Step-by-step explanation:
let (-2,4)=(x1,y1)
given eqn: y=4x+11
comparing with y=mx+c
slope (m)=4
now using point and slope form,
(y-y1)=m (x-x1)
(y-4)=4 (x+2)
y-4=4x+8
4x-y+12=0 is required eqn.
Answer:
slope: 4
y - 4 = 4(x + 2)
y - 4 = 4x + 8
y = 4x + 12
kristin was charged $42.25 for parking. how many hours did she park her car at the garage? enter your answer as a mixed number in the simplest form. (unit rate is $6.5 per hour. i just need this answer right now!)
Answer: Kristin parked her car at the garage for 6 hours and 30 minutes.
Step-by-step explanation:
Hi, to solve this problem we have to analyze the information given:
Parking cost: $42.25 Rate per hour: $6.5 per hourWe have to divide the parking cost by the cost per hour to obtain the hours that the car was parked at the garage.
Mathematically speaking:
$42.25 / $6.5 = 6.5 hours = 6 hours and 30 minutesIn conclusion, Kristin parked her car at the garage for 6 hours and 30 minutes.
Find the sum of the first 6 terms in the following series. 6+(-18)+54+(-162)
Answer:
The sum of the first 6 terms in the given series is -1,092.
The sum of the first 6 terms in the given series is -1,092.
What is the method of the sum of series?The sum of the first n terms in an arithmetic collection is (n/2)⋅(a₁+aₙ). it's far called the mathematics series components.
Which collection has a sum?An infinite collection that has a sum is known as a convergent collection and the sum Sn is referred to as the partial sum of the collection.
Learn more about the sum of the series here: https://brainly.com/question/24295771
#SPJ2
16. Which number has the greater value,
7 x 10-9 or 6 x 10-4?
in any case, the amount of zeros is more important than the significant digits. since 7X10-9 has a smaller exponent above the 10 than 6X10-4, it is safe to say 6X10-4 is the larger number
Answer:
7 x 10-9
Step-by-step explanation:
(7x10) (6 x 10)
70-9 60-4
61 56
2. In basketball, Dimitri is averaging
12.375 rebounds per game in a
tournament. What is 12.375 in
expanded form? In word form? (1-3)
20. Acid Mixture Bill Charlson needs 10% hydrochloric acid
for a chemistry experiment. How much 5% acid should he
mix with 60 milliliters of 20% acid to obtain a 10% solution?
Answer:
120 ml
Step-by-step explanation:
Let x ml of 5% acid should mix with 60 milliliters of 20% acid to obtain a 10% solution,
Thus, the quantity of resultant mixture = ( x + 60 ) ml,
Also,
Acid in x ml 5% acid + Acid in x ml 5% acid = acid in 10% resultant solution,
5% of x + 20% of 60 = 10% of ( x + 60)
[tex]\frac{5x}{100}+\frac{20\times 60}{100}=\frac{10\times (x+60)}{100}[/tex]
[tex]5x + 1200 = 10x + 600[/tex]
[tex]5x - 10x = 600 - 1200[/tex]
[tex]-5x = -600[/tex]
[tex]\implies x = \frac{-600}{-5}=120[/tex]
Hence, 120 ml of 5% acid should be mixed.
Jackie cut a 2-yard spool into 5 equal lengths of ribbon.
a. What is the length of each ribbon in yards? Draw a tape diagram to show your thinking.
b. What is the length of each ribbon in feet? Draw a tape diagram to show your thinking.
Answer:
a. [tex]\frac{2}{5}[/tex] yard
b. 1.2 feet
Step-by-step explanation:
a. Jackie cut a 2-yard spool into 5 equal length of ribbon.
We will divide 2 yard by 5 = 2 ÷ 5 = [tex]\frac{2}{5}[/tex] yard
5 units = 2 yard
1 unit = [tex]\frac{2}{5}[/tex] yard
Check : [tex]\frac{2}{5}[/tex] + [tex]\frac{2}{5}[/tex] + [tex]\frac{2}{5}[/tex] + [tex]\frac{2}{5}[/tex] + [tex]\frac{2}{5}[/tex] = [tex]\frac{10}{5}[/tex] = 2
b. Length of each ribbon in feet
Since 1 yard = 3 feet
therefore, 2 yard = 3 × 2 = 6 feet
6 feet in to 5 equal part = 6 ÷ 5
= 1.2 feet
check : 1.2 + 1.2 + 1.2 + 1.2 + 1.2 = 6.0 feet
Each ribbon cut from a 2-yard spool into 5 equal parts will be 0.4 yards or 1.2 feet in length. Tape diagrams represent this division into equal parts.
Explanation:To determine the length of each ribbon when a 2-yard spool is cut into 5 equal lengths, you need to divide the total length by the number of pieces.
2 yards ÷ 5 = 0.4 yards for each piece.To represent this with a tape diagram, imagine a line equally divided into 5 sections, with each section representing 0.4 yards.
For the length in feet, since 1 yard equals 3 feet, we multiply the length in yards by 3.
To show this with a tape diagram, you can divide a line into 5 sections with each section representing 1.2 feet.
How can you determine the coordinates of any image that is dilated with the center of dilation at the origin without graphing
Answer:
[tex](x,y)\rightarrow (kx,ky)[/tex]
Step-by-step explanation:
A dilation is an enlargement or reduction of an object by a scale factor and with a center of dilation. The scale factor refers to the change in size. The center of dilation is a point about which we are dilating an object.
The dilation with the center of dilation at the origin and a scale factor of k has the rule
[tex](x,y)\rightarrow (kx,ky)[/tex]
This means that the image of the point with coordinates (x,y) after the dilation by a scale factor of k with center of dilation at origin will have coordinates (kx,ky).
Solve (x - 2<5) n (x + 7 > 6).
Pls help
[tex]x - 2 < 5 \: and \: x + 7 > 6 \\ x < 7 \: and \: x > - 1[/tex]
The correct answer is the first one,
[tex] - 1 < x < 7[/tex]
Final answer:
To solve the given inequalities, (x - 2) < 5 and (x + 7) > 6, first isolate x in each one to get x < 7 and x > -1. The intersection of these solutions, which is the final answer, is -1 < x < 7.
Explanation:
The student has asked to solve two inequalities and find the intersection of their solutions. The inequalities are (x - 2) < 5 and (x + 7) > 6. To solve these separately:
For the first inequality, add 2 to both sides to get x < 7.
For the second inequality, subtract 7 from both sides to get x > -1.
To find the intersection, we look for values that satisfy both conditions: x > -1 and x < 7. Therefore, the solution is the set of all x such that -1 < x < 7.
what is 271,403 to the nearest thousand
Answer:
300,000
Step-by-step explanation:
hope this helps
Answer:
271,000
Step-by-step explanation:
Rounding depends on the place value, if you are rounding to the nearest thousand, look at the number in the hundred place. Is that number lower or higher than 5? If lower, the place you are rounding to stays the same, and the places below it turn to zeros. If 5 or higher, round up, add 1 to the place you are rounding to, then turn the places below to zeros.
In this case, the hundreds place is a 4. Meaning you round down.
If a+b-c=3 what is the value of 4(a+b-3)-(a+b+3c)?
3abc
Step-by-step explanation:
Final answer:
To find the value of 4(a+b-3)-(a+b+3c) given that a+b-c=3, we simplify to 3(a + b - c) - 12. Since a + b - c equals 3, the expression simplifies to -3.
Explanation:
The question provides the equation a + b - c = 3. To find the value of the expression 4(a+b-3)-(a+b+3c), we can simplify it using the given equation.
Let's break down the steps for simplification:
First, substitute the value of a + b - c from the given equation, which is 3, into the expression we want to simplify.Then, distribute the 4 across the first set of parentheses 4(a + b - 3) which becomes 4a + 4b - 12.Now, combining this result with the second part of the expression -(a + b + 3c) gives us 4a + 4b - 12 - a - b - 3c.Grouping like terms together and simplifying gives us 3a + 3b - 3c - 12 which is equivalent to 3(a + b - c) - 12.Since a + b - c = 3, the expression becomes 3(3) - 12, which simplifies to 9 - 12.Thus, the final value of the expression is -3.Find each of the following products. Show your work.
a. 57×23 b. 724•82 c. (345)(210)
Step-by-step explanation:
a. 57×23=1311
b. 724×82=59368
c. (345)(210)=72450
4y/5b=L+s solve for B
Answer:
[tex]b = \frac{4y}{5l + 5s} [/tex]
Step-by-step explanation:
[tex] \frac{4y}{5b} = l + s[/tex]
multiplying through by the L.C.M. which is 5b
[tex] \frac{4y}{5b} \times 5b = (l + s) \times 5b[/tex]
cancel out
4y =5bL+ 5bs
factorizing b out
4y=b ( 5L +5s ).
making be the subject by dividing through by ( 5L+ 5s )
[tex] \frac{4y}{5l + 5s} = \frac{b(5l + 5s)}{5l + 5s} [/tex]
[tex]b = \frac{4y}{5l + 5s} [/tex]
What is the solution for x in the equation? 29+15x=-x-3
Answer:
x = -2
Step-by-step explanation:
Mike wants to make meatloaf. His recipe
uses a total of 4 pounds of meat.
If he uses a 3 to 1 ratio of beef to pork, how
much pork will he use? Enter your answer as a
mixed number in simplest terms.
Total meat in the recipe he wants to use = 7 pounds
Beef : pork = 3 : 1
Total pork that he will use = x 7 pounds
= 7/4 pounds
hope this helps
Answer:
Amount of pork used was 1 pound.
Step-by-step explanation:
Mike wants to make meatloaf by adding beef and pork.
Ratio of the meat (beef and pork) is = 3 : 1
Recipe requires total amount of meat = 4 pounds
So the amount of pork used in the recipe = [tex]\frac{1}{(1+3)}\times 4[/tex]
= [tex]\frac{1}{4}\times 4[/tex]
= 1 pound
Therefore, total amount of pork used in the recipe is 1 pound.
Evaluate the expression (- n) ^ (n + n) + n ^ (n - n) , when n = 2
Answer:
17
Step-by-step explanation:
Substitute the value of the variable and simplify.
[tex](-(2))^{(2+2)} +2^{(2-2)}[/tex]
[tex]-2x^{2+2} =2^{4} = 16[/tex]
[tex]2^{2-2} =2^{0}[/tex]
Anything raised to the power of 0 is one.
16 + 1 = 17
Answer:
17
Step-by-step explanation:
How to do a repeating decimal and turn it into it's rational form for example 0.3 repeating???
Answer:
Step-by-step explanation: 0.3 repeating can be made rational by turning it into 1/3.
[tex]\bf 0.\overline{3}\qquad \qquad x=0.\overline{3}\qquad \qquad \begin{array}{llll} 10\cdot x&=&3.\overline{3}\\\\ 100\cdot x&=&33.\overline{3} \end{array}\qquad \qquad \begin{array}{rllll} \stackrel{100x}{33.\overline{3}}\\\\ -\stackrel{10x}{3.\overline{3}}\\ \cline{1-1} 30.0 \end{array} \\\\[-0.35em] ~\dotfill\\\\ 100x-10x=30\implies 90x=30\implies x=\cfrac{30}{90}\implies x=\cfrac{1}{3}[/tex]
Select all input values for which f(x) =2
A) x= -7
B) x= 0
C) x= 4
None of the above
Good morning ☕️
______
Answer:
The correct answer is A (x=-7)
___________________
Step-by-step explanation:
Look at the photo below for the details.
:)
Which of the following attributes does a line have?
Answer:
short or long, thin or thick, straight or curved, direct or meandering, zigzag or serpentine, distinct or blurred
Answer:
Length
Step-by-step explanation:
We know that a line segment has two end points with a definite length.
A straight line has neither starting nor end point and is of infinite length
The attribute of the line is the length
Hope this helps! :)
An ice cream sundae costs $1.75 plus an additional $0.35 for each topping. If the total
cost is $2.80, how many toppings did the sundae have?
Answer:
3
Step-by-step explanation:
$1.75 (ice cream) + $0.35 (topping) * x (some toppings) = $2.80, so I can rewrite it like that: 1.75+0.35x=2.80
1) Move the constant to the right side and change its sign: 0.35x=2.8-1.75
2) Substract the numbers: 0.35x=1.05
3) Divide the both sides of the equation by 0.35
4) x=3
"The correct number of toppings on the sundae is 3.
To solve the problem, we first establish the cost of the ice cream sundae without any toppings, which is given as $1.75. We also know that each topping costs an additional $0.35. The total cost of the sundae with toppings is $2.80.
Let's denote the number of toppings as \( t \). The total cost of the sundae with toppings can be represented by the equation:
[tex]\[ \text{Total cost} = \text{Cost of sundae} + (\text{Cost per topping} \times t) \][/tex]
Substituting the known values into the equation, we get:
[tex]\[ 2.80 = 1.75 + (0.35 \times t) \][/tex]
To find the number of toppings [tex]\( t \)[/tex], we need to isolate [tex]\( t \)[/tex] on one side of the equation. We do this by subtracting the cost of the sundae from both sides of the equation:
[tex]\[ 2.80 - 1.75 = 0.35 \times t \][/tex]
[tex]\[ 1.05 = 0.35 \times t \][/tex]
Now, we divide both sides of the equation by the cost per topping to solve for [tex]\( t \)[/tex]:
[tex]\[ \frac{1.05}{0.35} = t \][/tex]
[tex]\[ t = 3 \][/tex]
Find three consecutive integers so that the
sum of the first two integers is 10 more than the third
integer.
Final answer:
The three consecutive integers that satisfy the condition are 11, 12, and 13. These numbers are such that the sum of the first two is equal to the third integer plus 10.
Explanation:
The question asks to find three consecutive integers where the sum of the first two is 10 more than the third. To solve this, let's call the smallest integer 'x'. Therefore, the next two consecutive integers will be 'x+1' and 'x+2'. The problem states that the sum of the first two integers is 10 more than the third, which gives us the equation: x + (x + 1) = (x + 2) + 10.
Simplifying this equation gives us 2x + 1 = x + 12. To find the value of 'x', we subtract 'x' from both sides of the equation, which gives us x + 1 = 12. Next, we subtract 1 from both sides to get x = 11. The three consecutive integers in question are therefore 11, 12, and 13.
Checking our work: the sum of the first two integers is 11 + 12 = 23. The third integer plus 10 is 13 + 10 = 23. Since both sums are equal, our solution is correct.
Final answer:
To find three consecutive integers, let the first integer be x, the second integer be x+1, and the third integer be x+2. Solve the equation x + (x+1) = (x+2) + 10 to find x, then determine the three consecutive integers.
Explanation:
To find three consecutive integers, we can let the first integer be x, the second integer be x+1, and the third integer be x+2. We are given that the sum of the first two integers is 10 more than the third integer. This can be written as:
x + (x+1) = (x+2) + 10
Combining like terms and solving the equation, we get:
2x + 1 = x + 12
x = 11
So the three consecutive integers are 11, 12, and 13.
Factor out the GCF and factor completely. 9m3 - 16m
A
m(3m + 4)(3m - 4)
B
m(9m2 - 16)
C
m(9m - 4)
D
m(3m2 + 4)(3m2 + 4)
Answer:
Option A m(3m + 4)(3m - 4)
Step-by-step explanation:
we have
[tex]9m^{3}-16m[/tex]
Factor m
[tex]m[9m^{2}-16][/tex]
Apply difference of squares
we know that
[tex][9m^{2}-16]=(3m+4)(3m-4)[/tex]
substitute
[tex]m[9m^{2}-16]=m(3m+4)(3m-4)[/tex]
solve the inequality: | x/4 - 7 | < -2
Answer:
no solutionStep-by-step explanation:
[tex]\left|\dfrac{x}{4}-7\right|<-2[/tex]
We know: absolute value is always non-negative.
Therefore, this inequality has no solution.
Mariah started to find the solutions of x2 + 4x + 1 = 0. Her work is shown below. x2 + 4x + 1 = 0 x2 + 4x = –1 x2 + 4x + 4 = –1 + 4 (x + 2)2 = 3 Which describes the solutions of the equation?
since -2 and 3 are both rational, the sum and difference are both rational
since -2 and /3 are both rational, the sum and difference are both rational
since -2 is rational and /3 is irrational, the sum and difference are irrational.
Since /2 is rational and /3 is irrational, the sum and difference are irrational.
Answer:
Since -2 is rational and √3 is irrational, the sum and difference are irrational.
Step-by-step explanation:
Given equation,
[tex]x^2 + 4x + 1 =0[/tex]
[tex]x^2 + 4x = -1[/tex]
[tex]x^2 + 4x + 4 = -1+4[/tex]
[tex](x+2)^2 = 3[/tex]
[tex]x+2=\pm \sqrt{3}[/tex]
[tex]x=-2\pm \sqrt{3}[/tex]
Which is the solution of given equation.
Now, an integer is always a rational number ( that can be expressed as [tex]\frac{p}{q}[/tex], where, p and q are integers such that q ≠ 0 ),
So, -2 is a rational number,
Now, √3 can not be expressed as p/q so it is an irrational number,
We know that sum and difference of rational and irrational number is always irrational.
Thus, -2 + √3 and -2 - √3 are irrational.
Answer:
C
Since –2 is rational and StartRoot 3 EndRoot is irrational, the sum and difference are irrational.
Step-by-step explanation:
I NEED HELP ASAP! : An initial population of 175 quail increases at an annual rate of 22%. Write an exponential function to model the quail population. What will the approximate population be after 5 years?
Answer:
About 473 quails.
[tex]P=175(1.22)^t[/tex]
Step-by-step explanation:
Exponential equation with [tex]P_0[/tex] as the initial amount and rate of r is:
[tex]P=P_0(1+r)^t[/tex]
[tex]P=175(1+.22)^t[/tex]
[tex]P=175(1.22)^t[/tex]
After 5 years the population will be:
[tex]P=175(1.22)^5[/tex]
[tex]P \approx 472.9739[/tex]
So the population will be about 473 quails.
Answer:
1. A) (the graph is in the growth direction)
2. B) 130% increase
3. D) f(x)= 175 (1.22)^x ; 473
4. C) 7 years
5. D) y= 110(0.9)^x
Hope this helps.
Which of the following is congruent with the figure above?
Answer:
Step-by-step explanation:
It is obtion 4. See attached picture.
Joshua dived to a depth of 25 fr below sea level. How many feet must Joshua rise before returning to sea level which is 0 ft
Answer: 25
He's at -25, so -25 + 25 = 0!
General admission to The American Museum of Natural History is $19.
a. If a group of 125 students visits the museum, how much will the group’s tickets cost?
b. If the group also purchases IMAX movie tickets for an additional $4 per student, what is the new total cost of all the tickets? Write an expression that shows how you calculated the new price.
Answer:
(a) $2,375.
(b) $2,875.
Step-by-step explanation:
We have been general admission to The American Museum of Natural History is $19.
(a). To find the total cost of tickets for a group of 125 students, we will multiply 125 by $19.
[tex]\text{The total cost of tickets}=\$19\times 125[/tex]
[tex]\text{The total cost of tickets}=\$2,375[/tex]
Therefore, the total cost of 125 tickets would be $2,375.
(b). We have been given that the group also purchases IMAX movie tickets for an additional $4 per student.
The total cost of one ticket would be the cost of museum ticket plus movie ticket that is [tex]\$19+\$4=\$23[/tex].
The new total cost of 125 tickets would be 125 times $23.
[tex]\text{The new total cost of tickets}=\$23\times 125[/tex]
[tex]\text{The new total cost of tickets}=\$2,875[/tex]
Therefore, the new total cost of 125 tickets would be $2,875.
Suppose you invest $5,000 at 9% interest,
Compounded annually, for 10 years. Determine the
future value of your investment, using the
Compound interest formula!
Answer:
$5000*(1,09)^10=~ $11836.82
Step-by-step explanation:
Round 392,153 to the nearest hundred
Answer:
The answer is 392,200 if it's wrong I'm sorry
Answer:
392,200
Step-by-step explanation:
look at the right of the one (the hundreds place) and its a five. if its a five or above (which it is) bump up the one to the left of it, which was the one, and is now a two.
CAN EXPLAIN FURTHER IF THIS WAS UNCLEAR
A large western state consists of 2691 million acres of land. Approximately 65% of this pand is federally owned how to find the answer?
Answer:
Step-by-step explanation:
What you need to do is take your 65% and put it over 100% like this: 65/100
Then, you take 2691 and put it into the denominator and put x on the top like this: x/2691
Then you need to put them equal to each other and cross multiply like this 65/100=x/2691
Multiply the 2691 by 65 and x by 100
to get 100x=2691(65)
Finally, multiply the 2691 by 65 and then divide that whole thing by 100 to get x.
x will be the land in acres and your final answer.
Good luck! Hope this was clear!
65% of the total acres of the large western state is approximately 1749.15 million acres.
To find the answer:
Calculate 65% of 2691 million acres.
Divide the result by 100 to get the amount federally owned.
Therefore, the federally owned land in the large western state is approximately 1749.15 million acres.