The linear function of h is h(x) = -2x -13 and the values of h(3) = -19.
Two point form is a method for finding the equation of a function if two of its points are known. If (x1, y1) and (x2, y2) are the two points then equation of the function is given as-
(y - y1) = {(y1 - y2)/ (x1 - x2)} (x - x1)
Here, we are given that h(7) = -10 and h(-2) = 8
This, means that (7, -10) and (-2, 8) will satisfy the given function
Since, we have two points, we will use the two point form to find the equation of function h.
Substituting, x1 = 7, y1 = -10, x2 = -2 and y2 = 8 in the two point form equation we get-
( y - 7) = {(-10 - 8) / (7 + 2)} (x + 10)
y - 7 = (-18/9) (x + 10)
y - 7 = -2(x + 10)
y - 7 = -2x -20
y = -2x -20 + 7
y = -2x -13
Thus, h(x) = -2x -13
Hence, h(3) = -2(3) -13
= -6 -13
= -19
Therefore, h(3) = -19
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one cubic foot holds 7.48 gallons of water and one gallon of water 8.33 pounds. How much does 5.1 cubic ft of water weigh in pounds? In tons?
The 5.1 cubic ft of water weighs 317.77 pounds
The weight of 5.1 cubic ft of water in tons is 0.16 tons
Calculating weightFrom the question, we are to calculate how much 5.1 cubic ft of water weigh in pounds
From the given information,
"one cubic foot holds 7.48 gallons of water"
Therefore,
5.1 cubic ft of water = 5.1 × 7.48 gallons of water
= 38.148 gallons of water
Also,
"one gallon of water 8.33 pounds"
That is,
38.148 gallons of water = 38.148 × 8.33 pounds
= 317.77 pounds
Thus, 5.1 cubic ft of water weigh 317.77 pounds
For the weight in tons
NOTE: 1 pounds = 0.0005 tons
∴ 317.77 pounds = 0.0005 × 317.77 tons
= 0.158886 tons
≈ 0.16 tons
Hence, the weight of 5.1 cubic ft of water in tons is 0.16 tons
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How many board feet of wood are there in 750-2 x 10-16'?
Answer:
Step-by-step explanation:
Newton’s law of cooling describes the rate at which an exposed body changes temperature through radiation which is approximately proportional to the difference between the object’s temperature and its surroundings, provided the difference is small.
Definition: According to Newton’s law of cooling, the rate of loss of heat from a body is directly proportional to the difference in the temperature of the body and its surroundings.
Answer:
Radioactivity is the phenomenon of the spontaneous disintegration of unstable atomic nuclei to atomic nuclei to form more energetically stable atomic nuclei. Radioactive decay is a highly exoergic, statistically random, first-order process that occurs with a small amount of mass being converted to energy. Since it is a first-order process, each radioactive species is characterized by its own half-life, the length of time in which an initially very large number of such nuclei will have decayed to only half the original number.
Step-by-step explanation:
Find the area of the figure. (Sides meet at right angles.)
5 yd
4 yd
2 yd
2 yd
yd
2 yd
4 yd
Answer:
1,024yd
Step-by-step explanation:
a=a to the second,= 32(2)= 1,024
Determine a series of transformations
that would map Figure U onto Figure V.
i need help asap
Answer:
di ko maintindihan
Step-by-step explanation:
kase ala ako alam jan
A recent study of 50 U.S. chess players details such things as the number of years the players have been active and the chess ratings of the 50 players. (A chess rating is a number, with a higher number indicating greater expertise.) The chess rating data for the sample of 50 players are summarized in the following histogram.
Using the given histogram, we have that 90% of the players in the sample have scores that are less than 2300.
What is the missing information?This problem is incomplete, but researching it on a search engine, we have that the histogram states as follows:
6 of these players have scores between 300 and 700.6 of these players have scores between 700 and 1100.13 of these players have scores between 1100 and 1500.14 of these players have scores between 1500 and 1900.6 of these players have scores between 1900 and 1300.5 of these players have scores between 2300 and 2700.It asks the proportion of players in the sample with scores that are less than 2300.
What is an histogram?An histogram is a graph that shows the number of times each element of x was observed.
Above, we already gave the amounts presented by histogram, and we have that 45 out of 50 players have scores that are less than 2300, hence the proportion is given by:
p = 45/50 = 0.9.
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how many tablespoons are there in fluid ounces
Answer:
6
Step-by-step explanation:
There are six teaspoons in one fluid ounce - lots of conversion sites out there to get more info if needed.
Can somone help me with thisASAP
What is the turning point of the graph of f(x)=|x|+4 ?
(0, −4)
(0, 4)
(4, 0)
(−4, 0)
The turning point is the point where the function changes its slope for the given mode function f(x)=|x|+4 the turning point is at (0,4) so option (B) will be correct.
What is a graph?A graph is a diametrical representation of any function between the dependent and independent variables.
The graph is easy to understand behavior of the graph.
Given the mode function,
f(x)=|x|+4
For x < 0 the function f(x) will be
f(x) = -x + 4
For x > 0 the function f(x) will be
f(x) = x + 4
Now,
Slope at x < 0 → f'(x) = -1
Slope at x > 0 → f'(x) = +1
Since the slope is changing at x = 0 there fore x = 0 will be the turning point of the graph.
Hence "The turning point of the given mode function f(x)=|x|+4 will be at x = 0".
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The cost y (in cents) of producing x gallons of Ectoplasm hair gel is given by the cost equation y2 − 10xy = 200. Evaluate dy dx at x = 1. (Round your answer to two decimal places.)
The value of dy/dx at x = 1 is mathematically given as
dy/dx=5-1.8898i
This is further explained below.
What is the value of dy/dx at x = 1 ?Generally, Given that cost y of producing x gallons ag an implicit evaluation
y^2-10 x y=200
Differentiate the above equation as
[tex]\begin{aligned}&2 y y^{\prime}-10 y-10 x y^{\prime}=0 \\&y^{\prime}(2 y-10 x)=10 y \\&y^{\prime}=\frac{10 y}{2 y-70 x}=\frac{5 y}{y-5 x}\end{aligned}[/tex]
when x=1, substitute in the given equation to get y value
y^2-10 y=200
or
y=5+13.2288i
y=5−13.2288i
y represents the cost and hence cannot be negative Hence practical solution for y is y=5+13.2288i substitute in the ' y ' equation to get [tex]$\frac{d y}{d x}$ at $x=1$[/tex]
when x=13 y=5+13.2288i
Hence
d y/d x at x=1 will be
dy/dx[tex]=\frac{5(5+13.2288i)}{5+13.2288i-5}[/tex]
[tex]dy/dx=\frac{25+66.144}{13.2288i}[/tex]
dy/dx=5-1.8898i
In conclusion, the value of dy/dx at x = 1 i
dy/dx=5-1.8898i
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Just like Earth, other planets have
seasons. In fact, Neptune's seasons last
for 40 years! How many days would
winter last? (Hint: A year is 365 days).
Winter would last for 14,600 days
How to calculate the number of days that winter would last ?Planet can be described as celestial bodies that move around the sun. The earth and Neptune are typical examples of planets. There are 8 planets in the solar system.
Other planets have different seasons same way as Earth
Neptune's season last for 40 years
Therefore the number of days that winter would last can be calculated by multiplying the number of years which is 40 by the number of days in a year which is 365
1 year is 365 days
Since it 40 years then we multiply by 365
= 365 × 40
= 14,600
Hence Winter would last for 14,600 days
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To two decimal places,
√70
must lie between ____
and _____.
To two decimal places ✓70 just be between 8.36 and 8.37.
How to illustrate the information?It should be noted that we simply have to calculate the information is to find the square root of 70.
Therefore, this is approximately 8.366
Therefore, to two decimal places ✓70 just be between 8.36 and 8.37.
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Which of the following is a true statement?
a. Only option A will allow them to meet their goal.
b. Only option B will allow them to meet their goal.
c. Saving by either option A or option B will allow them to meet their goal.
d. Neither option A nor option B will allow them to meet their goal.
The true statement is c. Saving by either option A or option B will allow them to meet their goal.
What is a true statement?A true statement can be described as the statement that that the message is been stated or declared which could be in a communication (oral or written) in setting forth particulars or facts.
In this case, we can see that true statement is c. Saving by either option A or option B will allow them to meet their goal this is because we can see a fact from how both option present their words.
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COMPLETE QUESTION:
Option A: Stay with saving the original amount each week but take the class a week later than originally planned.
Option B: Increase the amount of money he saves each week by $15 from his original plan.
Question 2 of 10 Suppose a population consists of 5000 people. Which of the following numbers of members of the population being surveyed could result in a sample statistic but not a parameter ? A. Both 50 and 5000 B. 50 C. Neither 50 nor 5000 D. 5000
Out of the population being surveyed, the one that could result in a sample statistic but not a parameter is; B: 50
What is the Sample Statistic?
A sample statistic is a piece of information you get from a fraction of a population.
A parameter is a number describing a whole population (e.g., population mean), while a statistic is a number describing a sample (e.g., sample mean).
Now, we are told that a population consists of 5000 people. This means that the sample statistic could be the sample mean which could be 50 but certainly not 5000 as the sample statistic can't be same as the population.
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Dave took an exam with 40 questions. He answered 32 correctly. What
was his grade for the exam? Write the grade as a percent.
www
% (Round to the nearest percent as needed.)
Step-by-step explanation:
40 = 100%
1% = 100%/100 = 40/100 = 0.4
how many % are 32 ?
as many % as 1% (0.4) can fit into 32 :
32 / 0.4 = 80%
his grade was 80%.
Write an equation letting
x
be the unknown number.
two subtracted from a number is 2.
Answer: x-2=2 (x=4)
Step-by-step explanation:
4 minus 2 equals 2
What is the least integer whose square root is an irrational number between 5 and 7? 13 6 25 26
Answer:
26
Step-by-step explanation:
Comment
Irrational means that the number cannot be represented as a fraction. This question means that the square root itself is between 5 and 7. Be careful how you read the question.
That means you have to take the square root of the given number and see where it lands.
√13 = 3.61 which is not between 5 and 7
√6 is going to be even smaller. Not the answer
√25 = 5 The question says between. Not the answer.
√26 = 5.09 which is greater than 5 and and less than 7
this I never got taught, need help bunch of points
Answer:
Absolute value is the distance from 0 all negative numbers become positive and positive stays positive.
Step-by-step explanation:
Use dimensional analysis to solve the following conversions. Be sure to show all work and answer with the correct number of significant figures. Please help!!
By using dimensional analysis we find the following two results:
a) 0.30 m = 0.984 ft
b) 150 km / h = 1.554 mi / h
How to use dimensional analysisIn this problem we must find a quantity of a given unit that is equivalent to another value of another unit of the same kind. For instance, we must look up for the quantity in a unit length equivalent to another quantity in another unit length. Now we proceed to obtain all the equivalencies by simple rule of three:
a) 0.30 m × (1 ft / 0.3048 m) = 0.984 ft
b) 150 km / h × (1 mi / 1.609 km) × (1 h / 60 min) = 1.554 mi / h
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9. A submarine is 140 ft
below sea level. It rose 30 ft.
What integer describes the
new depth of the submarine?
Answer:
it's easy if you set your mind to it, think about it angain
By which angle measures can the regular pentagon be rotated so it maps onto itself? Select each correct answer. 72° 72° 90° 90° 135° 135° 144° 144° 216° 216° 300°
The regular pentagon can be rotated through at angles of 72, 144°, 216°, and 288° to map it onto itself.
What is a regular polygon?A polygon is a two-dimensional geometric shape having a finite number of sides. Single-direction segments are connected end to end to make a closed shape on the sides or edges of polygons. The locations where two line segments converge to construct an angle are referred to as vertices or corners.
It is given that:
The pentagon has five sides.
As we know, the standard pentagon has five vertices and internal angles that are each 72 degrees. A regular pentagon also possesses rotational symmetry.
The angles are 72°.144°,216°, and 288°.
Thus, the regular pentagon can be rotated through at angles of 72, 144°, 216°, and 288° to map it onto itself.
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write 15/7 as a mixed number
The result can be shown in multiple forms.
Exact Form:
15/7
Decimal Form:
2.142857
Mixed Number Form:
2 1/7
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Usually I try to explain what to do, but it's been a hot second from when I learned this. I uploaded a picture that might help.
This is a free tool for solving math problems if you ever need help: (no spaces or exclamation point) mat h way . co!m
------------------------
much love <333 good bye!!
Identify the values of a, b, and c that could be used with the quadratic formula to solve the equation. Enter a as a positive
integer value.
x²=8(x-5)
Answer:
See below
Step-by-step explanation:
Expand to get x^2 - 8x + 40 = 0
a = 1 b = -8 c = 40
Why do banks charge a fee when clients transact on their accounts?
Answer:
Banks charge fees to help make a profit.
Step-by-step explanation:
Bank fees allow financial institutions to recoup operating expenses. Banks also make money on loans, via interest and other fees.
PLS HELP THANK YOU VERY MUCH
Given AB, explain how to construct a square with sides of length AB.
Answer:
because it is a square, you just need to make a square with the side lenghts all being a or b
Step-by-step explanation:
the difference of a number and eight is four. Find the number.
SOMEONE HELP PLEASE PLEASE
Answer: Stand A
Step-by-step explanation:
A.
3/4 of a pound is $2
[tex]\frac{4}{3} x=2\\\\\x=\frac{2}{\frac{3}{4} } =\boxed{\frac{8}{3} \ or\ 2.66}[/tex]
Therefore one pound is $2.7 rounded
B.
[tex]\frac{5}{4} x=3.45\\\\x=3.45*\frac{4}{5} \\\\x=\boxed{2.76}[/tex]
Therefore one pound is $2.8 rounded
C.
[tex]\frac{11}{2} x=14.85\\\\x=14.85\times\frac{2}{11} \\\\x=\boxed{2.7}[/tex]
Therefore one pound is $2.7
The stand that sold tomatoes for the least expensive price per pound is Stand A because they sold theirs for $2.66 while the other stands sold them for more.
ITS DUEE TODAY PLEASEDE
Answer:
scale factor from A to B = 3
Step-by-step explanation:
the scale factor is the ratio of corresponding sides, image to original
scale factor = [tex]\frac{9}{3}[/tex] = 3 ( measure of horizontal sides )
Please hurry due today I will give brainlest
Solve for c. a = 11+4b-4c
Answer:
yes i think thats right
Step-by-step explanation:
if not then it might be b
6 less the quantity 9 times a number
Answer:
6-9x
Step-by-step explanation:
Converted from word to standard form.
Hope it helps!
If the sum of a number and two is tripled, the result is five less than twice the number . Find the number
If the sum of a number and two is tripled, the result is five less than twice the number, the number is - 11
Let the given number be x,
the number, x is added with 2 and then it is tripled which means (x + 2)*3 is equal to five less than two times of that number which is 2x - 5
3(x + 2) = 2x - 5
3x + 6 = 2x - 5
3x - 2x = - 5 + (-6)
x = - 11
Therefore, If the sum of a number and two is tripled, the result is five less than twice the number, the number is - 11
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The length of a rectangle is 4 units greater than its width, and the area of the rectangle can be
expressed by the equation y = x + 4x. What is a reasonable domain for this function?
O
O
O
O
A y>0
By> 4
C X>0
D X> 2
The reasonable domain for this function is [tex](x > 0)[/tex] .
The collection of all feasible values for the independent variable is referred to as a function's domain.
When we substitute different values for the independent variable from the domain, the dependent variable's range refers to the set of all conceivable values for that variable.
Let the width of the rectangle be x units.
Thus as per given information length becomes x+4 units.
It is given, the area of rectangle can be expressed by the equation
[tex]y=x^{2} +4x[/tex]
Now let's find domain of this function.
clearly x cannot be zero and x cannot be negative because x represents the width of the rectangle and the width of a rectangle cannot be zero or negative.
Therefore the domain of the function is
[tex](0,\infty)[/tex] or x>0 .
Therefore the domain is given by the thirds option (c) x>0 .
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