A function, h(x), is defined as shown.
h(x) =
Which graph represents h(x)? {image Attached)
Answers
Answer:
option B
Step-by-step explanation:
We have three different function for h(x)
[tex]h(x)= \frac{1}{4}x-4, x<=0[/tex]
WE have x<=0, so the graph starts at x=0 and goes down
Plug in 0 for x
[tex]h(0)= \frac{1}{4}(0)-4[/tex]
So h(0)= -4
When x=0, y= -4
The graph starts at (0,-4) and goes down
[tex]h(x)= \frac{1}{3}x-3, 0<x<=3[/tex]
x lies between 0 and 3, so the graph starts at x=0 and ends at x=3
Plug in 0 for x
[tex]h(0)= \frac{1}{3}(0)-3[/tex]
So h(0)= -3
When x=0, y= -4
Plug in 3 for x
[tex]h(3)= \frac{1}{3}(3)-3=-2[/tex]
When x=3, y= -2
The graph starts at (0,-4) and ends at (3, -2)
[tex]h(x)= \frac{1}{2}x-2, x>=4[/tex]
WE have x>=4, so the graph starts at x=4 and goes to the right
Plug in 4 for x
[tex]h(4)= \frac{1}{2}(4)-2[/tex]
So h(4)= 0
When x=4, y= 0
The graph starts at (4,0) and goes to the right.
SEcond graph is correct
Answer:
B
Step-by-step explanation:
Related Questions
whats an irrational number between 9.7 and 9.9
Answers
9.5 < x < 9.7
square it
9.52<x2<9.72
90.25<x2<94.09
So pick any number between 90.25 and 94.09 to be x2, as long as it's not a perfect square. So if you pick 91, then
x2=91
x=91−−√→ irrational
approximation is 9.54
Which figures can be precisely defined by using only undefined terms? Check all that apply. angle arc circle line segment parallel lines
Answers
Answer:
circle, line segment, and parallel lines
Step-by-step explanation:
A circle is the set of all points a given distance from a fixed point called a center. This only uses the undefined term "point."
A line segment is a portion of a line with two distinct endpoints. This uses the undefined terms "line" and "point."
Parallel lines are lines that never intersect. This uses the undefined term "line."
An angle is two rays joined at a common point called the vertex. While this does use the undefined term "point," it also uses the defined term "ray." This is not one of our options.
An arc is a portion of the circumference of a circle. This uses the term "circle," so it is not one of our options.
Drawn
two arrays that represent 12
Answers
An array can be utilized to represent the multiplication of two numbers in Mathematics. In this representation, the number 12 can be depicted by a 3x4 or 2x6 arrays. There can be various arrays to represent a number such as 12.
Explanation:In mathematics, specifically in multiplication, arrays are often used to represent and visualize the multiplication of two numbers. The number 12 can be represented by an array in multiple ways, here we will use two ways:
A 3 rows by 4 columns array, which represents the equation 3 times 4 equals 12. You have 3 rows and 4 columns, so when you count every spot where a row and column intersect, you get 12.A 2 rows by 6 columns array, which represents the equation 2 times 6 equals 12. You have 2 rows and 6 columns, if you count every intersection, you get 12.
Remember, for any number, there can be multiple arrays that represent it. For the number 12, for instance, other arrays such as 1 row by 12 columns (1x12) or 12 rows by 1 column (12x1) are possible as well.
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lisa runs 3.6 km on monday 4.2 km on wednsday and 5.7 km on saturday.what is the average distance she ran each day during the week
Answers
XY=7a,YZ=5a,XZ=6a+24
Answers
6a = 24
a = 4
XZ = 6(4) + 24
XZ = 48
Lorraine invested $5500 in a savings account with a yearly interest rate of 6% for 9 years. How much simple interest did she earn?
Answers
Lorraine earned $2970 in simple interest over the 9 years.
We can use the formula for simple interest, which is:
[tex]\[ I = P \times r \times t \][/tex]
where:
[tex]\( I \)[/tex] is the interest earned,
[tex]\( P \)[/tex] is the principal amount (the initial amount of money),
[tex]\( r \)[/tex] is the annual interest rate (in decimal form), and
[tex]\( t \)[/tex] is the time the money is invested for, in years.
Given:
[tex]\( P = \$5500 \)[/tex] (the principal amount),
[tex]\( r = 6\% \)[/tex] per year (which we convert to a decimal by dividing by 100.
[tex]\( r = 0.06 \)[/tex]
[tex]\( t = 9 \)[/tex] years (the time period).
Now, we can calculate the simple interest:
[tex]\[ I = \$5500 \times 0.06 \times 9 \][/tex]
[tex]\[ I = \$5500 \times 0.54 \][/tex]
[tex]\[ I = \$2970 \][/tex]
If K is between J and L then JK + KL = JL
Answers
By setting up an equation based on the fact that K is between J and L, we found that x = 6. Substituting this value back into the expression for KL, we determined that KL = 8.
To find the value of x and KL, we'll first set up an equation using the fact that K is between J and L, which means JL = JK + KL. Substituting the given expressions:
5x - 10 = 2x + (x + 2)
Now, solve for x:
[tex]\[5x - 10 = 2x + x + 2\][/tex]
[tex]\[5x - 10 = 3x + 2\][/tex]
[tex]\[5x - 3x = 2 + 10\][/tex]
[tex]\[2x = 12\][/tex]
[tex]\[x = 6\][/tex]
Now that we have found the value of [tex]\(x\)[/tex], we can find [tex]\(KL\)[/tex] by substituting \(x = 6\) into the expression for KL:
[tex]\[KL = x + 2 = 6 + 2 = 8\][/tex]
So, x = 6 and KL = 8.
The question probable maybe:
Find the value of x and KL if K is between J and L. JK=2x, KL=x+2, and JL=5x-10.
What is the surface area to volume ratio of this cube ( 5cm on all sides)
Answers
so, the cube is really, just a rectangular prism, which is really just 6 rectangles stacked up to each other at the edges.
so, the area of it is just the area of those sides
top and bottom 5x5, 25 each
left and right, 5x5, 25 each
front and back, 5x5, 25 each
so the area is 50+50+50, or 150 cm²
the volume is either face, times the length, so just 25 * 5, or 125 cm³.
now, let's check their ratio. [tex]\bf \cfrac{area}{volume}\qquad 150:125\implies \cfrac{150}{125}\implies \cfrac{6}{5}[/tex]
The surface area to volume ratio for a cube with sides of 5 cm can be calculated using the formulas for surface area and volume of a cube. After calculating, the ratio is found to be 1.2 cm^-1.
Explanation:The concept you're asking about relates to both geometry and biology, particularly cell biology. The surface area to volume ratio is important in determining how substances move in and out of cells.
To calculate the surface area and volume of a cube with sides measuring 5 cm, we use these two formulas:
Surface Area (SA) = 6 x (side length)^2Volume (V) = (side length)^3Substituting 5 cm into these formulas, we get:
SA = 6 x (5 cm)^2 = 6 x 25 cm^2 =150 cm^2V = (5 cm)^3 = 125 cm^3Finally, to get the surface area to volume ratio, divide the surface area by the volume:
SA:V Ratio = SA/V = 150 cm^2/125 cm^3 = 1.2 cm^-1So, the surface area to volume ratio for a cube with sides of 5 cm is 1.2 cm^-1.
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Solving equations 6x+7=8x–13
Answers
"Solving equation:[tex]6x+7=8x-13[/tex]?"...
Solve for x.
[tex]6x+7=8x-13[/tex]
Add 13 to both sides.
[tex](6x+7)+13=(8x-13)+13[/tex]
Simplify
[tex]6x+20=8x[/tex]
Subtract both sides by 6x.
[tex](6x+20)-6x=(8x)-6x[/tex]
Simplify.
[tex]20=2x[/tex]
Divide both sides by 2.
[tex](20)/2=(2x)/2[/tex]
Simplify.
[tex]10=x[/tex]
The answer would be 10.
Hope this helps.
-Benjamin
what statement best describes inductive reasoning vs deductive reasoning
Answers
compare the values of each 3 in the number 633,248
Answers
The difference of each 3 is that they have different place values.
The 3 on the right side is int he 1000s (thousands) place, and the 3 on the left is in the 10,000s (ten thousands) place. :)
The one in the 10,000s place is 10 times larger than the one in the 1,000s place!
The second 3 is in the Ten thousand place which is 10 times larger than the first 3 which is in the Thousand place.
Here,
The number is 633,248.
We have to compare the values of each 3 in the number 633,248.
What is Place value?
The value represented by a digit in a number on the basis of its position in the number is called the place value.
Now,
The number is 633,248.
From right the first 3 has place in Thousand place.
So, place value of this 3 is thousands place.
And, From right the second 3 has place in Ten thousands place.
The difference of each 3 is that they have different place values.
Therefore, The second 3 is in the Ten thousand place which is 10 times larger than the first 3 which is in the Thousand place.
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Evaluate the expression. Must rewrite the expression without the exponent before evaluating (-12)^2
Answers
Answer:
(-12)^2 = -12 * -12 = 144
Find an equivalent mixed number for the decimal number 16.3
Answers
Answer:16 3/10
Step-by-step explanation:
The sum of 3 consecutive integers is 270. what is the second number in the sequence
Answers
from the top of a vertical tower 248 m high , a stone is projected vertically downwards with a speed of 8 ms . After x seconds another stone is projected vertically upwards from the level of the base of the tower with a speed 25 ms . Given that two stones are at same height moving in the same direction 6 seconds after projection of the first stone , calculate :
1) value of x
2) the velocity of the second stone at this instant
Answers
The value of x, which is the time delay between the two stones' projections, is 1.4 seconds. The velocity of the second stone 6 seconds after the first stone's projection (so 1.4 seconds after its own projection) is 11.32 m/s.
Explanation:This question involves physics concepts, particularly with motion under gravity, velocity, and displacement. We need to use these principles of Physics to solve the problem.
First, let's calculate the displacement of the first stone 6 seconds after it is thrown. Since the stone is thrown downwards, its final displacement (S1) is given by the equation of motion:
S1 = ut + 0.5gt2, where u is initial velocity (8 m/s), g is acceleration due to gravity (9.8 m/s2), and t is the time (6 seconds).
Therefore, S1 = 8*6 + (1/2)*9.8*6*6 = 48 + 176.4 = 224.4 m.
The first stone is thrown from a tower of height 248 m, so its displacement from the base of the tower is
248 - S1 = 248 - 224.4 = 23.6 m.
The second stone is thrown upwards from the base of the tower, Therefore, after t=x seconds, it travels upward by S2 = ut - 0.5gt2 (=25x - 0.5*9.8*x2).
At t=6 seconds, it must be at a the same height as the first stone (23.6 m). So we set 25x - 0.5*9.8*x2 = 23.6, and solve this quadratic equation to find x = 1.4 seconds.
The second part of the question asks for the velocity of the second stone at this instant. The velocity of an object thrown upward-moving object is given by
v = u - gt, here u = initial velocity = 25 m/s, g = 9.8 m/s2 and t=x=1.4 seconds. Plugging in these values, we find that v = 25 - 9.8*1.4 = 11.32 m/s.
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Find the slope and Y intercept for 6x - 2y=12
Answers
6x-2y=12
-2y=-6x+12
y= 3x-6
Final answer: slope= 3, y intercept= -6
In a city, the distance between the library and the police station is 3 miles less than twice the distance between the police station and the fire station. The distance between the library and the police station is 5 miles. How far apart are the police station and the fire station?
Answers
4 miles
In England, mass is measured in units called stones. One pound equals 1/14 of a stone. A cat weighs 3/4 stone. How many pounds does the cat weigh?
Answers
f(x)=(x)^2 is vertically stretched by a factor of 4 and translated 4 units left to create g(x)
Answers
[tex]\bf \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]
[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{{{ B}}}[/tex]
[tex]\bf \stackrel{\textit{vertically stretched by a factor of 4}}{A=\frac{1}{4}}\qquad \stackrel{\textit{translated 4 units left}}{C=+4} \\\\\\ f(x)=x^2\implies f(x)=1(1x+0)^2+0\implies f(x)=\stackrel{A}{\frac{1}{4}}(1x\stackrel{C}{+4})^2+0 \\\\\\ f(x)=\frac{1}{4}(x+4)^2[/tex]
what is the counterexample "the difference of two numbers less than the greater number"
Answers
The counterexample of the statement "the difference of two numbers is greater than the greater number if the smaller number is greater than twice the additive inverse of the greater number"
How to determine the counterexample?The statement is given as: "the difference of two numbers less than the greater number"
Let the numbers be x and y, where x > y.
So, the interpretation of the statement is:
x - y < x
Add x to both sides
-y < 2x
Rewrite as:
y > -2x
This means that the statement is true only when the smaller number is greater than twice the additive inverse of the greater number
Hence, the counterexample of the statement "the difference of two numbers is greater than the greater number if the smaller number is greater than twice the additive inverse of the greater number"
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A light on a computer comes for 26700 microseconds is 10-6 seconds.
Workout the length of time ,in seconds,that the light is on.
A) in standard form,
B)as a decimal
Answers
A) 2.67 x 10^-3
B) 0.00267 seconds.
A) In standard form, the length of time the light is on is [tex]2.67 \times 10^{-2} \text{ seconds}[/tex]
B) As a decimal, the length of time the light is on is [tex]0.0267 \text{ seconds}[/tex]
Step 1: Understanding the conversion
1 microsecond ([tex]\mu s[/tex]) is equal to [tex]10^{-6}[/tex] seconds.Therefore, 26700 microseconds is equal to [tex]26700 \times 10^{-6}[/tex] seconds.Step 2: Converting microseconds to seconds
First, let's calculate the time in seconds as a decimal:
[tex]26700 \times 10^{-6} = 0.0267[/tex]
Step 3: Converting seconds to standard form
Standard form (also known as scientific notation) expresses numbers as a product of a number between 1 and 10 and a power of 10.
Here, [tex]0.0267[/tex] can be written as:
[tex]2.67 \times 10^{-2}[/tex]
In the diagram below bd is parallel to xy what is the value of x
Answers
It’s 83
Step-by-step explanation:
How many minutes are there in a 40 hours week?
Answers
What is the sum of the first 10000 numbers?
Answers
sum = 10000(10000-1)/2
sum = 10000(100001)/2
sum = 100010000/2
sum = 50,005,000
On Monday, a local hamburger shop sold a combined total of 504 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Monday?
Answers
.3333... = 1/3. What is .23232323... = as a fraction?
Answers
Answer:121
Step-by-step explanation:
Mari and Jen each work 20 hours a week at different jobs. Mari earns twice as much as Jen. Together they can earn $480. How much does each girl earn in a week?
Answers
In word problems, remember that not every number they give you is important. For example, here, they tell you that they both work 20 hours a week. This information isn't important in creating an equation to represent the situation.
Let's say that x is the amount that Jen makes. Therefore, 2x will be the amount that Mari makes since she makes twice as much as Jen. Together, the amounts they make adds up to 480, meaning that the entire equation will be:
x + 2x = 480
All we need to do is solve this for x, plug x back into the equation, and solve.
1x + 2x = 480 (combine 1x and 2x)
3x = 480 (divide both sides by 3)
x = 160
Now, plug 160 in for x in the original equation to check and solve for how much Mari makes (she's represented by 2x).
160 (Jen) + 2(160) (Mari) = 480
160 (Jen) + 320 (Mari) = 480
480 (Jen + Mari) = 480
Jen makes $160 a week and Mari makes $320 a week.
Hope this helped you out! :-)
Lee can frame a cabin in 4 days less than Ron. When they work together, they will do the job in 4 days. How long would each of them take to frame the cabin alone?
Answers
To frame a cabin:
Lee will take 6.47 days and Ron will take 10.47 days.
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
Given:
Lee can frame a cabin in 4 days less than Ron.
Ron can frame,
= 1 cabin/(x+4) days.
Lee can frame,
= 1 cabin/(x) days.
When they work together, they will do the job in 4 days.
That means,
4/x+4 + 4/(x) = 1
4(x+4+x)/x(x+4) = 1
x²-4x-16 = 0
Solving the quadratic equation,
x = 2 ± 2√5
Then,
x = -2.47 and x = 6.47.
Therefore, Lee can frame a cabin in 6.47 days and Ron will take 10.47 days.
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A pair of parallel lines is cut by a transversal:
What is the measure of angle x?
60 degrees
70 degrees
80 degrees
100 degrees
Answers
x = 60
answer
60 degrees
A company added a new oil thank that holds 350 barrels of oil than its old oil tank.together they hold 3650 barrels of oil.how much does each thank hold?
Answers
The required solution of the given question is Capacity of old oil tank and Capacity of New oil tank is 1650 and 2000 barrels respectively.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
A company added a new oil thank that holds 350 barrels of oil than its old oil tank . Together they hold 3650 barrels of oil.
According to given question we have
Let the Capacity of old oil tank = x barrels
Let the Capacity of New oil tank = x + 350 barrels
So,
x + x + 350 = 3650
2x = 3300
x = 1650 barrels
∴Capacity of old oil tank = 1650 barrels
Capacity of New oil tank
= x + 350
=1650 +350
=2000 barrels
Therefore, the required solution of the given question is Capacity of old oil tank and Capacity of New oil tank is 1650 and 2000 barrels respectively.
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