15 ft = 15*12 = 180 inches
180/4 = 45
so the scale is 1/45
Find an equation of a linear function given h(1)=6 and h(4)=-3
We can rewrite this in the form of h (t):
at t = 1, h = 6
at t = 4, h = -3
The linear equation is in the form of:
h = mt + b
where m is the slope and b is the h-intercept
So calculating for the slope m:
m = [-3 – 6] / (4 – 1)
m = (-9) / 3
m = -3
So,
h = -3t + b
Solving for b by plugging in any pair:
6 = -3(1) + b
b = 9
Therefore:
h = -3t + 9
what is the measure of an angle that turns through 1/12 of a circle
The measure of an angle that turns through 1/12 of a circle is 30 degree.
What is Angle?A pair of rays (half-lines) with a shared terminal are combined to form an angle. The latter is referred to as the angle's vertex, and the rays are sometimes referred to as the angle's legs and other times as its arms.
We know the complete is 360 degree.
Then, to turn 1/12 of circle
= 360 x 1/2
= 360 / 12
= 30 degree
Thus, the measure of angle is 30 degree.
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simplify
14+4(12−34)2
Answer: The required simplified answer is 1950.
Step-by-step explanation: We are given to simplify the following algebraic expression :
[tex]E=14+4(12-34)^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To simplify the given expression, first we evaluate the square term, multiply it by 4 and add the result to 14.
From expression (i), we get
[tex]E\\\\=14+4(12-34)^2\\\\=14+4(-22)^2\\\\=14+4\times484\\\\=14+1936\\\\=1950.[/tex]
Thus, the required simplified answer is 1950.
The Hamptons family has a fish tank holding 10,450 ml of water. The water is leaking at a rate of 270 ml per minute. Define the input and output in the given scenario
The input is any variable which goes into the system. In this case there is no input.
While the output is any variable going out of the system. In this case the output is the amount of water which leaked out.
Answer:
The number of minutes represents input and remaining water represents output.
Step-by-step explanation:
Given,
The original quantity of the water in the tank = 10,450 ml,
Also, the quantity of the water leaked per minute = 270 ml,
Thus, the quantity water leaked in x minutes = 270x
∵ Remaining water in the tank ( say y ) = Original water - leaked water
⇒ y = 10450 - 270x,
Which is the equation that shows the given scenario.
In this equation, x represents the input value and y represents the output value,
Hence, the number of minutes represents input and remaining water represents output.
70 is 20% of what number
A soccer player runs 1 5/6 miles during the first half of a match and 2 1/2 miles during the second half. How many miles does he run during the match in total?
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The total cost CC (in dollars) to participate in a ski club is given by the literal equation C=85x+60C=85x+60, where xx is the number of ski trips you take
How many ski trips do you take if you spend a total of $315? $485?
Answer:
The total cost C (in dollars) to participate in a ski club is given by the literal equation :
[tex]C=85x+60[/tex]
Where x is the number of ski trips you take.
1. When C = 315 ;substituting the value of C in the above equation.
[tex]315=85x+60[/tex]
=> [tex]85x=315-60[/tex]
=> [tex]85x=255[/tex]
x = 3 trips.
2. When C = 485
[tex]485=85x+60[/tex]
=> [tex]85x=485-60[/tex]
=> [tex]85x=425[/tex]
x = 5 trips.
Which represents a rational Number and how can you tell?[tex] \sqrt{17} \sqrt{36} \sqrt{50} \sqrt{101} [/tex]
Dos angulos consecutivos de un paralelogramo estan e la relacion de 2 a 7. calcula el mayor angulo del paralelogramo
if a=b then ac=bc. this called the of quality.(2words)
Stan and hilda can mow the lawn in 35 min if they work together. if hilda works twice as fast as stan, how long would it take stan to mow the lawn alone?
There is 6/8 of a birthday cake leftover after a birthday party. How many 1/4 pieces can be made from the leftover cake?
divide both 6 & 8 by 2 6/2 = 3
8/2 = 4
so 6/8 = 3/4
there is 3 pieces
Elton pours 41 1/4 ounces of water from a large pitcher into a bottle. That amount is 2/5 of the water that was in the pitcher. There were _____ ounces of water in the pitcher.
Write your answer as a mixed number in lower terms.
Which pair of angles are interior angles?
A. 1 and 8
B. 3 and 6
C. 3 and 4
D. 3 and 5
3 & 5 are the interior angles
Answer is D
The Kendal Company manufactures automobile engine parts. Running the manufacturing operations requires 12 watts (units of electricity per hour). The amount of electricity required to run the manufacturing operations and lighting the facility is given by y = 12x + 24, where x is the number of hours of manufacturing and y is the amount of electricity expended. How much electricity is used on a day when no parts are manufactured? (x 0, y 0)
Answer:
The answer is 24 watts.
Step-by-step explanation:
Running the manufacturing operations requires 12 watts (units of electricity per hour).
The amount of electricity required to run the manufacturing operations and lighting the facility is given by [tex]y=12x+24[/tex]
Here x is the number of hours of manufacturing and y is the amount of electricity expended.
When there are no parts manufactured, then x = 0
[tex]y=12(0)+24[/tex] = 24.
what is the solution of 1/3b = -3
If x represent a number , then write an expression for one half the sum of x and 7
the sum of x and 7 would be x+7
then to get half of that you would divide by 2
so equation is (x+7)/2
If r = x, y, z and r0 = x0, y0, z0 , describe the set of all points (x, y, z) such that |r − r0| = 5.
We are concern about the vector (x-x0, y-y0, z-z0) equaling to 5.
This happens when √(x-x0)^2 + (y-y0)^2 + (z-z0)^2 = 5
Square both side:
(x-x0)^2 + (y-y0)^2 + (z-z0)^2 = 25 , a sphere
Which you will recognize as a circle of radius one centered at (x0, y0, z0)
Answer:
Point [tex]\left ( x,y,z\right )[/tex] represents a sphere
Step-by-step explanation:
Take [tex]r=\left ( x,y,z \right )\,,\,r_0=\left ( x_0,y_0,z_0 \right )[/tex]
We need to describe the set of all points (x, y, z) such that [tex]\left | r-r_0 \right |=5[/tex]
Solution :
For [tex]r-r_0=\left ( x,y,z \right )-\left ( x_0,y_0,z_0 \right )[/tex], we will subtract the respective elements .
[tex]r-r_0=\left ( x,y,z \right )-\left ( x_0,y_0,z_0 \right )=\left ( x-x_0,y-y_0,z-z_0 \right )[/tex]
Therefore, [tex]\left | r-r_0 \right |=\sqrt{(x-x_0)^2+(y-y_0)^2+(z-z_0)^2}[/tex]
As [tex]\left | r-r_0 \right |=5[/tex], we get
[tex]\sqrt{(x-x_0)^2+(y-y_0)^2+(z-z_0)^2}=5[/tex]
On squaring both sides, we get
[tex]\left ( \sqrt{(x-x_0)^2+(y-y_0)^2+(z-z_0)^2} \right )^2=5^2\\(x-x_0)^2+(y-y_0)^2+(z-z_0)^2=25[/tex]
The general equation of a sphere is (x - a)² + (y - b)² + (z - c)² = r², where (a, b, c) denotes the center of the sphere and r represents the radius .
So, [tex](x-x_0)^2+(y-y_0)^2+(z-z_0)^2=25[/tex] represents a sphere with center as [tex]\left ( x_0,y_0,z_0 \right )[/tex] and radius equal to 5 units
About 36,100,000 households in the U.S. have cats and about 43,300,000 households have dogs. About how may more households dogs and cats
It takes the earth 24 hours to complete a full rotation. It takes mercury approximately 58 days, 15 hours, and 30 minutes to complete a full rotation. How many hours does it take mercury to complete a full rotation?
Mercury takes approximately 1407.5 hours to complete a full rotation, calculated by converting 58 days, 15 hours, and 30 minutes entirely into hours.
Explanation:To calculate how many hours it takes for Mercury to complete a full rotation, we need to convert the given time of approximately 58 days, 15 hours, and 30 minutes into hours. Here are the step-by-step calculations:
First, convert the days into hours. Since there are 24 hours in a day, we multiply 58 days by 24 hours per day.58 days × 24 hours/day = 1392 hoursNext, add the additional hours to the total from the days.1392 hours + 15 hours = 1407 hoursFinally, convert the minutes to hours. There are 60 minutes in an hour, so we divide 30 minutes by 60.30 minutes ÷ 60 minutes/hour = 0.5 hoursAdd this to the total number of hours.1407 hours + 0.5 hours = 1407.5 hoursTherefore, it takes Mercury approximately 1407.5 hours to complete a full rotation.
Using graphite furnace atomic absorption spectrometry, the mean cadmium (cd2 ) content value in a homogenized sample of 40 zebra mussles was found to be 7.50 ppb cd2 with a standard deviation (s) of 0.52 ppb cd2 (assume that s is a good approximation of σ). calculate the 90% and 95% confidence intervals (ci) for: (a) two analyses and (b) five analyses of this homogenized sample.
Whats the rule for this pattern, 3,1.5,0,-1.5,-3
Final answer:
The rule for the pattern 3, 1.5, 0, -1.5, -3 is to subtract 1.5 from the previous term in the sequence.
Explanation:
The rule for the number pattern 3, 1.5, 0, -1.5, -3 is subtracting 1.5 from the previous number each time. To identify this, observe the difference between consecutive terms:
From 3 to 1.5 we subtract 1.5 (3 - 1.5 = 1.5).
From 1.5 to 0 subtract 1.5 (1.5 - 1.5 = 0).
From 0 to -1.5 subtract 1.5 (0 - 1.5 = -1.5).
And from -1.5 to -3, again subtract 1.5 (-1.5 - 1.5 = -3).
This pattern consistently decreases by 1.5, and it can be continued indefinitely by keeping this rule in mind.
Which expression is equivalent to x6 – 9?
Answer:
(x3)2 – 32
Step-by-step explanation:
Which word describes the slope of the line?
positive
negative
zero
undefined
Answer:
positive
Step-by-step explanation:
The slope is the inclination of the line with respect to the x-axis. It is denoted by the letter [tex]m[/tex]. In mathematical language, the slope [tex]m[/tex] of the line is defined as the difference on the y-axis divided by the difference on the x-axis for two different points [tex]P_1(x_1,y_1)[/tex] and [tex]P_2(x_2,y_2)[/tex] on the line:
[tex]m=\frac{\Delta y}{\Delta x} =\frac{y_2-y_1}{x_2-x_1}[/tex]
If:
[tex]m>0[/tex] The slope is positive and the line is increasing from left to right[tex]m<0[/tex] The slope is negative and the line is decreasing from left to rightIf a line is vertical the slope is undefined[tex]m=0[/tex] is a constant function.
Since the graph of the linear function shown is increasing from left to right, we can conclude that the slope is positive.
Is it possible for two different numbers, when squared, to give the same result? What does this result tell you about solving an equation when the variable is squared? How many solutions will an equation like this have? Will there always be the same number of solutions for any equation with a squared variable? Explain.
Grandpa Schmidt is 75 years old this is nine years less than seven times the age of Junior submit how old is Junior
Natalia is making gift bags for her son's birthday party. Each bag costs $3.24 to make and she needs to make 15 bags. How much will the 15 bags cost?
A.) $48.60
B.) $47.40
C.) $486.00
D.) $4.74
Answer:
48.60
Step-by-step explanation:
The answer is $48.60 you just have to multiply the amount of bags times the cost of each bag to get your amount so
15 x 3.24 =48.60
An arithmetic sequence with a thrid term of 8 and constant difference of 5
In winter, the price of apples suddenly went up by \$0.75$0.75dollar sign, 0, point, 75 per pound. Sam bought 333 pounds of apples at the new price for a total of \$5.88$5.88dollar sign, 5, point, 88.
Write an equation to determine the original price per pound (p)(p)left parenthesis, p, right parenthesis.
Your formula would be 3(p+0.75)=5.88
Because you have 3 pounds and 0.75 for each.
Solving the equation by distributing, you will get P=1.21
Hope this helps!
The equation will be 3 (p + 0.75) = 5.88. Then the original price per pound p will be 1.21.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
In winter, the price of apples suddenly went up by a $0.75 dollar sign per pound. Sam bought 3 pounds of apples at the new price for a total of $5.88 dollar sign.
The original price per pound p will be
3 (p + 0.75) = 5.88
p + 0.75 = 1.96
p = 1.96 - 0.75
p = 1.21
The equation will be 3 (p + 0.75) = 5.88. Then the original price per pound p will be 1.21.
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