We define the following notation:
• z = cost of an item from shelf A,
,• y = cost of an item from shelf B.
From the statement, we know that:
• 3 items from shelf A and 2 from shelf B cost $26, so we have:
[tex]3z+2y=26,[/tex]• 2 items from shelf A and 5 from shelf B for $32, so we have:
[tex]2z+5y=32.[/tex]We have the following system of equations:
[tex]\begin{gathered} 3z+2y=26, \\ 2z+5y=32. \end{gathered}[/tex]1) To solve this system, we multiply the first equation by 2 and the second equation by 3:
[tex]\begin{gathered} 2\cdot(3z+2y)=2\cdot26\rightarrow6z+4y=52, \\ 3\cdot(2z+5y)=3\cdot32\rightarrow6z+15y=96. \end{gathered}[/tex]2) We subtract equation 1 to equation 2, and then we solve for y:
[tex]\begin{gathered} (6z+15y)-(6z+4y)=96-52, \\ 11y=44, \\ y=\frac{44}{11}=4. \end{gathered}[/tex]We found that y = 4.
3) We replace the value y = 4 in the first equation, and then we solve for z:
[tex]\begin{gathered} 3z+2\cdot4=26, \\ 3z+8=26, \\ 3z=26-8, \\ 3z=18, \\ z=\frac{18}{3}=6. \end{gathered}[/tex]Answer
The cost of the items are:
• z = 6, for items from shelf A,
,• y = 4, for items from shelf B.
Find 3 ratios that are equivalent to the given ratio 6:13
In order to find equivalent ratios, we can multiply the numerator and denominator by the same value.
For example, let's multiply by 2, by 3 and by 4:
[tex]\begin{gathered} 6:13\\ \\ =6\cdot2:13\cdot2\\ \\ =12:26\\ \\ \\ \\ 6:13\\ \\ =6\cdot3:13\cdot3\\ \\ =18:39\\ \\ \\ \\ 6:13\\ \\ =6\cdot4:13\cdot4\\ \\ =24:52 \end{gathered}[/tex]Therefore the equivalent ratios are 12:26, 18:39 and 24:52..
identify the form of line of the following equation 4x+5y=6
To make the graph of the equation, we need to solve for y
[tex]\begin{gathered} 4x+5y=6 \\ 5y=-4x+6 \\ y=-\frac{4}{5}x+\frac{6}{5} \end{gathered}[/tex]Then, the slope of the line is -4/5, this means that the line decreases 4 units when we move 5 units to the right. Also, the y-intercept, that is, the point where the line crosses the y axis, is 6/5
A city is built on the banks of a river and some islands in the river. The map below shows the bridges connecting the various land masses. Draw a graph that models the connecting relationships in the map below. The vertices represent the land masses and the edges represent bridges connecting them. Is it possible to find a circuit through the city that uses each bridge once? If so, enter the sequence of land masses(vertices) visited, for example ABDEA. If it is not possible, enter DNE. Use Fleury's algorithm and show all work and the graph as demonstrated in class.
We can graph the model as:
The Fleury's algorithm start with any vertex, and then select an edge that start from this vertex and go to another vertex. Then we pick another edge that starts from the last vertex, and so on. The condition is that all the vertices in the graph are always connected to each other: that is, there is always a path to conect any two vertices.
We start with A.
We can go to C, then B, then D, then E, then A.
After this part, we are left with these edges:
As the last vertex was A, we start from there.
We go to D, then to B, then to C, then to A again and we end in E.
We are never able to go back to the vertex we start (A), so there is no possible sequence.
Answer: DNE
A straw is placed in a rectangular box that is 6 inches by 4 inches by 8 inches, as shown. If the straw fits exactly in the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.
Explanation
you can solve this by using the distance between 2 points formula
[tex]D_{ab}=\sqrt[]{(x-x_1)^2+(y-y_1)^2+(z-z_1)^2}[/tex]then
Step 1
Let
P1(0,0,0)
P2(6,4,8)
now , replace
[tex]\begin{gathered} D_{ab}=\sqrt[]{(x-x_1)^2+(y-y_1)^2+(z-z_1)^2} \\ D_{ab}=\sqrt[]{(6-0)^2+(4-0)^2+(8-0)^2} \\ D_{ab}=\sqrt[]{(6)^2+(4)^2+(8)^2} \\ D_{ab}=\sqrt[]{36^{}+16+64} \\ D_{ab}=\sqrt[]{116} \\ D_{ab}=\sqrt[]{4\cdot29} \\ D_{ab}=2\sqrt[]{29} \end{gathered}[/tex]I hope this helps you
the function g is a transformation of f. The grab below shows us as a solid blue line and g as a dotted red line. what is the formula of gA) g(x) =(x/2+1)²-3B) g(x) =(2x+1)²-3C) g(x) =(x/2-1)²-3D) g(x) =(x/2+1)²+3
First we notice that the vertex of the parabola is shift one unit to the left and three units down. To begin we need to remember the following rules:
Suppose c>0. To obtain the graph of
y=f(x)+c, shift the graph of f(x) a distance c units upwards.
y=f(x)-c, shift the graph of f(x) a distance c units downward.
y=f(x-c), shift the graph of f(x) a distance c units to the right.
y=f(x+c), shift the graph of f(x) a distance c units to the left.
Once we have this rules and knowing that the vertex move like we mentioned before we have that the new function should be of the form:
[tex]f(x+1)-3[/tex]From the graph we also notice that the function g is stretch by a factor of two, remembering the rule for stretching graphs:
If c>1 then the function y=f(x/c), stretch the graph of f(x) horizontally by a factor of c.
With this we conclude that the function g has to be of the form:
[tex]f(\frac{x}{2}+1)-3[/tex]Finally, we notice that the function f is:
[tex]f(x)=x^2[/tex]Threfore,
[tex]g(x)=(\frac{x}{2}+1)^2-3[/tex]then the answer is A.
HAve a nice day !
Which Platonic solid has twenty faces that are equilateral triangles?A. HexahedronB. OctahedronC. IcosahedronD. Dodecahedron
STEP - BY - STEP EXPLANATION
What to find?
The platonic solid that has twenty faces that are equilateral triangles.
Given:
Platonic solid.
Let's check each option.
A hexahedron is a polyhedron with 6 faces.
So this is not an option.
An octahedron is a polyhedron with 8 faces.
This option is also ruled out.
A Dodecahedron is a polyhedron with 12 faces.
This is also not an option.
An Icosahedron is a polyhedron whose faces are 20 equilateral triangles.
Hence Icosahedron is the correct option.
ANSWER
C. Icosahedron
What is the volume of a sphere with a diameter of 7.5 cm, rounded to the nearesttenth of a cubic centimeter?
Given the parent graph f(x)=e^x, which of the following functions has a graph that has been translated 3 to the left and reflected over the x-axis?following functions given to pick from are g(x)=−e^x+3g of x is equal to negative e raised to the x plus 3 powerg(x)=e^−(x+3)g of x is equal to e raised to the negative open paren x plus 3 close paren powerg(x)=e^3−xg of x is equal to e raised to the 3 minus x powerg(x)=−e^3−x
Given the parent function:
[tex]f(x)=e^x[/tex]Let's determine the function that has a graph which has been translated 3 units to the left and reflected over the x-axis.
To find the function, apply the transformation rules for functions.
• After a translation 3 units to the left, we have:
[tex]g(x)=e^{x+3}[/tex]• Followed by a reflection over the x-axis:
[tex]g(x)=-e^{x+3}[/tex]Therefore, the function that has a graph which has been translated 3 units to the left and reflected over the x-axis is:
[tex]g(x)=-e^{x+3}[/tex]How many square feet of outdoor carpet are needed for this hole
The area of a rectangle is:
[tex]Ar=l\cdot h[/tex]Where:
Ar = area of the rectangle
l = lenght
w = width
And the area of a triangle is:
[tex]At=\frac{1}{2}\cdot b\cdot h[/tex]Where:
At = area of the triangle
b = base
h = height
To solve this problem divide the figure into triangles and rectangles, according to the figure below.
And the square feed (A) needed will be:
A = A1 - A2 + A3 + A4 + A5
Step 01: Calculate A1.
Figure 1 is a rectangle with sides 5 and 6 ft.
[tex]\begin{gathered} A1=5\cdot6 \\ A1=30ft^2 \end{gathered}[/tex]Step 02: Calculate A2.
Figure2 is a rectangle with sides 2 and 3 ft.
[tex]\begin{gathered} A2=2\cdot6 \\ A2=6ft^2 \end{gathered}[/tex]Step 03: Calculate A3.
Figure 3 is a triangle with base 4 (12 - 6 - 2 = 4) and height 3 ft.
[tex]\begin{gathered} A3=\frac{4\cdot3}{2} \\ A3=\frac{12}{2} \\ A3=6ft^2 \end{gathered}[/tex]Step 04: Calculate A4.
Figure 4 is a rectangle with sides 4 (12 - 6 - 2 = 4) and 2 (5 - 3 = 2) ft.
[tex]\begin{gathered} A4=4\cdot2 \\ A4=8ft^2 \end{gathered}[/tex]Step 05: Calculate A5.
Figure 5 is a rectangle with sides 2 and 5 ft.
[tex]\begin{gathered} A4=2\cdot5 \\ A4=10ft^2 \end{gathered}[/tex]Step 06: Find the area of the figure.
A = A1 - A2 + A3 + A4 + A5.
[tex]\begin{gathered} A=30-6+6+8+10 \\ A=48ft^2 \end{gathered}[/tex]Answer: 48 ft² is needed for this hole.
The grade a student makes on a test varies directly with the amount of time the student spends studying. Suppose a student spends 5 hours studying and makes a grade of 89 on the test. What is an equation that relates the grade earned on a test, g, with the amount of time spent studying, t. in hours?
It is given that,
A student spends 5 hours studying and makes a grade of 89 on the test.
To write an equation that relates the grade earned on a test in t hours.
Let us take,
For 5 hours, the grade is 89
For 1 hour, the grade will be,
[tex]\frac{89}{5}=17.8[/tex]Then for t hours, the general equation will be,
[tex]g=17.8t[/tex]Hence, the answer is g=17.8t.
The Young family has collected movies. They have 18 action movies. 16 comedies. 8 mysteries, and 12 dramas. How many movies do they have in total?
The family has 54 movies in total
Explanation:The movies the family have in total is the addition of the number of movies in each category:
18 + 16 + 8 + 12
= 54
Jim was playing a game in which he gained and lost points. First, helost four points. Next, he lost nine points. Write the total change to hisscore as an integer.
Let the total game played be x
The first game he played he lost 4 points
Mathematically,
Total game = lost game + gained game
x = 4 + gained game
gained game = x - 4
next game he lost 9 points again
out of the total x game he had already lost 4 and now losing 9 points
The remaining game after losing 4 will be x-4
x - 4 = lost game
the new lost game is 9 points
x - 4 = 9
isolating x
you have x = 9+4
x = 13
Find the value of x and the value of y.A. x = 15, y = 10sqrt3B. r = 20, y = 10sqrt3C. r = 20sqrt3, y = 5sqrt3D. x=15, y = 5sqrt3
To find the values of x and y it is necessary to use trigonometric ratios.
To find x it is necessary to use sine. Sine is the ratio between the opposite side to a given angle and the hypotenuse. In this case, the given angle is 60°, the opposite side is x and the hypotenuse is 10 sqrt 3. Use this information to find x:
[tex]\begin{gathered} \sin 60=\frac{x}{10\sqrt[]{3}} \\ 10\sqrt[]{3}\cdot\sin 60=x \\ x=15 \end{gathered}[/tex]To find y it is necessary to use cosine. It is the ratio between the adjacent side to a given angle and the hypotenuse. The given angle is 60°, the adjacent side is y and the hypotenuse is 10 sqrt 3. Follow the same procedure as with sine:
[tex]\begin{gathered} \cos 60=\frac{y}{10\sqrt[]{3}} \\ 10\sqrt[]{3}\cdot\cos 60=y \\ y=5\sqrt[]{3} \end{gathered}[/tex]The correct answer is D. x=15, y=5sqrt3.
Find the measure of chord EF. Enter your numerical answer.
Notice that each chord (CD and EF) defines a segment in the circle whose arc length has the same value. Thus, the length of both chords has to be the same; then,
[tex]\begin{gathered} CD=EF \\ \Rightarrow9x-1=41-5x \\ \Rightarrow14x=42 \\ \Rightarrow x=3 \end{gathered}[/tex]Finding the length of EF,
[tex]\begin{gathered} x=3 \\ \Rightarrow EF=41-5*3=26 \end{gathered}[/tex]Therefore, the answer is 26
Find the lowest multiple of each group.show the factors you used.1. 5,20,28
Given the following question:
1, 5, 20, 28
1 = 1
5 = 5
20 = 2 × 2 × 5
28 = 2 × 2 × 7
2 × 2 × 5 × 7
2 × 2 = 4
4 × 5 = 20
20 × 7 = 140
LmM = 140
Every week a company provides fruit for its office employees. They canchoose from among five kinds of fruit. What is the probability distribution forthe 30 pieces of fruit, in the order listed?FruitNumber ofpiecesProbabiltyApples Bananas62
Answer:
D.
Explanation:
We were given that:
A company provides fruit for its employees
The employees can pick among five kinds of fruit
The fruits obtained this week is:
Apples = 6 pieces
Bananas =2 pieces
Lemons = 10 pieces
Oranges = 8 pieces
Pears = 4 pieces
Total = 30 pieces
The probability distribution for this is given by:
[tex]\begin{gathered} P(apples)=\frac{Number\text{ of apples}}{Total}=\frac{6}{30}=\frac{1}{5} \\ P(apples)=\frac{1}{5} \\ \\ P(bananas)=\frac{Number\text{ of bananas}}{Total}=\frac{2}{30}=\frac{1}{15} \\ P(bananas)=\frac{1}{15} \\ \\ P(lemons)=\frac{Number\text{ of lemons}}{Total}=\frac{10}{30}=\frac{1}{3} \\ P(lemons)=\frac{1}{3} \\ \\ P(oranges)=\frac{Number\text{ of oranges}}{Total}=\frac{8}{30}=\frac{4}{15} \\ \\ P(pears)=\frac{Number\text{ of pears}}{Total}=\frac{4}{30}=\frac{2}{15} \\ P(pears)=\frac{2}{15} \\ \\ \therefore P=\frac{1}{5},\frac{1}{15},\frac{1}{3},\frac{4}{15},\frac{2}{15} \end{gathered}[/tex]Therefore, the answer is D
A triangle has side lengths of 6, 8, and 10Is it a right triangle?
To be a right triangle it must comply with the following:
[tex]a^2+b^2=c^2[/tex]Where:
a = 6
b = 8
c = 10
So:
[tex]\begin{gathered} 6^2+8^2=10^2 \\ 36+64=100 \\ 100=100 \end{gathered}[/tex]This means that it is a right triangle.
Answer: Yes, It is a right triangle
Hello, I need help on how to read attached graph based on the questions.Thank you
As can be seen in the above graph:
(a) g(x) > 0 in the interval: (-4, -2) U (0, 2)
(b) g(x) < 0 in the interval: (-2, 0)
(c) g(x) = 0 at the next x-values: -4, -2, 0, 2
Graphically, the derivative of a function evaluated at a point is seen as the slope of the tangent line that passes through that point of the function.
Then, if the slope is positive, the derivative is positive, if the slope is zero (a horizontal line), the derivative is zero, and if the slope is negative, the derivative is negative.
In the next graph, we can see some of these slopes:
Therefore, the intervals where g'(x) is positive, negative or zero are:
(d) g'(x) > 0 in the interval: (-4, -3) U (-1, 1)
(e) g'(x) < 0 in the interval: (-3, -1) U (1, 2)
(f) g'(x) = 0 at the next x-values: -3, -1, 1
2. The line plot shows the results of a survey about kitchen sinks. Kitchen Sink Survey + 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Capacity (gallons) Write a paragraph summarizing the data set. In your summary include the following A description of the data, including the unit of measure The number of data values The shape of the distribution The value of an appropriate measure of center The value of an appropriate measure of spread
Given: The information and line plot showing
..
From the plot we can write a table of values for the data
From the table we can get the mean
[tex]\begin{gathered} M_{\text{ean}}=\frac{\Sigma fx}{\Sigma f} \\ M_{\text{ean}}=\frac{(12\times0+13\times1+\ldots+24\times1+25\times0)}{1+2+4+5+...+1+0} \\ M_{\text{ean}}=\frac{354}{21} \\ M_{\text{ean}}=16.86 \\ M_{\text{ean}}\approx17 \end{gathered}[/tex]The standard deviation
[tex]\begin{gathered} S_{\text{tandard deviation}}=\sqrt[]{\frac{\Sigma f(x-\mu)^2}{\Sigma f}} \\ S_{\text{tandard deviation}}=\sqrt[]{\frac{0(12-17)^2+1(13-17)^2+\cdots+1(24-17)^2}{21}} \\ S_{\text{tandard deviation}}=\sqrt[]{\frac{150.571}{21}} \\ S_{\text{tandard deviation}}=2.68 \end{gathered}[/tex]ANSWER SUMMARY
It can be observed that the capacity of the kitchen sink ranges from 12 gallons to 25 gallons. There are 21 kitchen sink with different capacity in gallons. The shape of the distribution is skewed right with an appropriate measure of centre (that is the mean) as 17 gallons. The measure of spread including the range (between 13 gallons to 24 gallons) is 11 gallons, the median is 16 gallons sink and the standard deviation is 2.68 gallons
Answer:
poopsicle
Step-by-step explanation:
Disprove each statement , and then find all values of a and b for which the statement happens to be true . Explain your results If f(x) = x ^ (1/3) does f(a + b) = f(a) + f(b) ?
We are given the following function:
[tex]f(x)=x^{\frac{1}{3}}[/tex]To determine the value of f(a) we will replace the value of "x" for "a" in the function:
[tex]f(a)=a^{\frac{1}{3}}[/tex]Using the same procedure we determine the value of f(b):
[tex]f(b)=b^{\frac{1}{3}}[/tex]Now we determine the value of f(a+b):
[tex]f(a+b)=(a+b)^{\frac{1}{3}}[/tex]We are asked about the equatity:
[tex]f\mleft(a+b\mright)=f\mleft(a\mright)+f\mleft(b\mright)[/tex]replacing the values we get:
[tex](a+b)^{\frac{1}{3}}=a^{\frac{1}{3}}+b^{\frac{1}{3}}[/tex]We get an equality that is not true for any value of "a" and "b" since the left expression can't be converted into the right expression for any "a" or "b". The statement is false.
The statement could be right if "a" or "b" equal zero, for example, let's take a = 0, we get:
[tex](0+b)^{\frac{1}{3}}=(0)^{\frac{1}{3}}+b^{\frac{1}{3}}[/tex]Simplifying:
[tex]b^{\frac{1}{3}}=b^{\frac{1}{3}}[/tex]Which is a true statement. .
In the figure below, AB is an angle bisector. What is the value of x? Show and explain work
Since AB is the angle bisector:
[tex]\begin{gathered} m\angle CAB=m\angle DAB \\ so\colon \\ 33=4x+1 \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} 4x=33-1 \\ 4x=32 \\ x=\frac{32}{4} \\ x=8 \end{gathered}[/tex]Answer:
x = 8
special right triangle find the value of the variables answer must be in simplest radical form
Here, we have a special right triangle.
Let's solve for the variables, x and y.
Given:
common side = x
Hypotenuse of the larger triangle = 8
Let's find x using trigonometric ratio.
We have:
[tex]\begin{gathered} \sin \theta=\frac{opposite}{hypotenuse} \\ \\ \sin 30=\frac{x}{8} \\ \\ x=8\sin 30 \\ \\ x=8(0.5) \\ \\ x=4 \end{gathered}[/tex]To solve for y, we have:
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent} \\ \\ \tan 60=\frac{x}{y} \\ \\ \tan 60=\frac{4}{y} \\ \\ \text{Multiply both sid}es\text{ by y:} \\ y\tan 60=\frac{4}{y}\ast y \\ \\ y\tan 60=4 \\ \\ \text{Divide both sides by tan60} \\ \\ \frac{y\tan 60}{\tan 60}=\frac{4}{\tan60} \\ \\ \\ y=\frac{4}{\tan 60} \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} y=\frac{4}{\sqrt[]{3}} \\ \\ \end{gathered}[/tex]Multiply both numerator and denominator by √3:
[tex]\begin{gathered} y=\frac{4}{\sqrt[]{3}}\ast\frac{\sqrt[]{3}}{\sqrt[]{3}} \\ \\ y=\frac{4\sqrt[]{3}}{3} \end{gathered}[/tex]ANSWER:
[tex]\begin{gathered} x=4 \\ \\ y=\frac{4\sqrt[]{3}}{3} \end{gathered}[/tex]Which of the following is an arithmetic sequence? A. 1, 0, 1, 0, 1, 0, ...B. 800, 200, 50, ...C. 10, 7, 4, 1, -2, ...D. 1, 3, 9, 27,...
Given:
The sequences in options.
Required:
Which of the sequence is an arithmetic sequence.
Explanation:
The arithmetic sequence has a common ration, that is equal for every pair of number
[tex]d=a_2-a_1,d=a_3-a_2[/tex]Now, in option c
[tex]\begin{gathered} d=7-10=-3 \\ d=4-7=-3 \\ d=1-4=-3 \end{gathered}[/tex]So, common ratio is -3 and hence sequence is arithmetic sequence.
Answer:
So, option c is correct.
Choose the correct answer(s) below. Select all that apply.N A. ZHDEB. ZGFDC. ZHDFD. ZBDCE. ZGDFF. There are no angles adjacent and congruent to ZBDG
OK
These angles are
HDE and GFD
Letter A
Letter B
Letter C
Which of the following expressions is equivalent to -5(-2x - 3)? If you get stuck, use boxes like the ones we used tohelp organize our class work.(А) 3х - 3B 10x - 3C 10x + 15D10x - 15
We want to find the expression equivalent to -5(-2x - 3), we would have to expand the expression;
[tex]\begin{gathered} -5(-2x-3) \\ -5(-2x)-5(-3) \\ =10x+15 \end{gathered}[/tex]Therefore, the answer is 10x+15, Option C
Please help me on my hw I need help on #2
Given:
The number is,
[tex]5.232323\ldots\text{.}[/tex]To express the given number into fraction . it means in the form,
[tex]\frac{a}{b}[/tex]We can express the given number into geometric series as,
[tex]\begin{gathered} 5.232323\ldots=5+\frac{23}{100}+\frac{23}{10000}+\frac{23}{100000}+\text{.}\ldots\ldots \\ =5+\frac{23}{100}+23(\frac{1}{100})^2+23(\frac{1}{100})^3+\text{.}\ldots\ldots\text{.}\mathrm{}(1) \\ \frac{23}{100}+23(\frac{1}{100})^2+23(\frac{1}{100})^3+\text{.}\ldots=-23+\sum ^{\infty}_{n\mathop=1}23(\frac{1}{100})^{n-1} \\ =-23+\frac{23}{1-\frac{1}{100}} \\ =-23+\frac{23(100)}{99} \\ =-23+\frac{2300}{99} \\ =\frac{-2277+2300}{99} \\ =\frac{23}{99} \end{gathered}[/tex]Now, equation (1) becomes,
[tex]5+\frac{23}{99}=\frac{518}{99}[/tex]Answer:
[tex]\frac{518}{99}[/tex]write an equation to find the area of each figure. Then determine the area of the composite figure. When pi is used, the area will be an approximation.
ANSWER:
The area of the composite figure is 34 m^2
STEP-BY-STEP EXPLANATION:
To calculate the area of the complete figure, you have to separate the figure in two ways, just like this:
Figure A is a square and we calculate the area like this:
[tex]\begin{gathered} A_A=l^2 \\ A_A=4^2=16 \end{gathered}[/tex]Figure B is a trapezoid and we calculate the area like this:
[tex]\begin{gathered} A_B=\frac{b_1+b_2_{}}{2}\cdot h \\ A_B=\frac{4+8}{2}\cdot3 \\ A_B=18 \end{gathered}[/tex]Now the total area is the sum of both parts:
[tex]\begin{gathered} A_T=A_A+A_B \\ A_T=16+18 \\ A_T=34 \end{gathered}[/tex]jamial walked 210 miles he has walked 70%of the way how many more miles does he have left
Given that: jamial walked 210 miles he has walked 70%of the way
So 70% of the total walked he covered
[tex]210\times\frac{70}{100}=147\text{ miles}[/tex]He covered 147 miles
The remaining distance he have to be cover :
[tex]210-147=63\text{ miles}[/tex]if f(x) = 13 when f(x)=5x -√8, find x.
Given that we have the function f(x) = 5x-√8, it is equal to 13 at some value of x. This relation can be written in equation as
[tex]5x-\sqrt[]{8}=13[/tex]Move √8 to the other side of the equation so that only the term with x will be left on the left-hand side. We have
[tex]5x=13+\sqrt[]{8}[/tex]Divide both sides by 5, we get
[tex]\begin{gathered} \frac{5x}{5}=\frac{13+\sqrt[]{8}}{5} \\ x=\frac{13+\sqrt[]{8}}{5} \end{gathered}[/tex]The square root of 8 can be further simplified as
[tex]\sqrt[]{8}=\sqrt[]{4\cdot2}=2\sqrt[]{2}[/tex]Hence, the value of x can also be rewritten as
[tex]x=\frac{13+2\sqrt[]{2}}{5}[/tex]Thus, the value of x to satisfy f(x) = 13 when f(x)=5x -√8 is
[tex]x=\frac{13+\sqrt[]{8}}{5}=\frac{13+2\sqrt[]{2}}{5}=\frac{13}{5}+\frac{2\sqrt[]{2}}{5}[/tex]2. Consider the linear expression.
3.2a - 1 - 4 1/3a + 7 - a
(a) What are the like terms in the expression?
(b) Simplify the linear expression.
Please type ALL the steps down.
a. The like terms are: 3.2a, -4⅓a, and -a; and -1 and 7.
b. The linear expression is simplified as: -2.1a + 6.
How to Simplify a Linear Expression?To simplify a linear expression, the like terms in the expression are combined together. Like terms in a linear expression are terms that have the same variables or variables with the same powers. Constant terms are also like terms. These like terms are combined together to simplify any given expression.
a. Given the linear expression, 3.2a - 1 - 4⅓a + 7 - a, the following are the like terms that exist in the expression:
3.2a, -4⅓a, and -a are like terms because they have the same variable.
-1 and 7 are like terms, because they are constants.
b. To simplify the linear expression, 3.2a - 1 - 4⅓a + 7 - a, combine the like terms together:
3.2a - 4⅓a - a - 1 + 7
3.2a - 4.3a - a - 1 + 7
-2.1a + 6
Learn more about like terms on:
https://brainly.com/question/15894738
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