 3/5
Step-by-step explanation:
first collect the like terms:
2-1/2n=3n+16
then...
3n-1/2=16-2
==2 1/2n = 14
===n=5 3/5
On the Mertler's vacation to Florida, they drove 180 miles in 3 hours before stopping for lunch. After lunch they drove 120 miles in 2 hours before stopping for gas. Are these rates equivalent? Explain your reasoning.
Which of the following is a complex number?
-7
2 + √3
4 + 9i
pie (no symbol available)
Answer:
The correct answer is option C , 4 + 9i
Step-by-step explanation:
A complex number is the one which has a real number and an imaginary number.
In all the example given , option C 4 + 9i has "i" which signifies the imaginary number which nothing but a negative square root.
Can someone plz help me ♀️
Answer: (D) 4
Step-by-step explanation:
Average rate of change means slope (m) from point a to point b.
when x = 5, y = -2 → coordinate (5, -2)
when x = 7, y = 6 → coordinate (7, 6)
slope (m) = [tex]\dfrac{6-(-2)}{7-5} = \dfrac{8}{2}=4[/tex]
Can someone help me with these real quick?
1) write 13%20 as a decimal
2) write 7•7•7•7•7 in exponential form
3) *picture is attached
[tex]1)\\p\%=\dfrac{p}{100}\\\\13\%=\dfrac{13}{100}=0.13\\\\13\%\ of\ 20\ is\ 0.13\cdot20=2.6\\\\2)\\\underbrace{7\cdot7\cdot7\cdot7\cdot7}_{5}=7^5\\\\3)\\Use:\\a^n\cdot a^m=a^{n+m}\\\\\dfrac{a^n}{a^m}=a^{n-m}\\\\12.\ 6^2\cdot6^{-4}=6^{2+(-4)}=6^{2-4}=6^{-2}\\\\13.\ 2^{-3}\cdot2^{-2}=2^{-3+(-2)}=2^{-5}\\\\14.\ \dfrac{4^4}{4^2}=4^{4-2}=4^2}\\\\15.\ \dfrac{8^3}{8^{-2}}=8^{3-(-2)}=8^{3+2}=8^5[/tex]
A hudson valley farmer has 26 employees.He pays each employee $410 per week.After paying his workers for one week,the farmer has $162 left in his bank account.how much money did he have at first?
Hi there!
A valley farmer has 26 employees and he pays each of them $410 per week.
After paying them for one week he has $162 dollars left. We need to find how much money he had at first.
So the first step is to multiply $410 on 26 since he gives 410 dollars to each employee, which he has 26.
$410 · 26 = $10,660
So he had $10,660 before he paid the workers, but he still had $162 left. To find out his overall total of money he had we need to add $10,660 and $162 which will be $10,822.
The farmer had $10,822
Hope this helped!~
state if each triangle is a right triangle
Answer:
both 17 and 19 are right triangles because they both have a right angle
Step-by-step explanation:
Solve the equation 7h-5(3h- 8) = -72
Answer: h=14
Step-by-step explanation:
7h-5(3h-8)=-72
7h-15h+40=-72 > I distributed the -5(3h-8) to get rid of parenthesis
-8h+40=-72 > I combined the like terms 7h-15h
-8h=-112 > I subtracted 40 from both sides
h=14 > I divided -8 from both sides
The solution is h = 14.
What are Equivalent Expressions?These are the expressions which give the same or the equivalent result.On solving, both the expressions will get the same value.Given: Equation
7h - 5(3h - 8) = -72
Now, we will solve the equation for the value of h.
⇒ 7h - 5(3h - 8) = -72
⇒ 7h - 15h + 40 = -72
⇒ 7h - 15h = -72 - 40
⇒ -8h = -112
Dividing both sides by -8, we get:
⇒ h = 14
Therefore, the solution of the given equation is h = 14.
Learn more about the Equivalent Expressions here: https://brainly.com/question/4348710
#SPJ2
Find the value of x and pls explain!!❤❤❤
Answer:
x = 11
Step-by-step explanation:
∠CAB = ∠DCA = 33° ( alternate angles )
∠ACB = 180 - 5x ( straight angle )
the sum of all 3 angles in a triangle = 180°, hence
33 + 180 - 5x + 2x = 180
- 3x + 213 = 180 ( subtract 213 from both sides )
- 3x = - 33 ( divide both sides by - 3 )
x = 11
which is the better buy ? 22 vitamins for $1.97 or 40 vitamins for $3.25
A ramp has a base that is 60 inches long and a height of 11 inches. Let x equal the length in inches of the slanted side of the ramp. What is the value of x?
Answer:
\\\90
Step-by-step explanation:
Answer:
61 inches
Step-by-step explanation:
took the test
The top deck of a boat is 9.5 feet above the surface of a lake, while the bottom of the boat is 24 feet below the surface of the lake. What is the vertical distance between the top deck and the bottom of the boat? Drag and drop the correct value into the box to complete the statement
The vertical distance is___________________ feet.
A. -33.5
B. -14.5
C. 14.5
D. 33.5
Answer:
The answer would D.) 33.5 because 9.5+24 is 33.5 and since vertical distance is always an absolute value, it will never be a negative number.
The vertical distance between the top and bottom of the boat is calculated by summing the distances above and below the lake's surface, which total 33.5 feet, making option D correct.
To calculate this, we consider that the top deck of the boat is 9.5 feet above the surface of the lake, while the bottom of the boat is 24 feet below the surface. The total vertical distance would be the sum of these two values, as one needs to account for the entire distance the boat covers from top to bottom.
So, the calculation would be as follows: 9.5 feet + 24 feet = 33.5 feet. Therefore, the vertical distance between the top deck and the bottom of the boat is 33.5 feet. This makes option D the correct answer.
Lines g, h, and I are parallel and
m< 2= 115°.
BRAINLIEST ASAP!!!
what is m<11?
A. 35°
B. 65°
C. 115°
D. 145°
♥️♥️♥️♥️
Answer: Choice C) 115 degrees
Focus on the parallel lines G and L, which are the top and bottom most horizontal lines. Notice that the transversal cut forms the alternate exterior angles 2 and 11. The angles are on the outside or exterior of the "train tracks" of the parallel lines. Also, they are on opposite sides of the transversal line. So that is how we can consider them to be alternate exterior angles.
Similar to alternate interior angles, alternate exterior angles are congruent if we have a transversal cutting a pair of parallel lines.
So in short, angle 2 and angle 11 are congruent. We are given angle 2 to be 115 degrees. Angle 11 is also 115 degrees.
10 is increased to 35
What is the percent increase?
SUPER EASY AND URGENT!
Answer:
The percent increase is 250 percent
Step-by-step explanation:
To find the percent increase we use the formula
percent increase = (new-original)/original * 100
= (35-10)/10 * 100
= 25/10 *100
250
The percent increase is 250 percent
There is a 250% increase.
Work is attached in the image provided.
A shop has 15% sale. Originally a computer cost £275. How much does the computer cost in the sale?
Answer:
= 233.75
Step-by-step explanation:
To find the discount, we multiply the original price by the percent off
discount = 275* .15
= 41.25
To get the sale price, take the original price and subtract the discount
sale price = 275-41.25
= 233.75
A wheel barrow can carry up to 300 pounds of weight. A bag of soil wieghs 20 pounds. Write and solve an inequality to respresent the number of bags of soil the wheelbarrow can carry.
The inequality 20x ≤ 300 represents the number of 20-pound bags of soil a 300-pound capacity wheelbarrow can carry. Solving the inequality, we find x ≤ 15, meaning the wheelbarrow can carry up to 15 bags of soil without exceeding its weight limit.
Explanation:To represent the problem as an inequality, let's say the number of bags of soil the wheelbarrow can carry is represented by x. Each bag of soil weighs 20 pounds, and the wheelbarrow can carry up to 300 pounds. So, the inequality would be 20x ≤ 300.
To solve the inequality, we divide both sides by 20: x ≤ 300/20. Therefore, x ≤ 15. This means the wheelbarrow can carry up to 15 bags of soil without exceeding its 300 pounds weight limit.
Learn more about Inequality here:https://brainly.com/question/30231017
#SPJ3
how to plot 850 integer and it's opposite on a plot
Final answer:
Plotting the integer 850 and its opposite involves marking the points on a coordinate system. The point 850 is plotted 8.5 units to the right of the origin, and its opposite, -850, is plotted 8.5 units to the left, assuming a scale where each unit represents 100.
Explanation:
To plot an integer and its opposite, let's use the number 850 and its opposite, -850, as an example. A plot in mathematics typically refers to marking points on the coordinate system, which consists of two intersecting lines, usually perpendicular, called axes. The horizontal axis is known as the x-axis, and the vertical axis is the y-axis.
To plot the integer 850, you first need to establish a scale suitable for the values you intend to plot. In this example, if each unit on your plot represents 100, then the point representing 850 would be placed 8.5 units to the right of the origin (0,0). Conversely, to plot the opposite of 850, which is -850, you would move 8.5 units to the left of the origin.
In coordinate form, the point 850 can be represented as (850,0), and its opposite, -850, would be (-850,0). This illustration shows how to plot integers and their opposites on a simple two-dimensional graph.
What is the slope of a line perpendicular to line B
Answer:
Step-by-step explanation:
Where is line B?
It cost Marc $29.75 a week to feed his dog .About how much does it cost him to feed his dog for 3 weeks?
Answer:
$89.25
Step-by-step explanation:
If one week is 29.75, then you can infer that each week separately would be the same amount. With this information, you can form this equation:
y = 29.75x
X would be the number of weeks while y would be the final amount based off the number of weeks.
If you substitute x with 3, then you should get the final answer of 89.25.
Hope this helps!
Solve the inequality
-5(3m-2)>30
Answer:
m < −4/3
Step-by-step explanation:
−5(3m−2)>30
Simplify both sides of the inequality.
−15m+10>30
Subtract 10 from both sides.
−15m+10−10>30−10
−15m>20
Divide both sides by -15.
−15m/−15 > 20/−15
m<−4/3
[tex]-5(3m-2)>30\qquad\text{use distributive property}\\\\(-5)(3m)+(-5)(-2)>30\\\\-15m+10>30\qquad\text{subtract 10 from both sides}\\\\-15m>20\qquad\text{change the signs}\\\\15m<-20\qquad\text{divide both sides by 15}\\\\m<-\dfrac{20}{15}\qquad\text{simplify}\\\\m<-\dfrac{20:5}{15:5}\\\\\boxed{m<-\dfrac{4}{3}}[/tex]
2−1/2n=3n+16 what is n
Answer:
n = -4
Step-by-step explanation:
2 - 1/2n = 3n + 16
First isolate n
2 - 16 = 3n + 1/2n
-14 = 3 1/2n
n = -4
Answer:
n=-4
Step-by-step explanation:
2-.5n=3n+16 REWRITTEN
2=3.5n+16 ADDITION PROPERTY OF EQUALITY
-14=3.5n SUBTRACTION PROPERTY OF EQUALITY
n=-4 DIVISION PROPERTY OF EQUALITY
Tickets to a play cost $4 in advance and $5 at the door. The theater club president wants to raise at least $400 from the ticket sales. If the club sells 40 tickets in advance, what is the least number of tickets the club needs to sell at the door to reach the president’s goal?
Answer:
48 tickets
Step-by-step explanation:
I just had this question on a test and got it right! So this is how i did it:
if the advance price is $4, and you sell 40 tickets in advance, you do 40 times 4.
40 x 4 = 160
so you subtract the $160 from 400 and then that brings you $240 dollars left.
*these 240 dollars will be tickets bought at the door*
to determine the amount of tickets that need to be bought left, you need to do 240 divided by 5.
and that will give you a total of:
a least amount of 48 tickets
The least number of tickets the club needs to sell at the door to reach the president’s goal, 48.
What is word problem?A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
Given that, Tickets to a play cost $4 in advance and $5 at the door. The theater club president wants to raise at least $400 from the ticket sales. If the club sells 40 tickets in advance,
Since, the cost if advance ticket is $4 and they already sold 40,
Therefore, collected cost = 4 × 40 = $160
Now, cost to collect yet = 400 - 160 = $240
Cost of tickets at the door = $5
Therefore, tickets to be sold to meet the goal = 240/5 = 48
Hence, the least number of tickets the club needs to sell at the door to reach the president’s goal, 48.
Learn more about word problems, click;
https://brainly.com/question/29203255
#SPJ2
Arrange the steps to solve the equation
[tex] \sqrt{x + 3} - \sqrt{2x - 1} = - 2[/tex]
[tex]Domain:\\\\x+3\geq0\ \wedge\ 2x-1\geq0\\\\x\geq-3\ \wedge\ x\geq0.5\\\\D:x\in[0.5;\ \infty)[/tex]
[tex]\sqrt{x+3}-\sqrt{2x-1}=-2\qquad\text{square of both sides}\\\\(\sqrt{x+3}-\sqrt{2x-1})^2=(-2)^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(\sqrt{x+3})^2-2(\sqrt{x+3})(\sqrt{2x-1})+(\sqrt{2x-1})^2=4\qquad\text{use}\ (\sqrt{a})^2=a\\\\x+3-2\sqrt{(x+3)(2x-1)}+2x-1=4\qquad\text{combine like terms}\\\\3x+2-2\sqrt{(x+3)(2x-1)}=4\qquad\text{subtract 3x + 2 from both sides}\\\\-2\sqrt{(x+3)(2x-1)}=2-3x\qquad\text{square of both sides}\\\\\left(-2\sqrt{(x+3)(2x-1)}\right)^2=(2-3x)^2[/tex]
[tex]4(x+3)(2x-1)=2^2-2(2)(3x)+(3x)^2\qquad\text{use distributive property}\\\\(4x+12)(2x-1)=4-12x+9x^2\\\\(4x)(2x)+(4x)(-1)+(12)(2x)+(12)(-1)=4-12x+9x^2\\\\8x^2-4x+24x-12=4-12x+9x^2\\\\8x^2+20x-12=4-12x+9x^2\qquad\text{subtract }\ 9x^2\ \text{from both sides}\\\\-x^2+20x-12=4-12x\qquad\text{add 12 and}\ 12x\ \text{from both sides}\\\\-x^2+36x=16\qquad\text{change the signs}\\\\x^2-36x=-16\\\\x^2-2(x)(16)=-16\qquad\text{add}\ 16^2\ \text{to both sides}[/tex]
[tex]\underbrace{x^2-2(x)(16)+16^2}_{(a-b)^2=a^2-2ab+b^2}=16^2-16\\\\(x-16)^2=256-16\\\\(x-16)^2=240\iff x-16=\pm\sqrt{240}\\\\x-16=\pm\sqrt{16\cdot15}\\\\x-16=-\sqrt{16}\cdot\sqrt{15}\ \vee\ x-16=\sqrt{16}\cdot\sqrt{15}\\\\x-16=-4\sqrt{15}\ \vee\ x-16=4\sqrt{15}\qquad\text{add 16 to both sides}\\\\x=16-4\sqrt{15}\notin D\ \vee\ x=16+4\sqrt{15}\\\\\boxed{x=4(4+\sqrt{15})}[/tex]
20 blue jays out of 35 birds
Answer: 15 There would be 15 blue jays out of all the other birds
please mark as brainliest
Step-by-step explanation:
Answer:
Step-by-step explanation:
Its 4:7
Choose the number below that represents the digit in the tens place of the number 128
A). 10
B). 1
C). 2
D). 8
the answer is C) 2. the 8 is in the ones place, 2 is in the tenths, and 1 is in the hundreths.
Which best describes why these two figures are similar or not similar?
A. They are not similar because their corresponding angles are not congruent.
Their angles are not the same.
The 1st triangle is a scalene triangle (a triangle that has 3 unequal sides and angles)
The 2nd triangle is an isosceles triangle (a triangle that has 2 congruent/equal sides and 2 congruent angles)
Answer:
Step-by-step explanation:
Solve the equation 9x = 7(x + 2).
A) -7
B) -1
C) 1
D) 7
Answer:
The solution of the equation 9x=7(x+2) is:
Option D) 7
Step-by-step explanation:
9x=7(x+2)
Eliminating the parentheses applying distributive property:
9x=7(x)+7(2)
Multiplying:
9x=7x+14
Grouping the x's on the left side of the equation: Subtracting 7x both sides of the equation:
9x-7x=7x+14-7x
Subtracting:
2x=14
Solving for x: Dividing both sides of the equation by 2:
2x/2=14/2
Dividing:
x=7
Solution: x=7 (option D)
A roller coaster can give rides to 50 more people. Each car can hold 5 people. What is the best way to interpret the remainder of 50 / 5 so that everyone gets a ride?
A. Write the remainder as a fraction
B. Use the remainder as the answer
C. Use only the quotient
D. Add 1 to the quotient
Twenty four 750 milliliter bottles are shipping out of the warehouse. In total,how many liters were shipped
Answer:
18 L
Step-by-step explanation:
(a) Millilitres shipped
There are 750 mL/bottle.
Vol. shipped = 24 × 750
Vol. shipped = 18 000 mL
=====
(b) Litres shipped
1 L = 1000 mL
Vol. shipped = 18 000 × 1/1000
Vol. shipped = 18 L
6b+4b+5 need help asap
Answer:
10b + 5 is your answer
Step-by-step explanation:
Simplify the expression as much as possible. Combine terms with the same amount of variables.
6b + 4b = 10b
10b + 5
10b + 5 is your answer
~