Answers
According to the graph, the function that best describes the graph is
[tex]f(x)=|x| = \left\{ \begin{array}{cl}x - 2 \text{ for x \lt -3 } \\8 \text{ for -3 \lt x \lt 5}\\-x + 10 \text{ for x \gt 6}\end{array} \right.[/tex]
(option d).
As we all know that the term function is defined as a rule or relationship that maps each element in one set, called the domain, to exactly one element in another set, called the range.
While we looking into the graph we have identified that there is a straight line that cross the point (0, 8) within the range of -3 to 5.
And then the next line is moves downwards from the range of x whose value is greater than 6.
Final upward slope is moves the range of -3 or less While we looking into these range value we have identified that the the function that refers the graph is (option d).
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Related Questions
On a scale drawing of a soccer field, 0.5 cm equals 8 m.
If the drawing has dimensions 6.5 cm X 3.25 cm, what is the actual length of the soccer field, in meters?
Answers
[tex]\sf Length\, of\,the\,field=\boxed{\sf 104(m)}}.[/tex]
Step-by-step explanation:1. Create a conversion factor.A conversion factor is just a fraction that contains an equivalence. We make the numerator be the unit we want to have as a result and the denominator is the current unit that we have.
The problem states that 0.5 cm equals 8 m, and we want to convert from cm to m, therefore, a conversion factor for this problem is:
[tex]\sf \dfrac{8(m)}{0.5(cm)}[/tex]
2. Use the conversion factor to convert each unit,To use the conversion factor, just multiply each measure by the fraction:
[tex]\sf 6.5(cm) \dfrac{8(m)}{0.5(cm)}[/tex]
Here the centimeters (cm) cancel out each other and the ending answer is expressed in meters:
[tex]\sf 6.5(cm) \dfrac{8(m)}{0.5(cm)}=\boxed{\sf 104(m)}.[/tex]
For the other measure:
[tex]\sf 3.25(cm) \dfrac{8(m)}{0.5(cm)}=\boxed{\sf 52(m)}.[/tex]
So a soccer field, as you may already know, is always longer than it is wide, therefore, the greatest measure (104m) should be the length of the field.
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Enter your answer, rounded to the nearest tenth, in the box.
Answers
Answer:
[tex]f(0) = 6.2 \sqrt{4.5} + 18 = 31.2[/tex]
Navid earns a basic wage of $10.25 an hour. He works for 40 hours a week. He earns 20% more than his basic wage when he works overtime. Navid wants to earn at least $500 this week. Calculate the total number of hours he needs to work. Give your answer to the nearest hour.
Answers
$10.25/hour x 40 hours = $410
To earn at least $500, Navid needs to earn an additional $90 ($500 - $410).
To earn 20% more than his basic wage, Navid would earn:
$10.25/hour x 1.2 = $12.30/hour for each overtime hour
So, Navid needs to work:
$90 ÷ ($12.30/hour - $10.25/hour) = 47.4 hours
Since Navid cannot work a fraction of an hour, he needs to work 48 hours to earn at least $500.
Therefore, Navid needs to work for a total of 40 hours + 8 hours of overtime, which is 48 hours in total (rounded up to the nearest hour).
NEED HELP ASAP PLS AND THX PIC IS ATTACHED
Answers
The trigonometry functions when evaluated are shown below
Evaluating the trigonometry functionsIn trigonometry, sine (sin), cosine (cos), and tangent (tan) are three basic functions that relate angles to the sides of a right triangle.
They are defined as follows:
sin A = opposite side/hypotenuse.
cos A = adjacent side/hypotenuse.
tan A = opposite side/adjacent side.
So, we have
Figure 1
sin A = 6/9cos A = √5/3tan A = 6/√5Figure 2
sin A = √2/2cos A = √2/2tan A = 1Figure 3
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The ratio of two numbers is 7 to 3 and the sum of their squares is 232. Find the numbers.
Answers
We know that (7x)^2 + (3x)^2 = 232.
Expanding this equation, we get 58x^2 = 232.
Dividing both sides by 58, we get x^2 = 4.
Therefore, x = +/- 2.
Plugging this value of x into the expression for the two numbers, we get that the numbers are 14 and 6, or -14 and -6.
x/y = 7/3
We can use this information to solve for one of the variables in terms of the other. For example, we can solve for y in terms of x:
y = (3/7) x
Now we know that one of the numbers is equal to (3/7) times the other. We also know that the sum of their squares is 232, so we can write:
x^2 + y^2 = 232
Substituting y = (3/7) x, we get:
x^2 + (3/7)^2 x^2 = 232
Simplifying, we get:
(1 + (3/7)^2) x^2 = 232
(1 + 9/49) x^2 = 232
(58/49) x^2 = 232
x^2 = (232 * 49) / 58
x^2 = 196
Taking the square root of both sides, we get:
x = 14
Now we can use the equation y = (3/7) x to find y:
y = (3/7) * 14 = 6
Therefore, the two numbers are 14 and 6.
The perimeter of the quadrilateral is 34 centimeters. Find the length of each side.
x+8
x +4
2x - 2
x²-2x
Answers
Answer: x=4, sides = 12, 8, 6, 8
Step-by-step explain
Perimeter means the sum of all sides of a shape, in this example there are four sides add the sides and set it equal to 34.
X+8+x+4+2x-2+x²-2x=34
x²+2x+10=34
x²+2x-24
(x-4)(x+6)
x=4, x=-6
x can not be -6 because then the x+4 side would be -2, therefore it is extraneous and x=4 is the correct answer.
Now to find side lengths just plug in 4 for x
4+8=12
4+4=8
2*4-2=6
4*4-2*4=8
Factor the expression. x^2-14x-32
Answers
Answer:
[tex](x-2)(x+16)[/tex]
Step-by-step explanation:
Use graphing calculator and find the x-intercepts.
Starting from rest, an object travels at a constant speed of 150 cm/s (centimeters per second) along a straight line. If d is the total distance in cm that the object has traveled at time t seconds, then which of the following gives the equation expressing d as a function of t, and the total distance d in meters that the object has traveled at time t = 2 seconds?
Answers
The equation expressing d as a function of t can be found by using the formula for distance traveled with constant speed:
d = vt
where d is the distance, v is the constant speed, and t is the time elapsed.
In this case, the speed is 150 cm/s, so the equation is:
d = 150t
To find the total distance traveled in meters at t = 2 seconds, we need to first find the total distance traveled in centimeters at t = 2 seconds:
d = 150t
d = 150(2)
d = 300 cm
To convert to meters, we divide by 100:
d = 300/100
d = 3 meters
Therefore, at t = 2 seconds, the object has traveled a total distance of 3 meters.
Evaluate the following expression.
If x=12,y=8, and z=6.
X2y-2z over 4
Answers
The value of the expression "(x²y - 2z)/4", when x = 12 , y = 8 and z = 6, is (c) 285.
An "Expression" is defined as a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation, which are written using mathematical symbols and follow certain rules.
We have to evaluate the expression : (x²y - 2z)/4, if x = 12 , y = 8 and z = 6,
To evaluate , we substitute x = 12 , y = 8 and z = 6, in the expression,
So, We have,
⇒ (12² × 8 - 2×6)/4,
⇒ (144 × 8 - 12)/4,
⇒ (144 × 8 - 12)/4,
⇒ (1152 - 12)/4,
⇒ 1140/4,
⇒ 285,
Therefore, the value of the given expression, when x=12, y=8, and z=6, is 285, the correct option is (c).
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1. A rectangular block of wood has dimensions 24 cm by 9 cm by 7 cm. It is cut up into children's bricks. Each brick is a cube of side 3 cm.
(a) Find the largest number of bricks that can be cut from the block.
(b) Find the volume of wood that is left.
Answers
The dimensions of the rectangular block indicates;
(a) The largest number of bricks that can be cut from the block is 48 bricks
(b) The volume of the wood left is 216 cm³
What is the volume of a rectangular block?The volume of the rectangular block is the product of the length, L, width, W, and height, H.
1. The dimensions of the rectangular block indicates that the block volume is; V = 24 cm × 9 cm × 7 cm = 1,512 cm³
The largest number of bricks that have side lengths of 3 cm that can be cut from the block is therefore;
Number of cubes; (24)/3 × (9)/3 × (7)/3 ⇒ 8 × 3 × 2 = 48
48 cube bricks can be cut from the block(b) The volume of wood left = 1512 - 48 × 3 × 3 × 3 = 216
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what is the answer for this question
Answers
Answer:
The yellow region is 13.73 cm squared
Step-by-step explanation:
---
Area of square:
[tex]8 * 8 = 64 cm^2[/tex]
Area of the 4 quarter-circles:
[tex]4(\pi r^2)/4[/tex]
The fours cancel each other, we are left with:
[tex]\pi r^2[/tex]
r = 4, so substitute that, we get:
[tex]\pi 4^2 = 16 \pi cm^2[/tex]
Which can be approximated to 50.27 cm squared
Subtract the area of the circle from the square:
[tex]64 - 50.27 = 13.73 cm^2[/tex]
So the area of the yellow region is 13.73 cm squared
Need help with this question. Been stuck on this for 20 mins.
Answers
Answer:
see below
Step-by-step explanation:
The Reason for #1 is literally GIVEN to you.
Statement #2: Since the Base Angles of an isosceles triangle are congruent, this statement should be ∠CAB≅∠CBA.
Reason #3: Notice that the statement repeats itself (AB=AB). This demonstrates the REFLEXIVE property.
Reason #4: (Clue) Note which items have been Given or Proven congruent and use it as the triangle congruence property. It helps to actually mark them. Your choices are SSS, SAS, ASA, and AAS.
Reason #5: (Clue) Since the triangles of which AM and BN are of part are now proven congruent, these Corresponding Parts are Congruent as well.
I need help with the answer to the photo provieded
Answers
Answer:
26
Step-by-step explanation:
the line is parellel to graph of 2x-3y=7 and contains the point (-3,-3)
Answers
The equation of the line parallel to the graph of 2x - 3y = 7 and containing the point (-3,-3) is y = (2/3)x - 1.
What is the equation of the parallel line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the equation of the graph: 2x - 3y = 7.
First, we need to rearrange the given equation into slope-intercept form (y = mx + b) by solving for y:
2x - 3y = 7
-3y = -2x + 7
y = (2/3)x - 7/3
The slope of the given line is 2/3.
Hence, any line parallel to it will also have a slope of 2/3.
Using the point-slope form, we determine the equation of the line that passes through (-3,-3) and has a slope of 2/3:
y - y1 = m(x - x1)
y - (-3) = (2/3)(x - (-3))
y + 3 = (2/3)x + 2
y = (2/3)x - 1
Therefore, the equation of the line is y = (2/3)x - 1.
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PLS HELP IM FAILING ALGEBRA
Answers
Find the volume of the cone shown. Use 3.14 for pi. Round your answer to the nearest hundredth.
Answers
Answer: 100.48 cubic feet
Step-by-step explanation:
A rainwater collection system uses a cylindrical storage tank with a diameter of 50 cm and a height of 80 cm what is the total volume of water in cubic centimeters that can be collected
Answers
Answer:
157,000
Step-by-step explanation:
π r² h
if 3x+2y=36 and (5y)/(3x)=5, what is the value of x+y?
Answers
Answer:
16
Step-by-step explanation:
5y/3x = 5
3x = 5y/5
3x = y
3x + 2y = 36
y + 2y = 36
3y = 36
y = 36/3
y = 12
3x = y
3x = 12
x = 12/3
x = 4
x + y
= 4 + 12
= 16
x + y = 16
PLEASE HELP! Showing all work, solve for x and why and round to nearest tenth
Answers
Answer:
x = 7.9 (nearest tenth)
y = 24.6° (nearest tenth)
Step-by-step explanation:
Pythagoras Theorem explains the relationship between the three sides of a right triangle. The square of the hypotenuse (longest side) is equal to the sum of the squares of the legs of a right triangle.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
As we have been given the lengths of both legs of the right triangle, we can use Pythagoras Theorem to find the length of the hypotenuse, x:
[tex]\begin{aligned}3.2^2+7^2&=x^2\\10.24+49&=x^2\\59.24&=x^2\\x^2&=59.24\\x&=\sqrt{59.24}\\x&=7.6967525...\\x&=7.9\; \sf (nearest\;tenth)\end{aligned}[/tex]
Therefore, x = 7.9.
[tex]\hrulefill[/tex]
The tangent ratio is a trigonometric ratio that relates the angle of a right triangle to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
[tex]\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}[/tex]
As we have been given the lengths of the sides that are opposite and adjacent angle y, we can use the tangent trigonometric ratio to find the measure of angle y:
[tex]\begin{aligned}\tan(y)&=\dfrac{3.2}{7}\\y&=\tan^{-1}\left(\dfrac{3.2}{7}\right)\\y&=\vphantom{\dfrac12}24.5671713...^{\circ}\\y&=24.6^{\circ}\;\sf (nearest\;tenth)\end{aligned}[/tex]
Therefore, y = 24.6°.
Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.
United States Birth Rate (per 1000)
Birth Rate
A graph titled United States Birth Rate (per 1000) has year on the x-axis and birthrate on the y-axis. Points trend in a negative line.
Year
Source: National Center for Health Statistics, U.S. Dept. of Health and Human Services
a.
no correlation
b.
positive correlation; as time passes, the birth rate increases.
c.
positive correlation; as time passes, the birth rate decreases.
d.
negative correlation; as time passes, the birth rate decreases.
Answers
A negative correlation may be seen on the graph. The birth rate declines over time. This indicates that the number of births per 1000 persons in the US has been declining over time.
Factor by grouping. Then supply the term that is missing below. 4mn+3m+8n+6=(m+2)(?+3)
Answers
Answer:
4mn + 3m + 8n + 6 = (m + 2)(4n + 3)
The missing term is 4n.
A college student takes the same number of credits each semester. They had 19 credits when they started, and after 6 semesters, they had 67 credits. Which of these expresses the rate at which they is earning credits?
Answers
As per the given variables, the rate at which they earn credits is 8 credits per semester
Total number of credits = 19
Total number of semesters = 6
Credits after six semesters = 67
Calculating the change in credits -
Change in credits -
Credits after six semesters - Inital credits
= 67 - 19
= 48 credits
Total time = 6 semesters
Calculating the change in credits over the six semesters and dividing by the total time to get the pace at which the college student is acquiring credits.
Therefore, the rate at which the college student is earning credits is:
Rate = Change in credits / Total time
= 48 credits / 6 semesters
= 8 credits per semester
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An equilateral triangle is shown inside a square inside a regular pentagon inside a regular hexagon. Write an expression for the exact area of each shaded region in the figure. Then find the approximate area of the entire shaded region, rounded to the nearest whole unit.
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An expression for the exact area of each shaded region in the figure include the following:
Shaded area = area of the regular hexagon - area of the regular pentagon + area of the square - area of the equilateral triangle.
How to calculate the area of a regular polygon?In Mathematics and Geometry, the area of a regular polygon can be calculated by using the following formula:
Area of a regular polygon = (n × s × a)/2
Where:
n is the number of sides.s is the side length.a is the apothem.Based on the diagram (see attachment), the area of the first shaded region is given by;
Area of first shaded region = Area regular hexagon - Area regular pentagon
For the area of the second shaded region, we have;
Area of second shaded region = Area of a square - Area of the equilateral triangle
Therefore, the total area of all of the shaded regions is given by;
Total shaded area = {area of the regular hexagon - area of the regular pentagon} + area of the square - {area of the equilateral triangle}.
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Write the standard form of the following polynomial.
(2x-3)²-3(x-2)(x+4)-7
X² ? X+ ?
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(2x-3)²-3(x-2)(x+4)-7
= (2x-3)(2x-3) - 3(x²+2x-8) - 7
= 4x² - 12x + 9 - 3x² - 6x + 24 - 7
= x² - 18x + 26
Therefore, the standard form of the polynomial is x² - 18x + 26.
For two programs at a university, the type of student for two majors is as follows. find the probability a student is a graduate student, given they are a history major.
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The probability that a student is a graduate student given they are a history major is approximately 0.16.
What is probability?The likelihood or chance that an event will occur is quantified by probability. A number between 0 and 1, where 0 denotes that the occurrence is impossible and 1, denotes that the event is certain, is generally used to express it.
According to question:We are given the following information:
Total number of students who are history major: 463
Total number of graduate students: 261
Number of graduate students who are history major: 73
We can use the formula for conditional probability to find the probability that a student is a graduate student given that they are a history major:
P(graduate | history) = P(graduate and history)/P(history)
P(graduate | history) = 73/463
P(graduate | history) ≈ 0.1575 (rounded to the nearest hundredth)
Therefore, the probability that a student is a graduate student given they are a history major is approximately 0.16.
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 Cooper can purchase a item for $45.00, Which store has the best buy?
A. Store 1: 25% off coupon
B. Store 2: $15 dollars off
C. Store 3: 10% off
I’ll give brainly please help me
Answers
Santiago is going to see a movie and is taking his 3 kids. Each movie ticket costs $15 and there are an assortment of snacks available to purchase for $4.50 each. How much total money would Santiago have to pay for his family if he were to buy 6 snacks for everybody to share? How much would Santiago have to pay if he bought x snacks for everybody to share?
Answers
Answer:
25$ if the tickets were involved it would be 70$
Santiago would have to pay $87 in total if he bought 6 snacks for everyone to share. The cost increases to $60 + 4.5*x when a variable number of snacks, represented by x, are bought.
Explanation:The topic of this question is
Mathematics
, specifically about using multiplication and addition in problem-solving.
Firstly, Santiago is going to see a movie with his 3 kids. Therefore, he needs to buy 4 tickets. If each ticket costs $15, then the total cost for movie tickets will be 4 * 15 = $60.
Secondly, if Santiago buys 6 snacks for everybody to share with each snack costing $4.50, the total cost for snacks will be 6 * 4.5 = $27. The total money Santiago would have to pay for his family would then be the sum of the costs of the tickets and snacks, which is 60 + 27 = $87.
Regarding the case when Santiago bought x snacks for everybody to share, the total cost would become 60 + 4.5*x. This formula gives the total cost based on the given number of snacks.
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Line g has an equation of y = 2x + 1. Line h includes the point (-5, 2) and is perpendicular
to line g. What is the equation of line h?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
Submit
Answers
Slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept. Line g’s equation is already in the correct form. If line g has a slope m=ab, then line h perpendicular to it will have a slope m⊥=−ba.
2/1 = 2, so the reciprocal is 1/2. It will also be negative to become: y= (-1/2)x + b.
We want to find the y-intercept, b.
Plug in the coordinate that line h passes through (-5,2) for the (x,y) values in the equation.
2 = (-1/2)(-5) + b
2 = 5/2 + b
Subtract 5/2 from both sides:
Note that 2 is equal to 4/2, which makes it easier to deal with.
(4/2) - (5/2) = b
Simplify:
-1/2 = b.
Put all values into line h’s equation, and y = (-1/2)x - 1/2.
2raised to power m-3 = 1
Answers
Answer:
m = 3
Step-by-step explanation:
Given:
[tex]2^{m-3}[/tex] = 1
Take the logarithm of both sides (logarithm of 1 is 0):
m - 3 = 0
Add 3 to both sides:
m - 3 + 3 = 0 + 3
m = 3
Hence, m = 3.
Logarithm is the power to which a number must be raised in order to get some other number. For example:
The base ten logarithm of 100 is 2, because ten raised to the power of two is 100: log 100 = 2. Meaning [tex]10^{2}[/tex] = 100.A school purchases boxes of paints for the annual painting competition. The expression below represents the total price for the order including delivery to the school. $11.75x + $20
Answers
Answer:
The expression $11.75x + $20 represents the total price for the order, including delivery to the school.
In this expression, 'x' represents the number of boxes of paints being purchased, and $11.75 represents the cost of each box. The term $11.75x represents the total cost of the boxes of paints based on the number of boxes being purchased.
The term $20 represents the delivery cost to the school, which is added to the total cost of the boxes of paints.
By multiplying the cost per box ($11.75) by the number of boxes (x) and adding the delivery cost ($20), you can calculate the total price for the order, including delivery.