STEP - BY - STEP EXPLANATION
What to find?
The power function that the given graph resembles.
Given:
f(x)=(x − 3)³
First, we need to note that;
If f(x) is shifted left q - units, then the new formula of the function becomes f(x+q).
Let q=3
[tex]f(x)=(x-3)^3[/tex][tex]f(x)=(x-3+3)^3[/tex][tex]f(x)=x^3[/tex]ANSWER
y=x³
A wing of Samuel's model airplane is in the shape of a triangle with the dimensions shownbelow. What is the value of x?A. 75B. 55C. 35D. 573.
Given that, the triangle is a right angled triangle. Therefore,
[tex]\text{hypotenuse}^2=base^2+altitude^2[/tex]Given that, hypotenuse is 10, altitude is 5 and base is x. Thus,
[tex]\begin{gathered} 10^2=x^2+5^2 \\ x^2=100-25 \\ x^2=75 \\ x=5\sqrt[]{3} \end{gathered}[/tex]Hence, Option D.
Write the equation of the linear relationship in slope Intercept form, using decimals as needed. 0 2.5 100 200 300 375 725 1075 Enter the equation of the relationship.
Let us first calculate the slope of the function. We need 2 points (0,2.5) and (100,37.5)
so the slope is
[tex]m=\frac{37.5-2.5}{100-0}=\frac{35}{100}=\frac{7}{20}=0.35[/tex]So the equation is
[tex]y=0.35x+2.5[/tex]i have a question on one of my assignments i need to do its homework
the initial height is when the number of days is 0 from the graph we can notice is 4Cm
The graph is relationship lineal because is a line
The graph is relationship proportional because if time increases the size also increases
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).202,198,194,...Find the 37th term.
The first 3 terms of the sequence are 202, 198, 194
Since 198 - 202 = -4
Since 194 - 198 = -4, then
The sequence is Arithmetic and decreases by 4
The rule of the arithmetic sequence is
[tex]a_n=a+(n-1)d[/tex]a is the first term
d is the common difference
n is the position of the term
Since the first term is 202, then
a = 202
Since the common difference is -4, then
d = -4
Since we need to find the 37th term, then
n = 37
Substitute them in the rule above
[tex]\begin{gathered} a_{37}=202+(37-1)(-4) \\ a_{37}=202+(36)(-4) \\ a_{37}=202-144 \\ a_{37}=58_{} \end{gathered}[/tex]The 37th term is 58
3. Find the surface area of each object to the nearest tenth of a square unit. d=2.5 cm b) d=0.003 m 16cm wooden rod 16 m flag pole 62 MHD
The formula for the surface area of a cylinder is given:
[tex]A=2\cdot\pi\cdot r\cdot h+2\cdot\pi\cdot r^2[/tex]then, since the information given is a diameter, rewrite the expression using the diameter.
[tex]\begin{gathered} D=2\cdot r \\ r=\frac{D}{2} \\ \text{then, } \\ A=D\cdot\pi\cdot h+2\cdot\pi\cdot(\frac{D}{2})^2 \end{gathered}[/tex]Replace with the data given
[tex]\begin{gathered} A=(2.5)\cdot(\pi)\cdot(16)+2\cdot\pi\cdot(\frac{2.5}{2})^2 \\ A=40\pi+3.125\pi \\ A=43.125\pi \end{gathered}[/tex]consider a cone with a base radius of 3 ft and height of 10 ft. Find the volume of the cone
The volume V of a cone with radius r and height h is given by the formula:
[tex]V=\frac{1}{3}\pi r^2\times h[/tex]Substitute r=3ft and h=10ft to find the volume of the cone:
[tex]\begin{gathered} V=\frac{1}{3}\pi\times(3ft)^2\times10ft \\ =\frac{1}{3}\pi\times90ft^3 \\ =\pi\times30ft^3 \\ =94.24777961\ldots ft^3 \end{gathered}[/tex]Therefore, the volume of the cone is 30π cubic feet, which is equal to 94 cubic feet (to the nearest whole number).
the temperature at 3pm was 65 degrees it dropped 21 degrees by 7 pm what was the temperature at 7pm
Given:
it is given that the temperature at 3pm was 65 degrees it dropped 21 degrees by 7 pm.
Solution:
Now, the temperature at 7 pm will be
[tex]65-21=44[/tex]So, temperature at 7 pm is 44 degree.
Solve for Angle x given: 11x+30=54-5x 4. Od 3
hello
to solve for angle x, let's collect like terms
[tex]11x+30=54-5x[/tex]step 1
collect like terms to do this, we'll take variables of x one side of the eqaution and keep non-variables at the other side
[tex]\begin{gathered} 11x+30=54-5x \\ 11x+5x=54-30 \\ 16x=24 \\ \text{divide both sides by 16} \\ \frac{16x}{16}=\frac{24}{16} \\ x=\frac{24}{16}=\frac{6}{4} \end{gathered}[/tex]show the stepsHow do the graphs of y=1/x and y = 5/(x+6) compare?
• Slightly shifted up
,• Horizontally translated to the left 6 units
1) Consider this:
[tex]y=\frac{1}{x}[/tex]This is the parent function from the familiar of rational functions.
2) Note that on the other hand, the function below:
[tex]y=\frac{5}{x+6}[/tex]This is a transformed function from the first one. Take a look at the graph with both functions plotted:
In Rational functions the greater the numerator the farther from the origin is, shifting up the graph and the addition of 6 in the bottom number translates horizontally to the left.
3) Thus, we can state the answer as:
The graph of y=5/(x+6) is:
• Slightly shifted up
,• Horizontally translated to the left 6 units
7-18When solving a problem about the perimeter of a rectangle using the 5-DProcess, Herman built the expression below.Perimeter = x + x + 4x + 4x feeta.Draw a rectangle and label its sides based on Herman's expression.b. What is the relationship between the base and height of Herman'srectangle? How can you tell?c.If the perimeter of the rectangle is 60 feet, how long are the base and heightof Herman's rectangle? Show how you know.
a.
A rectangle has opposite side equal to each other . Therefore, it can be drawn below
perimeter = x + x + 4x + 4x
b.
The relationship between herman rectanngle base and height can be express below
[tex]\begin{gathered} 4\text{ times the height=base} \\ \text{let } \\ \text{height}=x \\ 4\times x=base \\ \text{base}=4x \end{gathered}[/tex]c.
perimeter = 60 feet
[tex]\begin{gathered} \text{perimeter}=x+x+4x+4x \\ 60=10x \\ x=\frac{60}{10} \\ x=6 \\ \\ \text{Base}=4x=4\times6=24\text{ f}eet \\ \text{height}=x=6\text{ f}eet \end{gathered}[/tex]The decay of a radioactive substance is given byA = 200(1/2) t/10. Which answer is an equivalent equationfor the decay that shows the approximate amount of/decayin 4 years?
The decay of a radioactive substance is given by
A = 200(1/2) t/10.
The equivalent equation for the decay that shows the approximate amount of decay in 4 years
Hence the correct option that approximately amounts to decay in 4years is
[tex]A=151.57(0.933)^{t-4}[/tex]Option C is the correct answer cause it matches the red image
The 8 foot diameter circular table has a 4 foot wide extension.1. What is the total area with the extension?2. How does the area compare to the area o4 ft.O8 ft. table with extension10 ft. table
1.- Area
[tex]\begin{gathered} \text{Area of the circle = 3.14 x (4)}^2 \\ \text{Area of the circle = 50.24 ft}^2 \end{gathered}[/tex]2.- Area of the extended table
Area = 50.24 + (8 x 4)
Area = 50.24 + 32
Area = 82.24 ft^2
Second question
Area = 3.14 x (5)^2
Area = 25 x 3.14
Area = 78.5 ft^2
The area of the larger circle is smaller than the area of the table with the extension.
Josh and Daniel each want to save $600 to attend a sports camp. Josh has saved 60% ofthe amount. Daniel has saved $320. Who has saved more money? How much more?
The total amount to save is $600
Josh saved 60%. This is the same as below
[tex]\begin{gathered} 60\text{ \% of \$600} \\ =\frac{60}{100}\times600 \\ =\frac{36000}{100} \\ =360 \end{gathered}[/tex][tex]\begin{gathered} \text{ 60\% } \\ =\frac{60}{100}=\frac{360}{600} \end{gathered}[/tex]Josh has saved $360.
Daniel has saved $320
It can be observed that $360 is more than $320, so Josh saved more money
The difference tells how much more
[tex]\begin{gathered} \text{ \$360 - \$320} \\ =\text{ \$40} \end{gathered}[/tex]Hence,
1. 60/100= x/600
2. Multiply both sides by 600
3. Josh has saved $360
4. Josh saved more money. Josh saved $40 more than Daniel
Complete each equation so that it is true for no values of x
By definition, an equation has no solution when does not exist a value of the variable that makes the equation true.
• In this case, you have this expression on the left side of the first equation:
[tex]3x+6_{}_{}[/tex]Then, knowing part of the right side, you can set up the following:
[tex]3x+6=3(x+1)[/tex]Notice that you need to write a value different from 6, in order to make the equation false, In this case, you cannot complete the missing value with 2, because;
[tex]3\cdot2=6[/tex]Then, having that equation. you can solve it as follows:
[tex]\begin{gathered} 3x+6=3x+3 \\ 3x-3x=3-6 \\ 0=-3\text{ (False)} \end{gathered}[/tex]• Given the second equation that has this left side:
[tex]x-2[/tex]The missing value must be:
What is the area of a circle with a radius of 4.6Area:
The formula for the area of a circle with radius R is;
[tex]A=\pi(R^2)[/tex]With R = 4.6 units
[tex]\begin{gathered} A=\pi\times4.6^2 \\ A=66.48\text{ square units.} \end{gathered}[/tex]Therefore the area of the circle is 66.48 square units.
Iif it cost 950 on my monthly cost for housing what is my yearly cost?
Firstly
cost per month = 950
12 months make a year
Yearly cost of housing = 12 x 950
= 11400
can someone please help me find the area of the following?
Mya, this is the solution:
Let's recall that the formula to solve for the surface area of a cylinder is:
A = 2 * π * r * h + 2 * π * r²
In our exercise, we have:
r = 8 cm
h = 7 cm
In consequence, replacing these values in the formula:
A = 2π * 7 * 8 + 2π * 8²
A = 2π * 56 + 2π * 64
A = 112π + 128π
A = 240π cm²
The correct answer is D. 240π cm²
In IJK, the measure of K=90 degrees, JI=53, IK=45, and KJ=28, What ratio represents the sine of I?
The given triangle is a right angle triangle. The diagram is shown below.
From the triangle, considering angle I as the reference angle,
hypotenuse = JI = 53
adjacent side = IK = 45
opposite side = KJ = 28
To find Sin I, we would apply the Sine trigonometric ratio which is expressed as
Sin # = opposite side/hypotenuse
Thus,
Sin I = 28/53
Solve for x. The polygons in each pair are similar..*:)24302420-5+5x56910The polygons in each pair are similar. Find the scale factor of the smaller figure tothe larger figure. *2135201830O 1:7
ANSWER
[tex]3\colon5[/tex]EXPLANATION
The polygons given are similar.
To find the scale factor of the smaller figure to the larger figure, we have to find the ratio of the side lengths of corresponding sides of the smaller triangle to the larger one.
Therefore, we have that the scale factor is:
[tex]\begin{gathered} 21\colon35 \\ \Rightarrow3\colon5 \end{gathered}[/tex]Find the measure of ZGHJ and LGIJ.68°H 31GK115angle GH) =degreesangle GIJ =degrees
Step 1: Find arc angle GJ
The sum of the arc angles of a circle is 360°.
Therefore,
[tex]\begin{gathered}step2: Find the angle GKJ, the angle subtended by the arc GJ
The angle GKJ is the angle subtended by the arc GJ at the center of the circle
Therefore,
[tex]<\text{GKJ }=\text{ m < GJ }=146^o[/tex]Step 3: Find m < GHJ
From Circle theorem, we know that the angle at the center of a circle is twice the angle at the circumference
Therefore,
[tex]\begin{gathered} <\text{GKJ }=2\timesHence, m 73°Step 4: Find m < GIJFrom Circle theorem, the angles in the same segment are equalTherefore,[tex]<\text{GIJ }=Hence, m < GIJ = 73°how do I show my work for (3 + 1/2) x 14
this is
[tex](3+\frac{1}{2})\times14=(\frac{7}{2})\times14=\frac{98}{2}=49[/tex]-11. Given points (x, y) and (x2, y2), derive the two-point form of a line. , , , 10. 13. Given that a line is parallel to the x-axis through (x, y), derive the parallel to x-axis form a line.
11. Given the two points (x1, y1) & (x2, y2) we will have the following line and we derivate it:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]y-y_1=m(x-x_1)\Rightarrow y=mx-mx_1+y_1[/tex]It's derivative is:
[tex]\frac{\delta y}{\delta x}=m=\frac{y_2-y_1}{x_2-x_1}[/tex]This is since the derivative of constants is 0 and the only variable accompanied m. This is proof that the derivative of a function can be interpreted as the slope of the function at that point.
13. If we have that the line is parallel to the x-axis and passes through the point (x1, y1), we will have that the line is a constant function, so when we derivate no matter the point, it will be equal to 0.
That is:
[tex]y=x_1[/tex][tex]\frac{\delta y}{\delta x}=0[/tex]***Explanation:
point 11:
Since we are given two points (x1, y1) & (x2, y2), we will always have that the slope of the line that passes through those points will always have the form:
Need help Which expression is equivalent to the given expression?(ab^2)^3/b^OA.a3/bOB.a3boc.a4/bOD.a3
Given the expression:
[tex]\frac{(ab^2)^3}{b^5}[/tex]We will use the following rules to modify the given expression:
[tex]\begin{gathered} (a^{m)n}=a^{mn} \\ \frac{a^m}{a^n}=a^{m-n} \end{gathered}[/tex]So, the answer will be as follows:
[tex]\frac{(ab^2)^3}{b^5}=\frac{a^3b^6}{b^5}=a^3b^{6-5}=a^3b[/tex]So, the answer will be option ⇒ B. a³b
A researcher wants to study the effects of sleep deprivation on motor skills. Nine people volunteer for the experiment: Amanda, Brian, Christine, David, Emily, Fred,George, Heather, and Ivan. Use the second row of digits in the random number table below to select a simple random sample of three subjects (ignore zeros). Theother six subjects will go into the control group. If the subjects are numbered through 9 alphabetically, what are the numbers of the three subjects selected? List thesubjects that will go in the treatment group.Line/Column(1)(2)(3)(4)177952454778618314079264955243209744831960479733397402669224773What are the numbers of the three subjects selected?{If not an answer please an explanation, I don’t understand how to get the numbers}
The second row has the following numbers:
64955, 24320, 97448, 26692
We are interested in numbers from 0 to 9, then we are only interested in the first digit of the numbers, which are: 6, 2, 9, 2.
Student 2 is Brian
Student 6 is Fred
student 9 is Ivan
Find the quotient and the remainder using the long division method
The question is to evaluate the quotient and remainder of the division using the long division method:
[tex]\frac{-3x^3+13x^2-14x+9}{x-3}[/tex]Step 1: Write out the problem in the long division format
Step 2: Divide the leading term of the dividend by the leading term of the divisor. Write down the calculated result in the upper part of the table. Multiply it by the divisor and subtract the dividend from the obtained result
[tex]\begin{gathered} \frac{-3x^3}{x}=-3x^2 \\ -3x^2(x-3)=-3x^3+9x^2 \end{gathered}[/tex]Step 3: Apply the steps from 2 above to the remainder at the bottom
[tex]\begin{gathered} \frac{4x^2}{x}=4x \\ 4x(x-3)=4x^2-12x \end{gathered}[/tex]Step 4: Apply the steps from 3 above
[tex]\begin{gathered} \frac{-2x}{x}=-2 \\ -2(x-3)=-2x+6 \end{gathered}[/tex]Step 5: Since the degree of the remainder is less than that of the divisor, we are done with the division. The quotient is the polynomial at the top and the remainder is at the bottom
[tex]\frac{-3x^3+13x^2-14x+9}{x-3}=-3x^2+4x-2+\frac{3}{x-3}[/tex]ANSWER
The quotient is:
[tex]-3x^2+4x-2[/tex]The remainder is
[tex]3[/tex]In a study of 200 students under 25 years old, 5% have not yet learned to drive. Howmany of the students cannot drive?
We can write 5% in decimal form as 5/100=0.05.
So if a 5% of the 200 students under 25 years old have not yet learned to drive, we can calculate the number of students that have not yet learned to drive as:
[tex]n=\frac{5}{100}\cdot200=5\cdot2=10[/tex]10 students out of the group of 200 can not drive.
Change the following expression to radical notation: 5x^1/9
To convert exponential to radical expression and vice versa, we follow the pattern below:
[tex]ab^{\frac{x}{n}}=a\sqrt[n]{b^x}^{}[/tex]In the given term in the question, a = 5, b = x, n = 9, and x = 1. Let's plug these values into the radical form shown above.
The radical form of the given term is:
[tex]5\sqrt[9]{x}[/tex]5. A soccer ball has a circumference of 70 centimeters at widest polne. What the volume and total surface area of the soccer boll
According to our question we have :-
[tex]\begin{gathered} 2\pi r=70 \\ r=\frac{70}{2\pi}=\frac{35}{\pi} \end{gathered}[/tex]Now volume of the ball will be:-
[tex]\begin{gathered} V=\frac{4}{3}\pi\times r^3 \\ =\frac{4}{3}\times\pi\times\frac{35}{\pi}\times\frac{35}{\pi}\times\frac{35}{\pi} \\ =\frac{4}{3}\times\frac{35}{\square}\times\frac{35\times7}{22}\times\frac{35\times7}{22} \\ =5787.5 \end{gathered}[/tex]So volume of ball ia 5787.5 cubic centimeter
Now surface area of ball will be :-
[tex]\begin{gathered} A=6\pi\times r^2^{} \\ =6\times\pi\times\frac{35}{\pi}\times\frac{35}{\pi} \\ =6\times35\times\frac{35\times7}{22} \\ =2338.6 \end{gathered}[/tex]So surface area of ball is 2338.6 centimeter square
4 ). Peter went to a bookstore to buy a pen and a binder. He used three- tenths of his money to pay the pen , while the rest of his money was used to pay the binder . the binder costs P64 more than the pen , what was the total price that Peter paid in the bookstore?
The total price that Peter paid in the bookstore is P91.43.
What is the total price?The first step is to determine the fraction of the amount that Peter has that he spent on the binder.
Fraction spent on a binder = 1 - fraction spent on pen
Fraction spent on a binder = 1 - 3/10
Fraction spent on a binder = 7/10
The next step is to divide the cost of the binder by the fraction spent on the binder.
Total price that Peter paid in the bookstore = price of the binder /fraction spent on the binder
Total price that Peter paid in the bookstore = P64 ÷ 7/10
Total price that Peter paid in the bookstore = P64 X 10/7 = P91.43
To learn more about cost, please check: https://brainly.com/question/14145412
#SPJ1
Ben wants to put the rabbit run and hutch on his lawn.. The space for the rabbit run must .be square 350cm by 350cm. have at least 50cm space to walk around it.the space for the rabbit hutch must be rectangular 200cm by 50 cm.the rabbit hutch will be Ina corner inside the rabbit run.the grid show us the plan of the lawn
Explanation:
We know that 1 square has 50 cm of side. The rabbit run must be a square of 350 cm by 350 cm, so we will use 7 times 7 squares on the grid, because
350/50 = 7
Additionally, it has at least 50 cm of space to walk around it, so we will let at least one square around the rabbit run.
The rabbit hutch is rectangular with measures of 200 cm by 50 cm, so it is equivalent to a rectangle of 4 squares by 1 because
200/50 = 4
50/50 = 1
Finally, the rabbit hutch will be in a corner of the rabbit run.
Answer:
Therefore, we can draw the spaces as