Answer:
there are 2 solutions in total
Step-by-step explanation:
x^2-4=0
x^2=4
x= ±2i
Answer:
x=±2
Step-by-step explanation:
x²-4=0
x²-2²=0
(x+2)(x-2)=0
either x+2=0,x=-2
or x-2=0,x=2
Sophia manages a landfill. She decides to measure the rate at which trash increases in volume to fill the landfill as the number of households served increases.
Answer:
[tex]\frac{m^3}{h}, \frac{cm^3}{h}, \frac{km^3}{h}[/tex]
Step-by-step explanation:
If you look at the objects thrown as garbage, it's a two- or three-dimensional item that takes up space and also has mass and this is a solid waste.
And the landfill that dumps such garbage is also three-dimensional.
Hence, the volume module, if the object inside is a solid, either would be
[tex]m^3,cm^4,Km^3[/tex]
As household numbers rise, landfill space increases.
So,
[tex]household\ number = Proportionality\times landfill\ space[/tex]
If H represents the number of household keeps, then it will be a sufficient unit for the purpose of Sophia that is
[tex]\frac{m^3}{h}, \frac{cm^3}{h}, \frac{km^3}{h}[/tex]
Hector is flying a kite. He has let out 86 feet
of string and is holding it 4 feet off the
ground. If the string is at an angle of
elevation of 42°15’30”, how high is the kite?
Answer:
Hector's kite is 61.84 feet from the ground.
Step-by-step explanation:
The angle of elevation of the kite is 42°15’30” when converted to decimals, it is [tex]42.258333^{0}[/tex] ≅ [tex]42.26^{0}[/tex]
Let the height of the kite to the horizontal of angle of elevation be represented as x. Applying the trigonometric function to the sketch of Hector's kite,
Sin θ = [tex]\frac{opposite}{hypotenus}[/tex]
Sin [tex]42.26^{0}[/tex] = [tex]\frac{x}{86}[/tex]
⇒ x = 86 x Sin [tex]42.26^{0}[/tex]
= 86 x 0.6725
= 57.835
x ≅ 57.84 feet
The height of Hector's kite from the ground = x + 4
= 57.84 + 4
= 61.84 feet
As a court reporter, your job is to take notes of everything that happens in court. After the first court session, you've recorded 47 lines of text. After the second session, you've recorded 33 lines of text. How many total lines of text did you record for the day?
Answer:
80 linesStep-by-step explanation:
In this problem we are expected to sum up the number of lines recorded during all court sessions for the day.
Also we know that the court report, reported for two (2) court session for that day.
Hence all the number of line is going to be from the 2 court sessions she reported
in the first court session we wrote 47 lines
in the second court session we reported 33 line
the total lines in all is 47+33= 80 lines
The total line recorded for the day is 80 lines
Which term is the question
Answer:
trinomial
Step-by-step explanation:
Given polynomial has three terms, therefore it is a trinomial.
can 4.7 be turned into a fraction
Answer:
Yes! It can
[tex]Fraction=4\frac{7}{10}[/tex]
Decimals can convert into fractions!
4 is the whole number
.70 is
70 out hundredths
7/10 or 7/100
So the fraction would be
[tex]4\frac{7}{10}[/tex]
Hope this helps!
[tex]Fishylikeswater[/tex]
Answer: 4 and 7/10
Step-by-step explanation: Using the place value chart below,
we can see that 4.7 means four and seven tenths.
This can be written as the mixed number 4 and 7/10.
I didn't understand this
help
for the “R=“
the choices are
-3
0
3
for the “S=“
the choices are
5
3
-3
Answers:
R = -3S = -3T = -9For each row, you're adding the values of 'a' and 'b'. The first row has 1+2 = 3.
When adding two negatives, add the positive versions of each number, then make the result negative. So -1 + (-2) can be thought of as 1+2 = 3, then you make everything negative.
When adding a negative to a positive, you'll subtract the positive version of each number. The final result is positive if the larger absolute value is positive, or otherwise it's negative. We have -4+1 that can be thought of as 4-1 = 3, but since the '4' is larger and it is negative, this means -4+1 = -3.
due soon!!
Find the measure of GE¯¯¯¯¯¯¯¯. A. 14 B. 20 C. 15 D. 16
Answer:
D. 16
Step-by-step explanation:
[tex] GH^2 = GF \times GE[/tex]
[tex] 12^2 = 9 \times (9+x - 2)[/tex]
[tex] 144= 9 \times (7+x)[/tex]
[tex] \frac{144}{9}= (7+x)[/tex]
[tex] 16= 7+x [/tex]
[tex] 16-7=x [/tex]
[tex] 9=x [/tex]
GE = 9 + x - 2 = 9 + 9 - 2 = 18 - 2
GE = 16
Answer:
D.16
Step-by-step explanation:
GE × GF = GH^2
9 × (9 + x - 2 ) = 12^2
63 + 9x = 144
9x = 81
x = 9
so, GE = 9 + x - 2
= 7 + 9
= 16
is the square root of 180 between 13 and 14
Answer:
The square root of 180 is:
13.416407865
So yes the square root of 180 IS between 13 and 14
Please please please please please help me
Answer:
[tex] {x}^{2} + 0x + 1[/tex]
Step-by-step explanation:
[tex]for \: g (fx) \:the \: function \: of \: f \: is \: inserted \: into \: the \: x \: for \: the \: g[/tex]
So the eqn becomes
[tex] ({x}^{2} - 1) + 2[/tex]
AND this equal to
[tex] {x}^{2} + 1[/tex]
Hence the variable x has 0 as its coefficient.
What is the value of the expression below when x = 3?
10x2 – 7x + 10
Answer:
79
Step-by-step explanation:
To find the value of [tex] 10x^2 – 7x + 10 [/tex], when x = 3, simply plug in the value of x in the expression and solve as follows:
[tex] 10(3)^2 – 7(3) + 10 [/tex]
[tex] 10(9) – 21 + 10 [/tex]
[tex] 90 – 21 + 10 [/tex]
[tex] 79 [/tex]
The value of [tex] 10x^2 – 7x + 10 [/tex], when x = 3, is 79
Answer:it's 79 or 49
q
Step-by-step explanation:
If the length of the given rectangle is increased by 7 and the width is decreased by 3, what is the rectangle's perimeter
Answer:
For a given length l and width w, the new perimeter is....
2(l + w) + 8
Step-by-step explanation:
Currently, the rectangle's perimeter is 2(l + w). You knew that.
Now, the question asked you to change l into l + 7, and w into w - 3. Substitute them, so we get
Perimeter New = 2(l + 7 w - 3) = 2 (l + w + 4)
Then, I chose to "pull out" + 4, so I multiply it with the 2. Hence, we get
Perimeter New = 2 (l + w) + 8
give two other names for cd
Answer:
Laser Disk, Digital Recording
Step-by-step explanation:
Which of the following is equal to the opposite of −45? −(−45) −45 −|−45| −|45|
Answer:
-(-45) and -|45|
Step-by-step explanation:
Opposite of a number can also me termed the conjugate of such number. For example, the conjugate (opposite) of a is -a.
Also any value in the modulus sign can either be a negative or positive value. For example |a| can be +a or -a.
According to the question, we are to find the numbers that are equivalent to opposite of -45 i.e which of them are conjugate of -45.
To do this, we are to select the values in the options that will return +45.
Let's look at each option.
For -(-45):
Since the product of two negative sign will give a positive(+), then -(-45) = +45 and hence the value is opposite of -45
For -45:
-45 is a negative value and can never be positive since 45 is not inside a modulus sign. Hence, -45 is not equal to opposite of -45.
For −|−45|, |-45| can only return a positive value since -45 is already in a modulus sign. What the modulus sign will do is convert it to positive value i.e |-45| = 45. Hence -|-45| ≈ -(45) which is not also equivalent to the opposite of-45.
For -|45|:
The value inside modules will return both +45 and -45, hence it can be written as -|45| = -(-45) = +45. This shows that -|45| is also equivalent to the opposite of -45.
Answer:
-(-45) and -|45|
Step-by-step explanation:
Graph the line with slope -3 passing through the point (5,1) .
Answer:
we know that,
y-y1=m(x-x1)
or, y-1=-3(x-5)
or, y-1=15-3x
or 3x+y-16=0 is the required equation
The graph of the line with slope -3 passing through the point (5,1) is attached.
The equation of the line in the slope-intercept form is y = -3x + 16.
The equation of the line in the standard form is 3x + y = 16.
What is the equation of a line?The equation of a line is the representation of a line on a coordinate plane (x-y plane), which shows the relation between x and y, for every point on the particular line.
The standard form of a line is ax + by = c, where x and y are variables and a, b, and c are constants.
The slope-intercept form of a line is y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept of the line.
What is the one-point formula of a straight line?The equation of a line passing through the point (x₁, y₁), having a slope m, is represented by the one-point formula: y - y₁ = m(x - x₁).
How do we solve the given question?We are asked to graph a line with a slope = -3, passing through the point (5, 1).
We use the one-point formula to determine the equation of this line, with slope m = -3, (x₁, y₁) = (5, 1).
Substituting these values in the equation y - y₁ = m(x - x₁), we get
y - 1 = -3(x - 5)
or, y = -3x + 15 + 1
or, y = -3x + 16.
or, 3x + y = 16
The equation of the line in the slope-intercept form is y = -3x + 16.
The equation of the line in the standard form is 3x + y = 16.
To graph this line we plot the points (5, 1) (as it is given that it passes through this point) and (0, 16) (as the y-intercept is at 16, so the line passes through the point (0, 16)). We join these points by a line and extend this line on both sides to get the required line.
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3. (2, 4), (-2, 2), (2, ο)
Is this set of numbers a function or not a function?
Answer:
not a function
Step-by-step explanation:
This is not a function
The input 2 goes to two different outputs
2 goes to the output of 4 and the output of 0
This makes it a relation and not a function
Consider the following set of data: 3, 6, 8, 15, 21, 22, 23 Define what is meant by “ measures of variation”. What is the interquartile range of data? What is the mean absolute deviation of the data?
Answer:
Below.
Step-by-step explanation:
A measure of variation is an estimate of the spread of the numbers.
For example the set of numbers 1 2 3 19 78 has a greater measure of variation than the set 1 2 3 5 9.
The interquartile range and the mean absolute deviation are measures of variation.
3 6 8 15 21 22 23
The median of the data is the middle number 15..
The lower quartile is 6 and the higher quartile is 22
The interquartile range is 22 - 6 = 16.
The mean absolute deviation (M.A.D.) is calculated as follows:
Mean = (3+6+8+15+21+22+23) / 7 = 98/7
= 14.
List the absolute differences from the mean
14 - 3 = 11
14-6 = 8
15-14 = 1
21-14= 7
22-14 = 8
23-14 = 9 ( all these have to be positive)
The sum of the differences is 11+8+1+7+8+9 = 44
So the MAD = 44/7 = 6.3 to nearest tenth.
Between which two consecutive whole numbers does the length of the diagonal fall?
Which whole number is it closer to? Use the drop-down menus to show your answer.
Answer:
4 and 5, closer to 4
Step-by-step explanation:
From the diagram above,
length of the diagonal = √18
√18 = 4.2426406871192
√18 is between 4 and 5
√18 is more than 4 by .2426406871192 but not up to 5
Rounding up 4.2426406871192 to an 1 significant figure,
We have 4
This means, the length of the diagonal, √18 is between 4 and 5 but it is closer to 4
Answer:
4 and 5, closer to 4
Step-by-ste
[tex]\sqrt18=4.24\\[/tex]
4.24 is closer to 4 than to 5
-8=v/3-3
solve for V
Answer:
-15 = v
Step-by-step explanation:
-8=v/3-3
Add 3 to each side
-8+3=v/3-3+3
-5 = v/3
Multiply each side by 3
-15 = v
Answer: v=-15
Step-by-step explanation:
Given
-8=v/3-3
Add 3 on both sides (addition property of equality)
-5=v/3
Multiply 3 on both sides (multiplication property of equality)
v=-15
Hope this helps!! :)
Please let me know if you have any question
Tara earns $8.50 an hour (after taxes) at the pizza place. She is scheduled to work four hours this afternoon. However, her friend Kayla called and asked her if she wants to go to the movie. A ticket to the movie costs $9.50. In addition, she always spends about $7 on snacks.
Answer:
2. Kayla's opportunity cost to go to the movie is $9.50
4. Tara's total cost of attending the movie is $50.5
Step-by-step explanation:
Complete question below:
Tara earns $8.50 an hour (after taxes) at the pizza place. She is scheduled to work four hours this afternoon. However, her friend Kayla called and asked her if she wants to go to the movie. A ticket to the movie costs $9.50. In addition, she always spends about $7 on snacks.
Which of the following statement are true? Select all that apply.
1. Tara's opportunity cost if she goes to work instead of the movie is $34.
2. Kayla's opportunity cost to go to the movie is $9.50.
3. There is no opportunity cost for Tara to go to the movie.
4. Tara's total cost of attending the movie is $50.5
5. Tara's opportunity cost if she goes to the movie instead of working is $34
Solution
Tara earns $8.50 per hour
She is scheduled to work for 4 hours
Total earnings=$8.50 × 4
=$34
Tara's opportunity cost of attending the movie instead of working is $34
Since, a ticket cost $9.50
And she always spend about $7 on snacks
Tara's total cost of going to the movies = opportunity cost of attending the movie + cost of tickets + cost of snacks
=$34 + $9.50 + $7
=$50.5
Opportunity cost refers to the cost of satisfying a want at the expense of another want. It can also be called REAL COST or TRUE COST.
Therefore,
2. Kayla's opportunity cost to go to the movie is $9.50
4. Tara's total cost of attending the movie is $50.5
2 and 4 are the answers
7 2/9 - 5 5/7 turn into a mixed number please :))
Answer:
12 1/9 is your answer.
Step-by-step explanation:
Since 7+5 is 12 you got your first part. Now you have to find a thing that matches which is 1/9
What is the approximate area of the triangle?
A)12.5
B)18
C)21.5
D)31
Answer:
21.5
Step-by-step explanation:
Counting the full squares: 16
Counting the squares that are more than 1/2: 6
The best estimate would be 21.5
This rule applies: rational + __________ = irrational.
Answer:
Rational+irrational =irrational is your answer.
Step-by-step explanation:
Hope it will help you :)
distance between (5, -3) and (9, 2).
Step-by-step explanation:
Using distance formula:
√(5 - 9)² + (-3 - 2)²
√(-4)² + (-5)²
√16+25
√41
Which pair of undefined terms is used to define the term parallel lines?
point and line
plane and line
point and ray
ray and line
Answer-
B) Plane and line
The pair which is undefined terms are used to define the term parallel lines is B. plane and line
What is meant by parallel line?Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect.
What are the properties of parallel lines?Properties of Parallel Lines
Corresponding angles are equal. Vertical angles/ Vertically opposite angles are equal. Alternate interior angles are equal. Alternate exterior angles are equal.
What is an example of a parallel?My dog not only likes to play fetch but also chase cars. Parallel: My dog not only likes to play fetch, but he also likes to chase cars. My dog likes not only to play fetch but also to chase cars. When you connect two clauses or phrases with a word of comparison, such as than or as, use parallel structure.
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Given g(x)=3x2+3 evaluate f(0) Please help me with this.
Answer:
Assume you meant: [tex]g(x) = 3x^{2}+3[/tex]
Answer is 3
Step-by-step explanation:
Replace x with 0:
[tex]g(0) = 3(0)^{2} +3[/tex] zero squared is zero
[tex]g(0) = 3(0) + 3[/tex]
[tex]g(0) = 0 + 3[/tex]
[tex]g(0) = 3[/tex]
Step-by-step explanation:
[tex]\huge\underline\bold\blue{ƛƝƧƜЄƦ}[/tex]
we have
[tex]g(x) = {3x}^{2} + 3[/tex]
in this we have x = 0
[tex]g(0) = 3( {0})^{2} + 3[/tex]
[tex]g(0) = 0 + 3[/tex]
[tex]g(0) = 3[/tex]
so we have x =3
Hope it helps
Molly can bake 3 cakes in 2 hours. How many cakes can she bake per hour?
Answer: 1.5 cakes per hour
Can someone help me find the domain and range of this graph?
Answer:
Domain: (-5, 6]
Range: [-3, 6]
Step-by-step explanation:
Domain is all x-values that can be inputted into function f(x).
Range is all the y-values outputted by function f(x) when we plug in x.
We see that our x-values span from -5 to 6. Since -5 is a open dot, we cannot input -5. Therefore, we have:
Domain: (-5, 6]
Parenthesis on -5 shows that it is not included and bracket on 6 shows it is included.
We see that our y-values span from -3 to 6. Since both points are closed dots, we can include both. Therefore, we have:
Range: [-3, 6]
Brackets on both numbers signify that both values are included in the graph.
Amy ran 8 miles. She recorded how long it took her to run each mile, rounded to the nearest 1/4 of a minute. How long did it take Amy to run her slowest and fastest mile combined?
Answer:
18 1/4
Step-by-step explanation:
To find how long it took Amy to run her fastest and slowest mile combined, we add the two values.
9\dfrac{2}{4}\text{ min} + 8\dfrac{3}{4}\text{ min}9
4
2
min+8
4
3
min9, start fraction, 2, divided by, 4, end fraction, start text, space, m, i, n, end text, plus, 8, start fraction, 3, divided by, 4, end fraction, start text, space, m, i, n, end text
Hint #44 / 5
\begin{aligned} 9\dfrac24+8\dfrac34&=(8+9)+\left(\dfrac{2}{4}+\dfrac{3}{4} \right)\\\\ &= 17+\dfrac{5}{4}\\\\ &=17+1\dfrac{1}{4}\\\\ &=18\dfrac{1}{4} \end{aligned}
9
4
2
+8
4
3
=(8+9)+(
4
2
+
4
3
)
=17+
4
5
=17+1
4
1
=18
4
1
Hint #55 / 5
It took Amy 18\dfrac1418
4
1
18, start fraction, 1, divided by, 4, end fraction minutes to run her fastest and slowest mile combined.
Disclaimer: The given question was incomplete, with the data missing. The complete question can be seen in the picture attached.
Analyzing and interpreting the given data, we can say that Amy took 18 1/4 minutes in total to run her slowest and fastest mile combined.
What are data analysis and interpretation?The process of attributing meaning to the acquired data and deciding the conclusions, relevance, and consequences of the results is known as data analysis and interpretation.
How do we solve the given question?We are given a data set, representing the time taken by Amy to run each mile while running 8 miles, nearest to 1/4th of a minute.
We are asked to find how long did it take Amy to run her slowest and fastest mile combined.
Analyzing the data, we can say that her slowest mile will be the one for which she took the maximum time, that is, 9 2/4 minutes. Whereas her fastest mile will be the one with the minimum time, that is, 8 3/4 minutes.
We are asked to tell the combined time for her slowest and the fastest mile, so we add times for both, to get
Combined time = 9 2/4 + 8 3/4
or, Combined time = 38/4 + 35/4
or, Combined time = 73/4
or, Combined time = 18 1/4.
∴ Analyzing and interpreting the given data, we can say that Amy took 18 1/4 minutes in total to run her slowest and fastest mile combined.
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factorise 6b²+3b+8b+5
Answer:
(6b + 5)(b + 1).
Step-by-step explanation:
6b² + 3b + 8b + 5
= 6b^2 + 11b + 5
= 6b^2 + 6b + 5b + 5
= 6b(b + 1) + 5(b + 1) b + 1 is common so:
= (6b + 5)(b + 1)
Answer:
( 6b + 5 ) ( b + 1 )
Step-by-step explanation:
6b² + 3b + 8b + 5
6b²+ 11b + 5
6b²+ 5b + 6b + 5
( 6b + 5 ) ( b + 1 )