Observe the given data carefully. The x-values increase at rate 4 while the y-values increase at rate 9. So it concludes that the increase is linear.
Also we know that only two points are sufficient two get the equation of a line.
Consider the first two points (4,9) and (8,19).
Apply the two point form of straight line,
[tex]undefined[/tex]Score on last try: 0 of 7 pts. See Details for more.> Next questionGet a similar questionYou can retry this question belowWater Pressure ApplicationIn certain deep parts of oceans, the pressure of sea water, P, in pounds per square foot, at a depth5of d feet below the surface, is given by the following equation P = 15+ d. Use this equation to13complete the statements below. Round your answers to the nearest tenth as needed.PThe pressure of sea water is 100 pounds per square foot at a depth of 1surface of the water.Ifeet below the+The pressure of sea water is 67.5x pounds per square foot at a depth of 80 feet below thesurface of the water.Question Help: D Video D Post to forum
1. The pressure of sea water is 100 pounds per square foot (P=100) at a depth (d):
[tex]100=15+\frac{5}{13}d[/tex]Solve d:
[tex]\begin{gathered} \text{Subtract 15 in both sides of the equation:} \\ 100-15=15-15+\frac{5}{13}d \\ \\ 85=\frac{5}{13}d \\ \\ \text{Multiply both sides of the equation by 13/5:} \\ \frac{13}{5}\cdot85=\frac{13}{5}\cdot\frac{5}{13}d \\ \\ 221=d \\ \\ d=221 \end{gathered}[/tex]Then, The pressure of sea water is 100 pounds per square foot at a depth of 221 feet below the surface of the water2. Find the pressure of the water (P) when d=80
[tex]\begin{gathered} P=15+\frac{5}{13}(80) \\ \\ P=15+\frac{400}{13} \\ \\ P=\frac{195+400}{13} \\ \\ P=\frac{595}{13} \\ \\ P=45.8 \end{gathered}[/tex]Then, the pressure of sea water is 45.8 pounds per square foot at a depth of 80 feet below the surface of the watersolve. x/5 + 3 = 2 help pls
Use the properties of equalities to solve the given equation:
[tex]\frac{x}{5}+3=2[/tex]First, susbtract 3 from both sides of the equation:
[tex]\frac{x}{5}+3-3=2-3[/tex]Simplify the expressions on both sides of the equation:
[tex]\frac{x}{5}=-1[/tex]Multiply both sides by 5:
[tex]\frac{x}{5}\cdot5=-1\cdot5[/tex]Simplify the expressions on both sides of the equation:
[tex]x=-5[/tex]Therefore, x=-5
chose the image that has the correct markings for the congruent statement.
We need to identify the image with the correct markings for the congruent statement:
[tex]\Delta MLK\cong\Delta MLR[/tex]Notice that the sequence of the letters in both triangles tells the corresponding angles, which are congruent. Also, it tells us the corresponding sides with the same lengths.
So, we must have:
[tex]\begin{gathered} M\hat{L}K\cong M\hat{L}R \\ \\ K\hat{M}L\cong R\hat{M}L \\ \\ L\hat{K}M\cong L\hat{R}M \end{gathered}[/tex]Also:
[tex]\begin{gathered} \overline{LK}=\overline{LR} \\ \\ \overline{KM}=\overline{RM} \end{gathered}[/tex]Since congruent angles or sides with the same lengths should have the same markings, the image that has the correct markings is:
Answer
Suppose that scores on a particular test are normally distributed with a mean of 110 and a standard deviation of 15. What is the minimum score needed to be in the top 20% of the scores on the test? Carry your intermediate computations to at least four decimal places, and round your answer to one decimal place.
Given:
mean of 110 and a standard deviation of 15.
Required:
Carry your intermediate computations to at least four decimal places, and round your answer to one decimal place.
Explanation:
Since we know the formula of
if Z has a standard normal probability distribution, what is the probability that Z is between -2.32 and 0.51?
Solution
Given
[tex]P(-2.32A student has 40 dimes and nickels. Their total value is $3.25. If d = number of dimes and n = number of nickels, this system of equations represents the situation:
Solution
Solving the two-equation simultaneously,
[tex]\begin{gathered} d+n=40\equiv10d+10n=400\text{ --------\lparen1\rparen} \\ \\ 0.10d+0.05n=3.25\equiv10d+5n=325\text{ ------\lparen2\rparen} \\ \\ (1)-(2) \\ \\ (10-5)n=400-325 \\ \\ 5n=75 \\ \\ n=15 \end{gathered}[/tex]When n = 15
[tex]\begin{gathered} d=40-n \\ \\ d=40-15=25 \end{gathered}[/tex]The correct option is C
A rectangular garden is 25 feet wide. Its length is 5 feet more than twice the width. What is the area of the garden?
Given:
A rectangular garden is 25 feet wide. Its length is 5 feet
Required:
To calculate the area
Explanation:
Area of rectangle =
[tex]l\times b=25\times5=125ft^2[/tex]Required answer:
125
An aquarium can be modeled as a right rectangular prism and it can hold 980 cubic inches of water when it is full. Its width is 7 in and height is 7 in. Find the length of the aquarium in inches. Round your answer to the nearest tenth if necessary.
Given:
Volume of the prism is 980 cubic inches.
Width is 7 in and height is 7 in.
Required:
To find the length of the prism.
Explanation:
The volume of the right rectangular prism is given by,
[tex]V=lwh[/tex]Therefore,
[tex]\begin{gathered} 980=l\times7\times7 \\ \\ 980=49l \\ \\ l=\frac{980}{49} \\ \\ l=20in \end{gathered}[/tex]Final Answer:
Length is 20 inches.
Answer:20
Step-by-step explanation:
rewrite y=1/5x + 1/5 in point slope form
Slope means the inclination of the line
the equation is Y - y1 = m (X - x1)
then we need to find a point in the line,
for example if x=1 then y=
y = 2/5
m the slope is the number that goes with X,
so the slope is 1.5
And finally repacing we find
Y - 1 =
The length of a rectangle is 11 meters and the width is 6 meters.What is the perimeter of the rectangle? Do not include units inyour answer.
34 meters
ExplanationThe perimeter of a rectangle is the sum of all its sides.
It is given by the equation:
2 x (side 1 + side 2)
In this case we have a rectangle with dimensions of 11 and 6:
If we add them, we will obtain the perimeter:
11 + 6 + 11 + 6 = 34
or using the equation:
2 x ( 11 + 6 ) = 2 x 17 = 34
That is why the perimeter is 34 meters.
Using Logarithmic functions and exponential functions simplify the following. Be sure to express with positive exponents.
For this problem, we need to simplify the following expression:
[tex](m\cdot n)^{-1}[/tex]Whenever a base is elevated to the power of a negative number, we need to invert the fraction, such that the base will transform into the denominator, as shown below:
[tex](m\cdot n)^{-1}=\frac{1}{m\cdot n}[/tex]Yesterday, 2/3 of the 120 students in a contest gave their speeches. How many students gave their speeches?Write your answer in simplest form.
Given:
2/3 of the 120 students in a contest gave their speeches.
so, the number of the students who gave their speeches =
[tex]\frac{2}{3}\cdot120=\frac{2\cdot120}{3}=\frac{240}{3}=80[/tex]so, the answer will be: 80 students gave their speeches
3. Estimate 2,137 68 by looking for a basic fact,
A basic fact that can be used is 21 ÷
4. Use the basic fact to rewrite
the division using numbers
near to the actual numbers.
5. Find the quotient of your
rewritten division problem.
Use a pattern to help.
1'
So, 2,137 ÷ 68 is about
2,137 ÷ 68
2,100 =
70 = ?
2,100
21 ÷ 7 =
210 ÷ 70 =
2,100 ÷ 70 =
21 tens divided into
groups of 7 tens
-210 tens divided into
groups of 7 tens
determine the range of y=√x/√2
We have the expression:
[tex]y=\frac{\sqrt[]{x}}{\sqrt[]{2}}[/tex]Wich means that x can be negative, so:
[tex]x\ge0[/tex]And that give us that y also is not negative, so:
[tex]y\in\lbrack0,\infty)[/tex]Find the distance CD rounded tothe nearest tenth.C = (7,-4) and D = (-8,-5)CD = [? ]HINT: Use the distance formula:d = V(x2 – xı)2 + (y2 – yı)2
Let:
[tex]\begin{gathered} (x1,y1)=(7,-4) \\ (x2,y2)=(-8,-5) \end{gathered}[/tex]Using the distance formula:
[tex]\begin{gathered} d=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ so\colon \\ d=\sqrt[]{(-8-7)^2+(-5-(-4))^2} \\ d=\sqrt[]{(-15)^2+(-1)^2} \\ d=\sqrt[]{226} \\ d\approx15.0 \end{gathered}[/tex]List the possible rational roots of the equation & solve:2x^4 -9x^3 + 13x^2 - x -5 =0
Given:
[tex]2x^4\:-\:9x^3\:+\:13x^2\:-x-5\:=\:0[/tex]Using the rational root theorem
The rational root theorem, also called rational root test, in algebra, theorem that for a polynomial equation in one variable with integer coefficients to have a solution (root) that is a rational number, the leading coefficient (the coefficient of the highest power) must be divisible by the denominator of the fraction and the constant term (the one without a variable) must be divisible by the numerator.
The following rational roots are possible:
[tex]\begin{gathered} \pm\text{ }\frac{1,5}{1,2} \\ \\ \pm\frac{1}{2},\text{ }\pm1,\text{ }\pm\frac{5}{2},\text{ }\pm5 \end{gathered}[/tex]Next, we validate the roots by plugging them into the polynomial
The only roots that satisfy the polynomial includes :
[tex]x\text{ = 1, x = -}\frac{1}{2}[/tex]Answer:
The possible rational roots are
[tex]\begin{gathered} x\text{ = 1} \\ x\text{ = -}\frac{1}{2} \end{gathered}[/tex]classify each quadrilateral be as specific as possible
1. it has two equal non-parallel sides, it is a trapezoid.
2. it has equal sides two by two and the 4 right angles, it is a rectangle.
3. equal sides two by two, it is a rhomboid.
4. it has 4 equal sides, it is a rhombus.
recently the number of visitors to Machu Picchu is limited to 2500 visitors daily the area of Machu Picchu is about 13 km squared to calculate Machu Picchu current daily visitor density daily visitors per square mile use dimensional analysis to show your work round to the nearest hundred people per square mile
recently the number of visitors to Machu Picchu is limited to 2500 visitors daily
the area of Machu Picchu is about 13 km squared
to calculate Machu Picchu current daily visitor density daily visitors per square mile use dimensional analysis
to show your work round to the nearest hundred people per square mile
Density of visitors per squared kilometer = 2500/13
13 km² = 5.01933 squared miles
Density of visitors per squared mile = 2500/5.01933 = 498.07 ≈ 500 rounded to the nearest hundred
Answer:
500 peple per square mile
Which equation finds the volume of a cube with a side length of 20 units?8n18cubic unitscubic unitso (278) 9 - 80 (210) * - 2016o 2(10) - 2016o 2(10) - Bntecubic unitscubic unitshelp please
The volume of a cube is found using the formula,
[tex]V=s^3[/tex]Where
V is the volume
s is the side length
Given
[tex]s=2n^6[/tex]Plugging into the formula,
[tex]\begin{gathered} V=s^3 \\ V=(2n^6)^3 \\ V=2^3n^{6\times3} \\ V=8n^{18} \end{gathered}[/tex]Answer[tex]8n^{18}\text{ cubic units}[/tex]In the diagram, E is the centroid of ABC. AD = 7.5 centimeters, AD BC and AE BD.
Determine the length of side AE.
[tex]\begin{gathered} AE=\frac{2}{3}AD \\ =\frac{2}{3}\cdot7.5 \\ =5 \end{gathered}[/tex]So length of side BD is equal to 5 cm.
Determine the length of side AB.
[tex]\begin{gathered} (AB)^2=(7.5)^2+(5)^2 \\ =56.25+25 \\ =81.25 \\ AB=\sqrt[]{81.25} \\ \approx9.01 \end{gathered}[/tex]The length of side AB and AC is equal so,
[tex]AC=9.01[/tex]Determine the perimeter of triangle.
[tex]\begin{gathered} P=2\cdot5+9.01+9.01 \\ =10+18.02 \\ =28.02 \end{gathered}[/tex]So perimeter of triangle is equal to 28.02 cm.
limf(x) = 3 and lime(x) = -620. Given thatEvaluate the followinglim [f(x) * g(x)]g(x)-f(x)[A] -2[B] 5[C]2[D] -6ABO O O O
Determine the value of expression by using the properties of the limit.
[tex]\begin{gathered} \lim _{x\to c}\frac{\lbrack f(x)\cdot g(x)\rbrack}{g(x)-f(x)}=\frac{\lim _{x\to c}\lbrack f(x)\cdot g(x)\rbrack}{\lim _{x\to c}\lbrack g(x)-f(x)\rbrack} \\ =\frac{\lim _{x\to c}f(x)\cdot\lim _{x\to c}g(x)}{\lim _{x\to c}g(x)-\lim _{x\to c}f(x)} \end{gathered}[/tex]Subtitute the given values of the function for the given in the given expression.
[tex]\begin{gathered} \frac{\lim _{x\to c}f(x)\cdot\lim _{x\to c}g(x)}{\lim _{x\to c}g(x)-\lim _{x\to c}f(x)}=\frac{3\cdot(-6)}{-6-3} \\ =\frac{-18}{-9} \\ =2 \end{gathered}[/tex]So answer is 2.
DO NOW: Slopes of ZERO and slopes that are UNDEFINED look very similar. What is the difference between the way those slopes look in fraction form?
The slope of a line that passes through points (x1, y1) and (x2, y2) is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]When the numerator is equal to zero, the slope is equal to zero.
When the denominator is equal to zero, the slope is undefined (you can't divide by zero).
so in the answer box it gives me a choice of 1. is not2. is so what's the answer for both of them?
In a function, an x-value can only have one y-value.
If A is the rule that assigns each student in the table to a lunch group:
The x-values are the students
The y-values are the lunch gro then rule A ___ a function.
$$
Write an explicit formula for a(n), the n^th term of the sequence 8, 48, 288,...
Answer:
a(n) = 8 x 6^(n-1)
Explanation:
The sequence 8, 48, 288, ... is geometric because each term is the term before multiply by a common ratio, so:
8
8 x 6 = 48
48 x 6 = 288
Therefore, the equation of a geometric sequence is:
[tex]a_n=a_1r^{n-1}[/tex]Where a1 is the first term of the sequence and r is the common ratio. So, replacing a1 by 8 and r by 6, we get that the equation fo the n^th term of the sequence is:
[tex]a_n=8\cdot6^{n-1}[/tex]So, the answer is:
a(n) = 8 x 6^(n-1)
1. Find the slope of the line and Write an equation for the line.
Given data:
The first coordinate on the graph is (2, 2).
The second coordinate on the graph is (6,10).
The slope of the given graph is,
[tex]\begin{gathered} m=\frac{10-2}{6-2} \\ =\frac{8}{4} \\ =2 \end{gathered}[/tex]The equation of the line is,
y-2=2(x-2)
y-2=2x-4
y=2x-2
Thus, the slope of the line is 2, and equation of the line is y=2x-2.
What is the distance between the movie theater and the Park? round to the nearest hundredth *
Let:
[tex](x1,y1)=(-4,-6)[/tex]The coordinates of the movie park
and
[tex](x2,y2)=(7,-5)[/tex]Using the distance formula:
[tex]\begin{gathered} d=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ d=\sqrt[]{(7-(-4))^2+(-5-(-6))^2} \\ d=\sqrt[]{(11)^2+(1)^2} \\ d=\sqrt[]{122} \\ d\approx11.05 \end{gathered}[/tex]Find the 59th term of the arithmetic sequence 26, 17, 8,.
From the present question. we can find the following relation, where n stands for the position:
[tex]A_n=35-9n[/tex]The 59th term is given by:
[tex]\begin{gathered} A_{59}=35-9\times59=35-531 \\ A_{59}=-496 \end{gathered}[/tex]The 59th term is -496A circular table has a radius of 2 1/2ft. Find its circumference
Given:
The radius of the circle is 2 1/2 ft.
To find:
The circumference of the circle
Explanation:
Using the formula of the circumference of the circle
[tex]C=2\pi r[/tex]On substitution we get,
[tex]\begin{gathered} C=2\times\frac{22}{7}\times2\frac{1}{2} \\ =2\times\frac{22}{7}\times\frac{5}{2} \\ C=\frac{220}{14}ft \\ C=\frac{110}{7}ft \\ C=15\frac{5}{7}ft \end{gathered}[/tex]Final answer:
The circumference of the circle is,
[tex]\begin{gathered} \frac{110}{7} \\ (or) \\ 15\frac{5}{7}ft \end{gathered}[/tex]In decimal,
[tex]C\approx15.71ft[/tex]8 * ( 4 * y ) - 5x = yneed help finding the solution
Given the equation:
[tex]8\times(4\times y)-5x=y[/tex]Multiply:
[tex]\begin{gathered} 8\times4y-5x=y \\ 32y-5x=y \end{gathered}[/tex]Then solve for x:
[tex]\begin{gathered} 32y-5x-32y=y-32y \\ -5x=-31y \\ \frac{-5x}{-5}=\frac{-31y}{-5} \\ x=\frac{31y}{5} \end{gathered}[/tex]Answer:
[tex]x=\frac{31y}{5}[/tex]find the coordinates of the points d (6, -3) and e (8,-2) after the transformation (X,Y) to (x -3, y -4).
Replace x and y in the transformation for the corresponding values of the first and second entries of the points d and e:
[tex](x,y)\rightarrow(x-3,y-4)[/tex]Then:
[tex]\begin{gathered} d(6,-3)\rightarrow d^{\prime}(6-3,-3-4)=d^{\prime}(3,-7) \\ e(8,-2)\rightarrow e^{\prime}(8-3,-2-4)=e^{\prime}(5,-6) \end{gathered}[/tex]Therefore, the coordinates after the transformation are: d'(3,-7) and e'(5,-6).