Answer:
Step 1: Isolate the absolute value expression.
Step2: Set the quantity inside the absolute value notation equal to + and - the quantity on the other side of the equation.
Step 3: Solve for the unknown in both equations.
Step 4: Check your answer analytically or graphically.
Step-by-step explanation:
Answer:
Rewrite the absolute value equation as two separate equations, one positive and the other negative
Solve each equation separately
After solving, substitute your answers back into original equation to verify that you solutions are valid
Write out the final solution or graph it as needed
Step-by-step explanation:
PLEASE HELP ME I WILL GIVE 5 STARS TO THE FIRST ONE WHO GETS THIS RIGHT !
Answer:
Option 1 and option 4
Step-by-step explanation:
The inverse of 12^2 is the √12 so option 4 is correct. 12^1/2 also equals √12 so option 1 is also correct.
Answer:
12 [tex]\frac{2}{1}[/tex]
Step-by-step explanation:
Diagram shows helicopter H flying towards an island P
When the helicopter is 100 m above sea level, the pilot sees a man fishing from boat Q. Given the angles of depression of the island P and boat Q from H are 22° and 61.5° respectively.
Calculate the distance, in M, of PQ
Please help me to explain :(
Answer:
193.21 m
Step-by-step explanation:
make a vertical line down from the helicopter that is 100m
tan 61.5 = 100/x x = 54.3 (distance from the point directly below helicopter to boat)
tan 22 = 100/x x = 247.51 (distance from the point directly below helicopter to the island
247.51 - 54.3 = 193.21 (distance from boat to island)
A square has a perimeter of 48 in. Find the perimeter of a triangle with each side 4 inches longer than the side of the square.
Answer:
48 in.
Step-by-step explanation:
square
P = 4s
4s = 48 in.
s = 12 in.
triangle
s = 12 in. + 4 in.
s = 16 in.
P = 3s = 3(16 in.)
P = 48 in.
Whats the mean of the box plot 50 60 70 80 90 100
Answer:
75
Step-by-step explanation:
Mean = sum of all numbers / how many of numbers
=> 50 + 60 + 70 + 80 + 90 + 100 / 6
=> 450 / 6
=> 75
So, the mean of this data is 75.
what is the gcf of 3x^2 +9
Answer:v
Step-by-step explanation:
3(x^2+3)
the gcf is 3
Answer: 3 is the gcf
Step-by-step explanation:
3 is a factor of both 3 and 9. 1 is the other common factor. 3 is the greatest common factor. If you were looking at larger numbers with many common factors like 24 and 48, factors include 1,2,3,4,6,8,12,&24 You might find other smaller factors useful, but most of the time it's the gif that needs to be factored out: 3(x^2 + 3)
It takes a copy machine 6 minutes to complete a job. How many minutes are left on a job if 2/3 of the job is now complete?
2/3 of the job was completed in 4 minutes. the job left will be completed in 2 minutes
the probability that 2 randomly selected points from Q,R,S,T and W are noncollinear is
Answer:
2/5Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = Expected outcome/Total outcome
Since we are to find the probability that 2 randomly selected points from Q,R,S,T and W are non-collinear
Non collinear points are points that doesn't lie on the same straight line. From the diagram given, the two point that are non colliear are (QR, QS, QT and QW making 4 2random non collinear points. Hence out expected number of outcome is 4.
For the total possible outcome, we are to find the number of ways we can randomly select two points from the 5 points given and this can be done using the combination rule.
This can therefore be done in 5C2 number of ways.
5C2 = 5!/(5-2)!2!
5C2 = 5!/3!2!
5C2 = 5*4*3*2*1/3*2*2
5C2 = 5*2
5C2 = 10 different ways
Hence the total possible outcome is 10
Therefore, the probability that 2 randomly selected points from Q,R,S,T and W are noncollinear will be 4/10 = 2/5
Questions attached below (❁´◡`❁)
Problem 2
Josh forgot to apply the square root to 16 when he went from [tex](x-3)^2 = 16[/tex] to [tex]x-3 = 16[/tex]
Also, he forgot about the plus/minus.
This is what his steps should look like
[tex]x^2 - 6x - 7 = 0\\\\x^2 - 6x = 7\\\\x^2 - 6x +9= 7+9\\\\(x-3)^2= 16\\\\x-3= \pm\sqrt{16}\\\\x-3= 4 \text{ or } x-3= -4\\\\x= 7 \text{ or } x= -1\\\\[/tex]
There are two solutions and they are x = 7 or x = -1. To check each solution, you plug it back into the original equation
Let's try out x = 7
x^2 - 6x - 7 = 0
7^2 - 6(7) - 7 = 0
49 - 42 - 7 = 0
0 = 0 ... solution x = 7 is confirmed. I'll let you check x = -1
====================================================
Problem 3
We will have
a = 1, b = -4, c = 3
plugged into the quadratic formula below to get...
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-4)\pm\sqrt{(-4)^2-4(1)(3)}}{2(1)}\\\\x = \frac{4\pm\sqrt{4}}{2}\\\\x = \frac{4\pm2}{2}\\\\x = \frac{4+2}{2} \ \text{ or } \ x = \frac{4-2}{2}\\\\x = \frac{6}{2} \ \text{ or } \ x = \frac{2}{2}\\\\x = 3 \ \text{ or } \ x = 1\\\\[/tex]
The two solutions are x = 3 or x = 1. You would check this by plugging x = 3 back into the original expression x^2 - 4x + 3. The result should be zero. The same applies to x = 1 as well.
Nan left her house at 1 p.m. driving at a constant speed of 40 miles perhour. If she continues at that same speed for the entire trip, she will reach
her destination at 4:45 p.m. If Nan were to drive 10 miles per hour faster,
how much quicker would she arrive?
Answer:
45 minutes faster
Step-by-step explanation:
Distance:
40 x 3.75 = 150
If travel 50 miles/h:
150/50 = 3
3.75 - 3 = 0.75 of hour
45 minutes
Hope that helped!!! k
90 to the nearest tenth
Answer:
90
Step-by-step explanation:
Hey there!
Well 90.000 to the nearest tenth is just 90 because there is no decimal places to round.
Hope this helps :)
Answer:
90
Step-by-step explanation:
90 has 0 ones so 90 is just 90, but rounded...
Choose all of the expressions that are equal to −9. |−9| −(−9) −|−9| −|9| the distance from zero to nine the opposite of nine
Answer:
|−9|, −|−9| and −|9|Step-by-step explanation:
Before we choose all the expression that is equal to -9, we must understand that the modulus of a value can return both its positive and negative value. For example, Modulus of b can either be +b or -b i.e |b| = +b or -b
Hence the following expression are all equal ro -9
a) |−9| is equivalent to -9 because the absolute value of -9 i.e |−9| can return both -9 and 9
b) −|−9| is also equivalent to -9. The modulus of -9 is also equal to 9, hence negating 9 will give us -9. This shows that −|−9| = −|9| = −9
c) −|9| is also equivalent to -9. This has been established in b above.
Answer: -|-9|, -|9|, and the opposite of nine
Step-by-step explanation: The absolute value symbol is | |. |-9| is 9 but add that - to it and it's -9. The absolute value of 9 is 9, add the - to it to get -9.
the opposite of 9 is -9.
A zucchini plant in Darnell’s garden was 10 centimeters tall when it was first planted. Since then, it has grown approximately 0.5 centimeter per day. a. Write a rule to describe the function. b. After how many days will the zucchini plant be 18.5 centimeters tall?
Answer:The number of days it will grow to be 18.5 cm tall is 17 days.
Step-by-step explanation:
To find how many days it will grow until it reaches 18.5 centimeters, first find the difference of the new height by the old height.
So= 18.5-10= 8.5cm
8.5 is the centimeters it needs to grow to be 18.5 cm tall.
Then, divide it by the number of centimeters it will grow in one day, which is 0.5, to find the days it grew 8.5 cm.
So= 8.5÷0.5= 17
I hope this helps! Ask me if you're confused.
Diego and Max are buying soft drinks for a neighborhood picnic. Each person is
expected to drink one can of soda. Diego says that if you multiply the unit price for a
can of soda by the number of people attending the picnic, you will be able to
determine the total cost of the soda. Max says that if you divide the cost of a 12-
pack of soda by the number of sodas, you will determine the total cost of the sodas.
Which choices best illustrates who is correct and why?
Max is incorrect because he calculated the cost of one can of soda
Diego is incorrect because he calculated the price of one can of soda
Max is correct because the total cost divided by the number of sodas gives you
the total cost of the sodas
Answer:
D. Diego is correct because the price of one can of soda multiplied by the number of sodas needed will give you the total cost of the soda.
Step-by-step explanation:
Each person is
expected to drink one can of soda.
Let p=price of each soda
q=number of people in the picnic
Total cost of soda=price of each soda × Total people attending the picnic
Total cost of soda=p×q
Diego says that if you multiply the unit price for a can of soda by the number of people attending the picnic, you will be able to
determine the total cost of the soda.
Max says that if you divide the cost of a 12-pack of soda by the number of sodas, you will determine the total cost of the sodas
A. Max is incorrect because he calculated the cost of one can of soda
B. Diego is incorrect because he calculated the price of one can of soda
C. Max is correct because the total cost divided by the number of sodas gives you the total cost of the sodas
D. Diego is correct because the price of one can of soda multiplied by the number of sodas needed will give you the total cost of the soda.
Please help! I’ve tried every site and nothing has helped
The answer is 11.8
Answer:
11.8%
Step-by-step explanation:
Here in this question, we want to find the probability of no success in the binomial experiment for 6 trials.
Let p = probability of success = 30% = 30/100 = 0.3
q = probability of failure = 1-p = 1-0.3 = 0.7
Now to calculate the probability, we shall need to use the Bernoulli approximation of the binomial theorem.
That would be;
P(X = 0) = 6C0 p^0 q^6
6C0 is pronounced six combination zero
= 6 * 0.3^0 * 0.7^6 = 1 * 1 * 0.117649 = 0.117649
This is approximately 0.1176
If we convert this to percentage we have 11.76%
But we want our answer rounded to the nearest tenth of a percent and that is 11.8%
Please please please please help
Answer:
m = 9
Step-by-step explanation:
8/12 = 6/m
8m = 72
m = 9
Evaluate the function below at x=5. Then, enter your solution. f(x)=3(2)^x
Answer:
Solution: f(5) = 96
Step-by-step explanation:
f(5) = 3(2)^5
f(5) = 3 (2 × 2 × 2 × 2 × 2)
f(5) = 3 (32)
f(5) = 96
Figure A is a scale image of Figure B. What is the value of x?
Answer:
x=30
Step-by-step explanation:
to find the value of x you have to find K(constant number).
[tex]\frac{x}{45}=\frac{18}{27}\\\frac{x}{45}=\frac{2}{3}\\ 3(x)=45*2\\3x=90\\x=\frac{90}{3}\\ x=30[/tex]
Answer:
The value of x is 30
Step-by-step explanation:
Step 1: Find the scale factor
[tex]\frac{FA}{F B} =\frac{45}{27}[/tex]
Step 2: Use the scale factor to solve for x
[tex]\frac{45}{27} =\frac{x}{18}[/tex]
[tex](45)(18) = 27x[/tex]
[tex]810 = 27x[/tex]
[tex]x = 30[/tex]
Therefore x = 30
Give the values of a, b, and c needed to write the equation's general form.
1/4x^2+5=0
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Let's solve your equation step-by-step.
[tex]\frac{1}{4} x^2+5=0[/tex]
For this equation: [tex]a=0.25, b=0, c=5[/tex]
[tex]0.25x^2 + 0x + 5 = 0[/tex]
Step 1: Use quadratic formula with [tex]a=0.25, b=0, c=5.[/tex]
[tex]x = \frac{-b ± \sqrt{b^2 - 4ac} }{2a}[/tex]
[tex]x = \frac{-(0) ± \sqrt{(0)^2 -4 (0.25) (5) } }{2(0.25)}[/tex]
[tex]x = \frac{0 ± \sqrt{-5} }{0.5}[/tex]
Answer : No Real Solutions.
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
If this helped you, could you maybe give brainliest..?
Also Have a great day/night!
❀*May*❀
The school's square parking lot has an
area of 3025 ft2. What is the length of each
side of the parking lot?
Answer:
The answer is 55ftStep-by-step explanation:
Since the school's parking lot is a square,
Area of a square = l²
where l is the length of one side
From the question
Area = 3025ft²
We have
3025 = l²
Find the square root of both sides
l = √3025
l = 55ft
The length of each side of the parking lot is 55ft
Hope this helps you
Which number line best shows how to solve −8 − (−2)? A number line from negative 10 to 10 is shown, with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 2. A number line from negative 10 to 10 is shown, with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to 2. A number line from negative 10 to 10 is shown, with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 6. A number line from negative 10 to 10 is shown, with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to 6.
Answer:
A number line from negative 10 to 10 is shown, with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 6
Step-by-step explanation:
A number line is a straight line with numbers placed at equal intervals. Positive numbers are placed to the right of 0 and negative numbers are placed to the left of zero.
When a number (x) is added x unit is moved to the right while if a number (x) is subtracted x units is moved to the left.
To solve -8 - (-2) = -8 + 2
Given a A number line from negative 10 to 10 with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8 then since 2 is added, we move 2 units right from negative 8 to negative 6.
Answer:
C (3rd option)
Step-by-step explanation:
simplified the top one
he greatest common factor of each term in the expression 60 a b minus 72 b is 12b. Which choice shows the expression written as a product?
Answer:
Hey there!
60ab-72b
12b(5a-6)
The GCF is 12b.
Let me know if this helps :)
Answer:
b
Step-by-step explanation:
An important factor in selling a residential property is the number of people who look through the home. A sample of 17 homes recently sold in the Buffalo, New York, area revealed the mean number looking through each home was 19 and the standard deviation of the sample was 4 people.
Develop a 98 percent confidence interval for the population mean. (Round your answers to 2 decimal places.)
Confidence interval for the population mean is between and ?
Answer:
Confidence interval for the population mean is between 15 homes and 19 homes
Step-by-step explanation:
Given that:
Sample (n) = 17 homes, mean (μ) = 19 homes, standard deviation (σ)= 4 people and confidence (C) = 98% = 0.98
α = 1 - C = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01.
The z score of 0.01 (α/2) corresponds to the z score of 0.49 (0.5 - 0.01) which from the normal distribution table is 2.33
The margin of error (E) is:
[tex]E=z_{0.01}*\frac{\sigma}{\sqrt{n} } =2.33*\frac{4}{\sqrt{19} }=2[/tex]
The confidence interval = μ ± E = 17 ± 2 = (15, 19)
Confidence interval for the population mean is between 15 homes and 19 homes
The pepper plant has 2/3 as many fruits on it as the tomato plant has. The tomato plant has 9 fruits on it. How many fruits does the pepper plant have on it?
Answer:
The pepper plant has 15 fruits on it.
Step-by-step explanation:
Let the tomato plant have x plants. Let the pepper plant have y plants. Since the pepper plant has 2/3 more fruits on it than the tomato plant, we have that y - x = 2x/3
collecting like terms,
y = 2x/3 + x
The above is the number of plants the pepper plant has.
y = 2x/3 + x
y = (2x + 3x)/3
y = 5x/3
Since x = number of fruits on tomato plant = 9, then
y = 5x/3
y = 5(9)/3
y = 5 × 3
y = 15
Since y = number of fruits on pepper plant = 15
So, the pepper plant has 15 fruits on it.
A zoo train ride costs $4 per adult and $1 per child. On a certain day, the total number of adults (a) and children (c) who took the ride was 27, and the total money collected was $60. What was the number of children and the number of adults who took the train ride that day, and which pair of equations can be solved to find the numbers? 1) 11 children and 16 adults Equation 1: a + c = 27 Equation 2: 4a + c = 60 2) 16 children and 11 adults Equation 1: a + c = 27 Equation 2: 4a + c = 60 3) 11 children and 16 adults Equation 1: a + c = 27 Equation 2: 4a − c = 60 4) 16 children and 11 adults Equation 1: a + c = 27 Equation 2: 4a − c = 60
Answer:
11 adults and 16 children
Step-by-step explanation:
a + c = 27 and 4a + c = 60
3a = 60 - 27 = 33
a= 11
so c = 16
(If gets it right get's brainliest)If the hypotenuse of an isosceles right triangle is 14, what is the area of the triangle?
Answer:
49 unit²
Step-by-step explanation:
Right triangle with equal legs given, let the leg be x.
Hypotenuse of isosceles right triangle is
√x² + x² = x√2Area of triangle:
1/2ah= 1/2x²Since we have hypotenuse = 14 units:
x√2=14x= 14/√2Then area:
1/2x² = 1/2*(14/√2)² = 1/2*14²/2 = 7² = 49 unit²Solve for d.
4d - 4 = 5d – 8
d =
Answer:
Step-by-step explanation:
-d - 4 = -8
-d = -4
d = 4
Answer:
d= 4
Step-by-step explanation:
4d - 4 = 5d – 8
Subtract 4d from each side
4d-4d - 4 = 5d-4d – 8
-4 = d-8
Add 8 to each side
-4+8 = d-8+8
4 =d
what is the perimeter of the rhombus ?
Answer:
20 units
Step-by-step explanation:
To find the hypotenuse length of one of the sides of this rhombus we have to use the pythagoram theorem.
if you make the point (1,0) the origin, we can see that it forms a triangle, with a base of 3, and a height of 4, next to the BE line.
a^2+b^2=c^2
9+16=c^2
25=c^2
c=5
if each diagnol length is 5 units long, the perimeter is
20 units.
Answer:
20 units.
Step-by-step explanation:
Formula for the perimeter of a rhombus = 4a.
Meaning all sides multiplied by 4
The point (1,0) is made A.
From D to F is 8 units, and from E to G is 6 units. Half of 6 is 3, and half of 8 is 4.
Imagine a right-angled triangle on one side of the rhombus(eg. ∆GAD), meaning that you'll have to find the hypotenuse.
*Use Pythagoras Theorem*
x² = 3² + 4²
x² = 9 + 16
x = √25
x = 5
The perimeter of the rhombus if one side is 5 units:
5 units × 4 sides = 20 units.
-5^2 find the power
Answer:
-25
Step-by-step explanation:
Answer:
Hey there!
When we have a^b, b is the power.
Thus, in -5^2, 2 is the power.
Let me know if this helps, or if you need more help :)
I need domain and range
Answer:
Domain: all real numbers/ (-inf,inf)/ -inf<x<inf
Range: all real numbers greater than -4/ [-4,inf)/ -4≤y<inf
Step-by-step explanation:
the graphs/equations of ALL quadratics (parabolas) have a domain of all real numbers
The vertex of the parabola is at y=-4 so the range cannot be any less than that, and then both ends point up, so they will continue on for infinity.
Hope i could help!
in this figure ST || QR, PT = 4cm, TR = 8cm, area of PQR = 90cm^2. Find PT:TR please help me
Answer: The required ratio is PT:TR = 1:2.
Step-by-step explanation:
Given: In triangle PQR, ST || QR, PT = 4cm, TR = 8cm, area of PQR = 90 cm².
To find : PT:TR
.i.e. Ratio of PT to TR.
Here, PT:TR[tex]=\dfrac{PT}{TR}[/tex]
[tex]=\dfrac{4\ cm}{8\ cm}[/tex]
Divide numerator and denominator by 4 , we get
[tex]\dfrac{1}{2}[/tex]
Therefore, the required ratio is PT:TR = 1:2.
