Answer:
x = -4/7, y = 2/7
Step-by-step explanation:
Given: f(x) = 3x + 2 and g(x) = - 4x - 2
The point of intersection of the two functions is the point at which both functions intersect. We have to solve the functions simultaneously to get the solution.
f(x) = y = 3x + 2
y = 3x + 2 (1)
g(x) = y = -4x - 2
y = -4x - 2 (2)
Subtract equation 2 from equation 1:
0 = 7x + 4
7x = -4
x = -4/7
Put x = (-4/7) in y = 3x + 2:
y = 3(-4/7) + 2 = -12/7 + 2 = 2/7
Benjamin works at a printing company. He
is making T-shirts for a high school volleyball
team. The press he runs can imprint 3 T-shirts
per minute with the school's mascot.
Answer:
The independent quantity is time and the dependent quantity is T-shirt printed
Step-by-step explanation:
We are asked to determine the dependent and independent quantity.
An independent quantity is a quantity that is not dependent on other quantities while a dependent quantity is a quantity that depends on other quantity. In the the question, the number of T-shirts being made depends on the amount of time the machine works making 3 T shirts per minute, this means that the number of T-shirts made is dependent on the time.
The independent quantity is time and the dependent quantity is T-shirt
VIOLI me eg 20(20-x) = 300 What is the value of x? Round to the units place.
Answer:
x=5
Step-by-step explanation:
20(20-x) = 300
Divide each side by 20
20/20(20-x) = 300/20
20-x = 15
Subtract 20 from each side
20-x-20 = 15-20
-x = -5
Multiply each side by -1
x = 5
Answer:
x = 5
Step-by-step explanation:
20(20-x) = 300
20( -x + 20) = 300
-20x + 20 * 20 = 300
-20x = 300 - 400
x = -100 / -20
x = 5
ANSWER FAST PLEAEE!:) I REALLY NEED HELP:)
Questions
1. How many theme is Noah considering?
2. How many locations is Noah considering?
3. How many days of the week is Noah considering
4. One possibility that Noah is considering is a party with a space theme at the skating rink on Sunday. Write two other possible parties Noah is considering
5. How many different possible outcome are in the sample space?
Answer:
1. 3 themes : space, safari, comics
2. 2 locations : skating rink, park
3. 3 days of the week : Friday, Saturday, Sunday
4. A safari theme at the skating rink on Saturday.
A comics theme at the park on Friday.
5. 6 different possible outcome are in the sample space.
I'm not sure if it's right but I hope it helps.
What are the roots of the graph below?
Answer:
(1, 0) and (-2, 0)
-2, 1, 2
Hope this helps anyone who needs it! :)
Grace weaves a rug that is 1/3 yard wide and 2 yards long. She wants to
weave a rug that uses the same design but is 1 yard wide. How long will
the rug be?
What did you do first to find the length? Why did you choose that method?
Answer:
6 yards long
Step-by-step explanation:
1/3 yards wide = 2 yards long
Let x = length of the other rug
1 yard wide = x yards long
1/3 : 2 = 1 : x
1/3 ÷ 2 = 1 ÷ x
1/3 × 1/2 = 1 / x
1/6 = 1/ x
Cross product
1*x = 6*1
x= 6 yards
Therefore, the length of the new rug with 1 yard wide is 6 yards long
The first thing to do is to find the ratio of wide to long of the two rugs by representing the long of the second rug with x
It is the simplest method to solve the question
What is the slope of the line that passes through the points (−6,−4) ) and (−12,−4)? Write your answer in simplest form.
Answer:
Slope: 0
Step-by-step explanation:
To find the slope use the expression y2 - y1/x2 - x1
Either of the coordinate can be y2 or y1 they just x1 and y1 have to be the same coordinate
Let's make (-12, -4) x2 and y2 & (-6, -4) x1 and y1
Next substitute the numbers into the expression
-4 +4/-12 + 6
This will equal 0/-6
The slope is only 0 because whenever you divide 0 by a number it will always be zero unless it is something like 14/0, this means it is undefined (only for slopes)
Answer:
0
Step-by-step explanation:
To find the gradient of a line, we take the change in the y value divided by the change in the x value.
In this instance, the line passes through (-6, -4) and (-12,-4) , that means the line has a constant y value.
Following the equation to find gradient, we take the difference in y divided by the difference in x
[tex]\frac{(-4) - (-4)}{(-6) - (-12)} = \frac{0}{6} = 0[/tex]
and we see that the gradient is 0, which means that it is a flat line
A new youth center is being built in erie . The perimeter of the rectangular playing field is 296 yards. The length of the field is 2 yards less than double the width. What are the dimensions of the playing field?
Answer:
The dimensions are 50 yards by 98 yards
Step-by-step explanation:
If the width is w, then the length is 2w - 2. Perimeter can be expressed by 2 * (length + width), therefore:
2 * (2w - 2 + w) = 296
2 * (3w - 2) = 296
3w - 2 = 148
3w = 150
w = 50 so 2w - 2 = 2 * 50 - 2 = 98
Answer:
[tex]\Large \boxed{\mathrm{98 \ yards \cdot 50 \ yards}}[/tex]
Step-by-step explanation:
Let the length be l.
Let the width be w.
[tex]l = 2w - 2[/tex]
The perimeter of the rectangle is 296 yards.
[tex]P = 2l + 2w[/tex]
Plug in the value for l and P.
[tex]296 = 2(2w-2) + 2w[/tex]
Evaluate and solve for w.
[tex]296 = 4w - 4 + 2w \\\\296 = 6w - 4 \\\\300 = 6w \\\\50 = w[/tex]
The width is 50 yards.
Let w = 50 for l.
Evaluate and solve for l.
[tex]l = 2(50) - 2 \\ \\ l = 100 - 2 \\\\l = 98[/tex]
The length is 98 yards.
Find the common ratio of the geometric sequence: 8, -2, 1/2, -1/8
Answer:
-1/4
Step-by-step explanation:
You just need to see what number is being divided from each term
For the solution (2,2) , find the value of ‘c’ in the equation 2x + cy = 8
We have a solution (2,2) so x = 2 and y = 2. Then:
[tex]2x+cy=8\\\\2\cdot2+c\cdot2=8\\\\4+2c=8\\\\2c=8-4\\\\2c=4\quad|:2\\\\\boxed{c=2}[/tex]
what is all the real solution of the equation
Answer:I think its C
Step-by-step explanation:
Answer:
x=1, or 6, or 4 (D)
Step-by-step explanation:
x³-11x²+34x-24=0 solve by factorizing
(x-1)(x-6)(x-4)=0
x-1=0
x=1
if x-6=0
x=6
x-4=0
x=4
check : x³-11x²+34x-24=0
x=1 : (1)³-11(1)²+34(1)-24=0
1-11+34-24=-35+35=0 (correct)
x=6 : 6³-11(6)²+34(6)-24=0 (correct)
x=4 : 4³-11(4)²+34(4)-24=0 (correct)
Larry runs 2.5 miles and sees a total of 12 dogs. If Larry runs for a total of 8 miles, approximately how many dogs will Larry see?
Answer:
38.4
Step-by-step explanation:
We have 8/2.5=3.2 What does this mean? Well, it means that (if the miles are porportional to the dogs) that means he will see 3.2 as many dogs. So, we have 12*3.2=38.4, or 38 if the homework is asking for a rounded number. Hope I helped!
Larry sees 12 dogs per 2.5 miles.
Your trying to find out how many dogs Larry sees in 8 miles.
[tex]\frac{2.5}{12} = \frac{8}{x}[/tex]
So you want to find x.
To go from 2.5 to 8, you have to multiply by 3.2
So do the same thing to the denominator; 12 × 3.2=38.4
Since there are 38.4 dogs, you have to round down because 0.4 dogs is no dog.
Larry sees 38 dogs in 8 miles.
♡ Hope this helped! ♡
❀ 0ranges ❀
How do you find the answer for? 4(3x+7)=19
Answer:
3/4
Step-by-step explanation:
open the brackets by multiplication
12x+28= 19
12x= 19-28
12x= -9 (divide)
-9/12x
x= 3/4
Answer:
[tex]\boxed{x=-0.75 }[/tex]
Step-by-step explanation:
4 ( 3x + 7 ) = 19
→ Expand the brackets
12x + 28 = 19
→ Minus 28 from both sides to isolate 12x
12x = -9
→ Divide 12 from both sides to isolate x
[tex]x=-\frac{9}{12} =- \frac{3}{4} =-0.75[/tex]
Evaluate 19 - (-13). The solution is.
Answer:
32
Step-by-step explanation:
19-(-13)
=19+13 (after removing the brackets, the minus sign becomes positive)
=32
Answer:
32
Step-by-step explanation:
if there are two negative signs next to each other (they willl usually be separated by parenthesis) they would become an addition sign, so this question would actually be 19+13
The hypotenuse of right triangle ABC, line segment AC, measures 13 cm. The length of line segment BC is 5 cm.
Answer:
Step-by-step explanation:
Pythagorean theorem: In a right angle triangle, the square of hypotenuse is equal to the sum of squares of other two sides
BC² + AB² = AC²
5² + AB² = 13²
25 + AB² = 169
AB² = 169 - 25
AB² = 144
AB = √144 = √12*12
AB = 12cm
Tim wants to find the area of the floor in
a room. If the room is square with length
and width 8, what expression with an
exponent can he write to show the area
of the room?
Step-by-step explanation:
Area of the room
= length x width
= 8 x 8
[tex] = 8^2 [/tex]
Suzie has 55 pairs of shoes which is 33 less than twice the amount of shoes Jamie has. how many pairs of shoes does Jamie have
Answer:
Jamie has 44 pairs of shoes
Step-by-step explanation:
Let
Jamie= x pairs of shoes
Suzie= 33 less than twice the amount of shoes Jamie has
2x - 33 = 55
Solve:
2x - 33 = 55
Collect like terms
2x = 55 + 33
2x = 88
Divide both sides by 2
2x / 2 = 88 / 2
x = 44
Jamie = x = 44 pairs of shoes
Therefore, Jamie has 44 pairs of shoes
Z=8+6x-px
I need to solve the literal equation for x. Please help!!
Answer:
x = (z-8)/(6-p)
Step-by-step explanation:
Here in this question, we are to solve for x.
In quite more understandable words, we are trying to make x the subject of the formula.
To do this, we simply bring together, the terms that have x common to them.
Let’s proceed mathematically;
z = 8 + 6x - px
Let’s take 8 to z to make it negative and factor out x since it’s common to the two terms on the right hand side of the equation.
z - 8 = x(6-p)
The final thing to do here is to isolate x and this gives the below;
We can do this by dividing both sides by the coefficient of x which is 6-p in this case.
Thus;
x = (z-8)/(6-p)
An ice cream shop is testing some new flavors of ice cream. They invent 252525 new flavors for customers to try, and throw out the 131313 least popular flavors. The shop makes 808080 cartons of each of the remaining flavors. It takes 222 cartons to get one liter (\text{L})(L)left parenthesis, start text, L, end text, right parenthesis of ice cream. How much total ice cream is in the cartons?
Answer:
480litres total ice creamStep-by-step explanation:
Total number of ice cream invented for customers to try = 25 new flavours
Amount of least popular flavors thrown out = 13 flavors
Remaining flavor nit thrown out = Total ice cream invented - amount thrown out = 25 - 13
= 12 flavors
The remaining number flavors that was produced is 12 flavors.
If 80 cartons of each of the remaining flavor was made, the total amount of cartons made = 12* 80 = 960 cartons.
Since 2 cartons contains 1 litre
960 cartons will contains (960*1/2) litres
Hence 960 cartons will contain 480litres of the ice cream.
This shows that there are total of 480 litres of ice cream in the cartons
please help me on this
Converse of the corresponding angles postulate
============================================
Explanation:
The corresponding angles postulate says that if we have two parallel lines, then the corresponding angles are congruent.
The converse of this is where we go in reverse: if we know the corresponding angles are congruent, then the lines are parallel.
Corresponding angles are ones where they are on the same side of the transversal line, and also on the same side of each adjacent parallel line. In this case, the angles 52 are to the right of the tranversal, and each are above their neighboring parallel line. We could say the two corresponding angles are both in the upper right hand corner (think of the two lines crossing to form 4 corners or regions)
What is the perimeter of this rectangle? *
5 cm
8 cm
ar swer
Answer:
Perimeter of rectangle = 2(l+b)
= 2(8+5)cm
= 2*13 cm
= 26cm
Answer in simplest form.
Chris spent 5/6 hour drawing and 2/6 hour reading. How much more time did he spend
drawing than reading?
Step-by-step explanation:
Time = 5/6 - 2/6 = 3/ 6 = 1/2
Pls answer ASAP!! I will make you brainliest! (Number 11.)
Answer:
$13
Step-by-step explanation:
R = 10A - 20
110 = 10A - 20
add 20 to both sides
130 = 10A
divide by 10
13 = A
$13
Answer:
13 dollars
Step-by-step explanation:
R = 10A -20
Let R = 110
110 = 10A -20
Add 20 to each side
110+20 = 10A -20+20
130 = 10A
Divide each side by 10
130/10 = 10A/10
13 = A
How To Multiply Decimals And Fractions
Answer:
[tex]\large \boxed{\mathrm{view \ explanation}}[/tex]
Step-by-step explanation:
Convert the decimal into a fraction, then multiply both fractions.
For example:
0.5 × 1/4
0.5 is also 5/10 or 1/2.
1/2 × 1/4
Multiply both fractions.
(1 × 1)/(2 × 4)
= 1/8
The sum of five consecutive even integers is 530 list integers from smallest to largest
Step-by-step explanation:
Let the 5 even integers be x-4,x-2,x,x+2,x+4
Hence, x-4+x-2+x+x+2+x+4=530
Hence, 5x=530
Hence, x=530/5
Hence,x=106
so.. the integers are 102,104,106,108,110
Andrew loves skiing-- he just hates the ski lift. To make matters worse, the ski lift has been acting up today. Andrew is using the GPS on his phone to track the ski lift's progress as it travels up the mountain. It moves at a steady rate of 400 feet per minute until it stops suddenly. Andrew calls his friends to tell them he is stuck. They talk on the phone for 10 minutes until finally the ski lift begins moving again. What is the independent quantity? What is the dependent quantity?
Answer:
1.) Time in minutes
2.) Distance in feet.
Step-by-step explanation:
What is the independent quantity?
Independent quantity are the domain. In this question since the rate is 400 feet per minute, this can be refer to slope.
The independent quantity is therefore the time in minutes.
What is the dependent quantity?
Dependent quantity depends on independent quantity. Since time is the independent quantity, distance in feet will be the dependent quantity.
Factor completely 2x2 + 9x + 4. (1 point) (2x + 2)(x + 4) (2x + 2)(x + 2) (2x + 4)(x + 1) (2x + 1)(x + 4)
Answer:
(2x + 1)(x + 4)
Step-by-step explanation:
2x² + 9x + 4 cannot be factored normally - we must use the grouping technique (a > 1).
First, check for a GCF. Because there is not a GCF within this (factors of 9 are 1 and 3 - taking a 1 out is pointless), we will instead break the equation into two factors.
2x² will be apart of the first factor. You want to break the 9x into factors that will evenly break down with the 2x^2, so 3x will not work.
Your grouping factors should then be (2x^2 + 8x)(x + 4).
Then, take out the GCFs of the factors.
2x can come out of (2x^2 + 8x), so your new factor is 2x(x + 4). Your second factor set has no GCF, so you take out a 1 and get 1(x+4). In order to verify you did this correctly, the terms having the GCF distributed cannot be different in anyway.
Your factors are now (2x + 1)(x + 4) take the two GCFs and make them a factor set, then the second factor is the common factor.
Answer:
Answer is the fourth option
Step-by-step explanation:
-2n(5+n-8-3n) n =3 algebra
Answer:
54Step-by-step explanation:
[tex] - 2n(5 + n - 8 - 3n) \\ n = 3 \\ - 2(3)(5 + 3 - 8 - 3(3)) \\ - 6(5 + 3 - 8 - 9)[/tex]
[tex] - 6(8 - 8 - 9) \\ - 6( - 9) \\ = 54[/tex]
cameras actual price was $ 400. after discount its price was $280. calculate the percentage reduction in the price of the camera.
Answer:
30% discount
Step-by-step explanation:
Let the percent reduction be x%
Actual price =$400
Discounted price=$280
Therefore, by the problem => [tex]400-x%400=280[/tex]%*400=280
=>[tex]400-\frac{x}{100} *400=280\\400-4x=280\\-4x=280-400\\-4x=-120\\4x=120\\x=120/40\\x=30[/tex]
There was 30% discount on the camera
0.1m + 8 - 12n when 30 and n = 1/4
0.1m + 8 - 12n when 30 and n = 1/4
= 3+8-3
= 3+8-3= 8
8
When you use the midpoint formula can you take either points as x ,y? Why or why not ?
Answer:
Yes, we can take either points as x and y because addition is commutative
Step-by-step explanation:
First of all, the midpoint formula is given as;
(x, y) = [((x₁ + x₂)/2), ((y₁ + y₂)/2)]
For example, if we assume that we have two endpoints having coordinates as (2, 5) and (4, 7)
Now, let (2, 5) represent the first coordinate and (4, 7) represent the second coordinate.
Thus, Coordinates of midpoint = [((2 + 4)/2), ((5 + 7)/2)]
This gives;
(x, y) = (3, 6)
Now,if we change the order of the coordinates by making (4, 7) to be the first coordinate and (2, 5) to be the second coordinate. Thus;
Coordinates of midpoint = [((4 + 2)/2), ((7 + 5)/2)] = (3, 6)
We can see that the coordinates of the midpoint remains the same even after interchanging the coordinates as first and second.
This is because we are adding two numbers and addition is commutative (in commutative properties, changing the order of the operands will not change the result). Thus, it doesn't matter in which order we have the endpoints.