Answer:
x≥-3
Step-by-step explanation:
the bracket means the the number is inclusive, so the answer would be
x≥-3
Final answer:
To convert the interval [-3,∞) to inequality notation, we would write x ≥ -3, indicating that x includes -3 and extends to positive infinity without an upper bound.
Explanation:
To convert the interval notation [-3,∞) to inequality notation using the variable x, we consider the meaning of the interval. The square bracket [ indicates that the number -3 is included in the interval, which corresponds to x ≥ -3. The infinity symbol (∞) suggests that there is no upper bound to the values of x, hence the interval does not include any particular largest number, which is why the parenthesis ) is used rather than a square bracket. Therefore, the equivalent inequality notation for the interval [-3,∞) is x ≥ -3.
Find the number, if 1.5 of it is 30
Answer is 30
Step-by-step explanation:
1.5 of X = 30
1.5*X = 30
X = 30/1.5
= 20
Answer:
20
Step by step explanation:
30/1.5
=20
y=x^(2)-12x+40 in vertex form
Answer:
[tex]y=(x-6)^2+4[/tex]
Step-by-step explanation:
Vertex Form Of The Parabola
The equation of a parabola can be expressed in either standard or vertex form. The standard form is
[tex]y=ax^2+bx+c[/tex]
and the vertex form is
[tex]y=a(x-h)^2+k[/tex]
Where (h,k) it the vertex of the parabola
Transforming one into the other form is easily achieved by applying simple algebra .
Our function is
[tex]y=x^2-12x+40[/tex]
Completing squares, we have
[tex]y=x^2-12x+36+40-36[/tex]
Reducing
[tex]\boxed{y=(x-6)^2+4 }[/tex]
The vertex of the parabola is the point (6,4)
Final answer:
To convert the quadratic equation y = x^2 - 12x + 40 into vertex form, the completing the square method is employed, resulting in y = (x - 6)^2 + 4, showing the vertex at (6, 4).
Explanation:
Converting a Quadratic Equation to Vertex Form
The question asks how to convert the quadratic equation y = x2 - 12x + 40 into its vertex form. The vertex form of a quadratic equation is y = a(x - h)2 + k, where (h, k) is the vertex of the parabola. To convert the given quadratic equation into vertex form, we'll use completing the square method.
Start with the original equation: y = x2 - 12x + 40.Factor out the coefficient of x2, which is 1 in this case, so this step doesn't change the equation.Rewrite the equation focusing on the x-terms: y = (x2 - 12x) + 40.To complete the square, take half of the coefficient of x (which is -12/2 = -6), square it (-62 = 36), and add and subtract it inside the parenthesis: y = (x2 - 12x + 36) - 36 + 40.Simplify and rewrite: y = (x - 6)2 + 4.This shows the quadratic equation in vertex form with the vertex at (6, 4).
Steve is driving 440 miles to visit the Grand Canyon he drives at an average rate of 55 mph explain how you could find the amount of time it will take Steve to get to the Grand Canyon
Answer:
8 hour.
Step-by-step explanation:
because for it takes 1 hour for 55 miles .
so,
here, divide the 440/55 =8 hours.
explanation,
it takes 1 hour to complete the 55 miles and here we have to complete the 440 miles.
so, above we divide the 440 miles by 55 miles for hour. result =8 hour
to verify the answer.
you can multifly by 8 * 55 and result=440miles. because it is directily propotional.
for another to verify the answer.
dived the 440/8 and result comes=55 miles / hour.becauseit is directly propotional.
Therefore, it will take Steve approximately 8 hours to drive to the Grand Canyon.
Explanation:To find the amount of time it will take Steve to get to the Grand Canyon, you can divide the distance he needs to travel (440 miles) by his average rate (55 mph). This will give you the time it takes in hours:
Time = Distance / Rate
So, in this case:
Time = 440 miles / 55 mph = 8 hours
Therefore, it will take Steve approximately 8 hours to drive to the Grand Canyon.
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15. At a school for, 70% of the people are under 16 years old. One of the people rema
there are 21 teachers at the fair how many people are there at the far total
h. 125
Answer:
210 people are there at the fair
Step-by-step explanation:
Let the total number of people at the fair = X
People under 16 years old = 70% of X = 0.7 X
People remaining = Total number of people - Under 16 years
= X - 0.7X = 0.3X
The number of teachers = 1/3 of People remaining = 1/3 of 0.3X
Since there are 21 teachers
1/3 of 0.3X = 21
1/3 x 0.3X = 21
0.1X = 21
Divide both sides by the coefficient of X
0.1X/0.1 = 21/0.1
X = 210
That is 210 people are there at the fair
Rearrange the equation so n is the independent variable.
3m – 2n = 12
To make 'n' the independent variable, solve the equation 3m - 2n = 12 by isolating n to obtain n = (3/2)m - 6.
Explanation:To rearrange the equation 3m - 2n = 12 so that n is the independent variable, you'll want to solve for n. Here's how you do it step by step:
Start with the original equation: 3m - 2n = 12.Isolate the term containing n by moving the other terms to the opposite side of the equation: -2n = -3m + 12.Divide both sides of the equation by -2 to solve for n: n = (3/2)m - 6.This way, n is now expressed as a function of m, making n the independent variable in the equation.
In the equation below, for what value of c does x = 4?
1 / (2x + 4) = 3x-c
Answer:
Option D.
Jenn's answer is not correct. She got it substituting [tex]c=4[/tex] into the equation and solving for "x".
Step-by-step explanation:
Given the following equation:
[tex]\frac{1}{2}(2x + 4) = 3x-c[/tex]
Since you need that [tex]x=4[/tex], you hace to substitute that value into the equation:
[tex]\frac{1}{2}(2(4) + 4) = 3(4)-c[/tex]
Now you need to solve for "c":
[tex]\frac{1}{2}(8 + 4) = 12-c\\\\\frac{12}{2}= 12-c\\\\6=12-c\\\\c+6=12\\\\c=12-6\\\\c=6[/tex]
Therefore for a a value of [tex]c=6[/tex], you get [tex]x=4[/tex]
Then, the you can identify that the correct answer is the one given in the Option D.
Jenn made a mistake, because she substituted [tex]c=4[/tex] into the equation and then solve for "x":
[tex]\frac{1}{2}(2x + 4) = 3x-(4)\\\\x+2=3x-4\\\\2+4=3x-x\\\\6=2x\\\\\frac{6}{2}=x\\\\x=3[/tex]
To determine the value of c when x equals 4 in the given equation, substitute x with 4 and solve for c. The resulting value of c is approximately 11.9167.
Explanation:To find the value of c for which x = 4 in the equation 1 / (2x + 4) = 3x - c, we start by substituting x with 4:
1 / (2×4 + 4) = 3×4 - c
1 / (8 + 4) = 12 - c
1 / 12 = 12 - c
Now we solve for c:
1 / 12 = 12 - c
c = 12 - 1 / 12
c = 12 - 0.0833
Finally, we find the value of c:
c = 11.9167
Therefore, for x = 4, the value of c is approximately 11.9167.
What is the best estimate for this sum? 1/8+1/6
The best estimate for the sum of 1/8 and 1/6 is 5/24.
Explanation:The best estimate for the sum of 1/8 and 1/6 is 5/24.
To find the sum of fractions, we need to find a common denominator, which is the least common multiple of the denominators. In this case, the LCM of 8 and 6 is 24.
Thus, we can rewrite 1/8 as 3/24 and 1/6 as 4/24.
Adding 3/24 and 4/24 gives us a total of 7/24, which can be simplified to 5/24.
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The best estimate for the sum of 1/8 and 1/6 is 1/4. Thus, the closest estimate is Option A.
To determine the best estimate for the sum of 1/8 and 1/6, we can use approximate fractions that are easier to work with. 1/8 is approximately equal to 0.125 and 1/6 is approximately equal to 0.167. Adding these decimal values together gives us:
0.125 + 0.167 ≈ 0.292
Given this, we can conclude that the sum will be closer to 1/4 than to 1/2 or 1. So, the best estimate for the given sum is Option A.
Complete question:
What is the best estimate for this sum?
1/8+1/6
A. The sum will be close to 1/4.
B. The sum will be close to 1/2.
C. The sum will be close to 1.
At West Painting, they get about three calls a day asking for an estimate of the cost for having the interior of a house painted. To write
up an estimate for the cost of a job, they need to know how much paint a job will take. If they average painting of a room with
5 of a gallon of paint, then they can paint, on average, 4 rooms per gallon
Answer:
West Painting can paint, on average, 1 7/8 rooms per gallon of paint
Complete statement and question:
At West painting, they get about three calls a day asking for an estimate of the cost for having the interior of a house painted. To write up an estimate for the cost of a job, they need to know how much paint a job Will take. If they average painting 3/4 of a room with 2/5 of a gallon of paint, then they can paint, on average ______ rooms per gallon.
Source:
Previous question that can be found at brainly
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Amount of paint needed to paint 3/4 of a room = 2/5 of a gallon
2. They can paint, on average how many rooms per gallon?
Let's use the Rule of Three Simple to answer this question, this way:
Paint Rooms
2/5 gallon 3/4
1 gallon x
x = Number of rooms on average painted with one gallon of paint
x * 2/5 = 3/4 * 1
x = 3/4 / 2/5
x = 3/4 * 5/2 = 15/8 = 1 7/8
West Painting can paint, on average, 1 7/8 rooms per gallon of paint
Water tank A has a capacity of 250 gallons and is 77% full. Water Tank B is 68% full. The ratio of the capacity of tank A to tank B is 5 : 14. What is the capacity of tank B?
Answer:
Water tank A has a capacity of 250 gallons and is 77% full. Water Tank B is 68% full. The ratio of the capacity of tank A to tank B is 5 : 14. What is the capacity of tank B?
Step-by-step explanation:
Water tank A has a capacity of 250 gallons and is 77% full. Water Tank B is 68% full. The ratio of the capacity of tank A to tank B is 5 : 14. What is the capacity of tank B?
by Thursday the Cutters and sewers in a clothing Factory had made 280 jackets. This is 87 1/2 % of the total number of jackets they were expected to make for the week. What is the total number of jackets the workers had to make that week?
Answer:
320
Step-by-step explanation:
87 1/2% (same as 87.5%) " of " the total jackets " is" 280
let j represent the total jackets
turn ur percent to a decimal....87.5% = 0.875
" of " means multiply , " is " means equals
0.875j = 280
j = 280 / 0.875
j = 320 <====== ur answer
Final answer:
The workers at the clothing factory were expected to make a total of 320 jackets for the week, as 280 jackets represented 87.5% of their weekly target.
Explanation:
To find the total number of jackets the workers were expected to make for the week, we'll set up a proportion where 87.5% corresponds to the 280 jackets they had made by Thursday. We know that 87.5% can also be expressed as the fraction 7/8. Therefore, if 7/8 of the total is 280 jackets, we need to divide 280 by 7 and then multiply by 8 to find the total number of jackets.
First, calculate the number of jackets corresponding to 1/8 of the total:
280 jackets
7 (parts) = 40 jackets
Next, multiply the value of 1/8 of the total by 8 to get the full 100%:
40 jackets
8 (parts) = 320 jackets
So, the workers were expected to make a total of 320 jackets for the week.
What is the slope of the line that passes through the points (-7, -7) and (-7, 1)? Write your answer in simplest form.
Answer:
undefined, stays on x so straight vertical - vertical line is undef slope
Answer: The slope is undefined
Step-by-step explanation:
The slope of a line is calculated using the formula :
m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]x_{1}[/tex] = -7
[tex]x_{2}[/tex] = -7
[tex]y_{1}[/tex] = -7
[tex]y_{2}[/tex] = 1
Substituting the values into the formula , we have :
m = [tex]\frac{1-(-7)}{-7-(-7)}[/tex]
m = [tex]\frac{8}{0}[/tex]
m = undefined
Use the given information to write the equation of each line
Passing through (1,-4) and (-2,5)
Answer:
y = -3x - 1Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have two points (1, -4) and (-2, 5).
Substitute:
[tex]m=\dfrac{5-(-4)}{-2-1}=\dfrac{5+4}{-3}=\dfrac{9}{-3}=-3[/tex]
Substitute the value of a slope and the coordinates of the point (1, -4) to the equation of a line:
[tex]-4=-3(1)+b[/tex]
[tex]-4=-3+b[/tex] add 3 to both sides
[tex]-4+3=-3+3+b[/tex]
[tex]-1=b\to b=-1[/tex]
Finally:
[tex]y=-3x-1[/tex]
g(x) = -x2 + 12x - 32
In vertex form
Answer: g(x) = -(x - 6)² + 4
Step-by-step explanation:
g(x) = -x² + 12x - 32
g(x) = -(x² - 12x) - 32
g(x) = -(x² - 2 × x × 6 + 6² - 6²) - 32
g(x) = -[ (x - 6)² - 36 ] - 32
g(x) = -(x - 6)² + 36 - 32
g(x) = -(x - 6)² + 4
Here, (6,4) is vertex.
evaluate 2-(-4)+(-y) where y = 7
Answer:
-1
Step-by-step explanation:
It’s just simple don’t worry just look I won’t make you need the explanation god bless :)
Pick the correct equation for the line below:
y=x^2 y + 90
y=3x + 90
y = 90x - 10
y = -10x + 90
Answer:
none of above because the correct equation is y= -3x+90
Please help me solve these three interval notations!!!!
Answer:
i) [0,4)
ii) [-2,-10]
iii) (-6,-4)
Step-by-step explanation:
i) the interval notation shown in the figure for the first option is [0,4) . Square bracket is used when an end value is included in the range as indicated by the black circle and a normal bracket is used to indicate when the end value is not included in the range as indicated by the white circle.
ii) the interval notation for the second option is given as [-2, 10].
iii) the interval notation for the third option is given by (-6, -4)
a company pays its salespeople $2,000 a month and a commission of 18% of their total sales (T). which of the following equations represents a salespersons total monthly income (I) ?
Answer:
2,360
Step-by-step explanation:
18% of 2,000 is 360
(0.18)*(2,000)=360
2,000 + 360 = 2,360
Answer: I=2000 + 0.18 T
Step-by-step explanation:
Enter an algebraic expression that represents the difference between e squared and twenty-one.
Answer:
e
[tex]d = e {}^{2} - 21 [/tex]
Answer:
e
Step-by-step explanation:
d = e {}^{2} - 21
A photographer stands 60 yards from the base of a lighthouse and observes that the angle between the ground and the top of the lighthouse is 41°. How tall is the lighthouse?
The height of lighthouse is 52.2 yards
Solution:
Given that photographer stands 60 yards from the base of a lighthouse and observes that the angle between the ground and the top of the lighthouse is 41 degree
The diagram is attached below
Consider a right angled triangle ABC
AB is the height of the lighthouse
BC is the distance between the base of a lighthouse and Photographer
As per given, BC = 60 yards
Angle between the ground and the top of the lighthouse is 41 degree
Angle ACB = 41 degree
To find: height of lighthouse i.e AB = ?
We know that,
[tex]tan(\angle ACB) = \frac{Perpendicular}{Base}[/tex]
Here Base is BC and perpendicular is AB
[tex]\tan 41^{\circ}=\frac{A B}{B C}[/tex]
Substituting the values,
[tex]\begin{aligned}&\tan 41^{\circ}=\frac{A B}{60}\\\\&0.8692=\frac{A B}{60}\\\\&A B=0.8692 \times 60=52.157 \approx 52.2\end{aligned}[/tex]
Thus the height of lighthouse is 52.2 yards
Answer:
52.2
Step-by-step explanation:
It was correct on my assignment
Write an equation that represents the sum of b and 5x2
Answer:
The expression that represents the sum of b and [tex]5x^2[/tex] is [tex]b+5x^2[/tex]
Step-by-step explanation:
Given that the sum of b and [tex]5x^2[/tex]
To find the expression that represents the sum of b and [tex]5x^2[/tex] :
The sum of b and [tex]5x^2[/tex] can be written as [tex]b+5x^2[/tex]
Therefore The sum of b and [tex]5x^2[/tex] is [tex]b+5x^2[/tex]
The expression that represents the sum of b and [tex]5x^2[/tex] is [tex]b+5x^2[/tex]
Which expressions are polynomials?
Select each correct answer.
6 + w
2x4−y
z + 1
y2−y√3+4
Answer:
It is 6+w, z=1, and 2x^4-y
Step-by-step explanation:
The expressions which are polynomials are;
6+ w2x⁴ - yz + 1y² - y√3 + 4What is a polynomial?A polynomial by definition is an expression which is composed of variables, constants and exponents, which are combined using the mathematical operations including addition, subtraction, multiplication and division.
On this note, all of expressions are polynomials.
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Evaluate
c
2
−
3
+
6
d
2
c
−3+
d
6
start fraction, c, divided by, 2, end fraction, minus, 3, plus, start fraction, 6, divided by, d, end fraction when
c
=
14
c=14c, equals, 14 and
d
=
3
Answer:
The answer = 6
Step-by-step explanation:
Given expression:
[tex]\frac{c}{2}-3+\frac{6}{d}[/tex]
To evaluate the given expression, when [tex]c=14[/tex] and [tex]d=3[/tex]
Solution:
We have:
[tex]\frac{c}{2}-3+\frac{6}{d}[/tex]
Plugging in [tex]c=14[/tex] and [tex]d=3[/tex] in the given expression, to evaluate.
⇒ [tex]\frac{14}{2}-3+\frac{6}{3}[/tex]
Evaluating:
⇒ [tex]7-3+2[/tex]
⇒ 6 (Answer)
Answer:
hmm 6
Step-by-step explanation:
Slope=2; (14,33)
What is the slope
Step-by-step explanation:
Hi! I am a little confused because in this question they would normally ask for the equation of the line but if you are wondering what the slope is, it says in the information that the slope is 2. I will solve for the line equation anyway though.
A line has this form: y=mx+b.
For this question they will want us to give the answer with x and y as variables (letters) and m and b (the slope and y-intercept respectivly) with numerical values.
First, we can put in the point into the equation. The point given is (14,33) so the x value is 14 and they y value is 33.
y=mx+b
33=m(14)+b
We know the slope is 2 (from the given information) so we can substitute that in for m.
33=(2)(14)+b
Solving for b, the Y-intercept, we get b=5.
Perhaps your question was "what is the Y-intercept" and then this would be the answer.
Finally, the final equation for the line is:
y=2x+5
Hope this helps!
PLEASE ANYONE!!!
The table below shows selected points from a function.
The rate of change for the interval shown in the table is
A. constant
B. not constant
part b
A. linear
B. not linear
What’s 448+1.75+80.3 step by step
Answer:
530.05
Step-by-step explanation:
you add 448 and 1.75 together, which is 449.75, then you add 449.75 and 80.3 together, which adds up to 80.3 hope this helps :)
Peter needs to sell 40 candy bars to raise money for his basketball team. He sold 16 bars last week and 18 bars this week. How many more candy bars does Peter need to sell?
16+18 = 34
40 - 34 = 6
He needs to sell 6 more candy bars.
16 please like I’m dying here
Answer:
well i need to see the graph
Step-by-step explanation:
Both forms are equivalent, just different ways to write the same thing
==============================================
Explanation:
Use the slope formula first
The points we plug in are (x1,y1) = (-3,4) and (x2,y2) = (6,1)
m = (y2-y1)/(x2-x1)
m = (1-4)/(6-(-3))
m = (1-4)/(6+3)
m = (-3)/(9)
m = -1/3
The slope of the line is -1/3
Use one of the points, say the point (x,y) = (-3,4) and the slope we just found with y = mx+b. The goal is to solve for b
y = mx+b
4 = (-1/3)*(-3) + b
4 = 1 + b
4-1 = b
3 = b
b = 3
We have m = -1/3 as the slope and b = 3 as the y intercept
Therefore, the equation in slope intercept form is y = (-1/3)x + 3
In standard form, Ax+By = C, this is is equivalent to x+3y = 9 after we multiply both sides by 3, then add x to both sides.
what is the equation of a line that passes through (1,3) and (4,9)
y = 2x + 1 is the equation of a line that passes through (1,3) and (4,9)
Solution:
Given that we have to write the equation of a line that passes through (1,3) and (4,9)
Let us first find the slope of line
The slope of line is given as:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Here the given points are (1,3) and (4,9)
[tex](x_1, y_1) = (1, 3)\\\\(x_2, y_2) = (4, 9)[/tex]
Substituting the values in formula, we get,
[tex]m = \frac{9-3}{4-1}\\\\m = \frac{6}{3} = 2[/tex]
Thus slope of line is 2
The equation of line in slope intercept form is given as:
y = mx + c -------- eqn 1
Where, "m" is the slope and "c" is the y - intercept
To find the y intercept, substitute (x, y) = (1, 3) and m = 2 in eqn 1
3 = 2(1) + c
c = 1
Thus the equation of line is:
Substitute c = 1 and m = 2 in eqn 1
y = 2x + 1
Thus equation of line is found
I am having trouble with the last question. “Suppose that y=2.5 when x=1.5. Write a formula that expresses y in terms of x.”
y=2x-0.5
Step-by-step explanation:
Given the expression of Δy in terms of Δx as;
Δy=4/2 Δx
Given y=2.5 and x =1.5 then substituting in the equation above will give;
y-2.5=2(x-1.5)
y-2.5=2x-3
y=2x-3+2.5
y=2x-0.5
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To write a formula that expresses y in terms of x, we can use the equation y = mx + b. Substitute the given values of x and y into the equation and solve for m and b. The final formula is y = 1.67x + 1.25.
Explanation:To write a formula that expresses y in terms of x, we need to determine the relationship between y and x. In this case, we know that when x = 1.5, y = 2.5. So we can start with the equation y = mx + b, where m is the slope and b is the y-intercept.
Using the given values, we can substitute x = 1.5 and y = 2.5 into the equation y = mx + b: 2.5 = 1.5m + b. Now we can solve for m and b by using the given values and algebraic manipulation.
By rearranging the equation and substituting the values of x and y, we can determine the formula that expresses y in terms of x. The final formula will be y = 1.67x + 1.25.
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Compare |− 4 25 | and |− 7 20 |.
Answer:
Step-by-step explanation:
| - 425 |=425
| - 720 |=720
Beacause 720>425=>| - 720 |>| - 425 |