Given the equation
[tex]5x+4=x+8[/tex]To solve this first pass all x-related terms to the left side of the equation and all other terms to the right side:
[tex]5x-x=8-4[/tex]And solve
[tex]\begin{gathered} 4x=4 \\ x=\frac{4}{4} \\ x=1 \end{gathered}[/tex]10. A recipe for banana bread calls for 3 bananas for every 6 cups of
What is the ratio of bananas to sugar?
(Solve the problem & round to four decimal places as needed.)
SOLUTION
Given:
[tex]ln0.0664=-2.7121[/tex]Final answer:
-2.7121
4x + x + 4 = 8x -3x + 4
x can take any real value
Explanation
[tex]4x+x+4=8x-3x+4[/tex]
Step 1
add similar terms in both sides
[tex]\begin{gathered} 4x+x+4=8x-3x+4 \\ 5x+4=5x+4 \end{gathered}[/tex]Step 2
subtract 5x+4 in both sides
[tex]\begin{gathered} 5x+4=5x+4 \\ 5x+4-(5x+4)=5x+4-(5x+4) \\ 0=0 \end{gathered}[/tex]0=00 means that as an equation, its solution is that x can take any real value .
I hope this helps you
help me please. using the axis of symmetry find the vertex for the follow quadratic function. f (x)=3x^2-6x+8
Answer:
[tex]P(1,5)[/tex]
Explanation: Axis of symmetry is a vertical line that makes function symmetrical along either side:
In case of parabla function or:
[tex]y(x)=3x^2-6x+8[/tex]We get axial symmetry where the first derivate is zero, and in fact, that is the x value for vertex:
Therefore:
[tex]\begin{gathered} f^{\prime}(x)=(3x^2-6x+8)^{\prime}=6x-6=0 \\ \therefore\rightarrow \\ x=\frac{6}{6}=1 \end{gathered}[/tex]And the corresponding y-value is:
[tex]f(1)=3(1)^2-6(1)+8=5[/tex]Therefore vertex is at the point:
[tex]P(1,5)[/tex]Which fraction is represented by point A on the numb 0 -1 O- 1 4. 4 1 1
The fraction that represent the point A is -1/4.
Since there are 4 divition in between -1 and 0.
Thus the length of one division is,
[tex]undefined[/tex]It's in the photo, it's a bit to hard to type out.
Perpendicular lines have slopes that are negative reciprocals.
If two perpendicular lines have slopes m1 and m2, then we have the following equation:
[tex]m_1=-\frac{1}{m_2}[/tex]Then, we can analyze each pair.
a) In this case, both lines have the same slope (m = 1/5). They are parallel, not perpendicular.
b) In this case, the slopes are different. They are reciprocals (m1 = 1/m2), but they are not negative reciprocals, so they are not perpendicular.
c) In this case the slopes are the negative of each other (2/3 and -2/3), but they are not negative reciprocals. Then, they are not perpendicular.
d) In this case, the slopes are negative reciprocals:
[tex]-\frac{1}{m_2}=-\frac{1}{-\frac{3}{2}}=\frac{1}{\frac{3}{2}}=\frac{2}{3}=m_1[/tex]Then, this lines are perpendicular.
Answer: Option d.
Question 37?Find the indicated function and state its domain in interval notation?
Given the functions:
[tex]\begin{gathered} f(x)=-\sqrt[]{x-3} \\ g(x)=3x \end{gathered}[/tex]You need to multiply them, in order to find:
[tex](f\cdot g)(x)[/tex]Then, you get:
[tex]\begin{gathered} (f\cdot g)(x)=(-\sqrt[]{x-3})(3x) \\ (f\cdot g)(x)=-3x\sqrt[]{x-3} \end{gathered}[/tex]In order to find the Domain, you need to remember that the Domain of a Radical Function are those input values (x-values) for which the Radicand is positive. Then, in this case, you need to set up that:
[tex]x-3\ge0[/tex]Now you have to solve for "x":
[tex]x\ge3[/tex]Therefore:
[tex]Domain\colon\lbrack3,\infty)[/tex]Hence, the answer is:
[tex]\begin{gathered} (f\cdot g)(x)=-3x\sqrt[]{x-3} \\ \\ Domain\colon\lbrack3,\infty) \end{gathered}[/tex]please help me thank you
Which of the following lists of data has the smallest standard deviation? Hint: you should not need to compute the standard deviation for each list.Select the correct answer below:11, 17, 9, 4, 4, 6, 6, 9, 8, 1829, 21, 21, 28, 28, 26, 24, 24, 17, 236, 8, 10, 6, 8, 8, 10, 7, 10, 1023, 19, 12, 19, 17, 18, 16, 10, 12, 2117, 12, 6, 6, 15, 16, 20, 20, 5, 17
Standard deviation is an important measure of spread or dispersion. It tells us how far, on average the results are from the mean.
The smallest standard deviation belongs to the dataset with the smallest range and almost no outliers. Closer the values are to the mean, less the value of the standard deviation.
Comparing those datasets, the one that fits this description is the third one.
[tex]\lbrace6,8,10,6,8,8,10,7,10,10\rbrace[/tex]An unsharpened, round pencil is in the shape of a right circular cylinder. For one such pencil, the radius is 4.6 mm and the length is 167.7 mm. Find the volume of the pencil. Round your answer to the nearest whole number. Do not type the units in the space below. (Be sure to use the pi button on your calculator to do the calculation.)
The volume of the cylindrical pencil to the nearest whole number is 11149cubic millimeters
What is a cylinder?A cylinder is a 3-D shape consisting of two circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder.
The volume of a cylinder is πr^2h
r is the radius, h is the height or length of the cylinder
putting the values of r and h in the formula and π=3.142
V= 3.142×4.6×4.6×167.7
there the volume of the cylindrical pencil is 11149cubic millimeters ( nearest whole number)
learn more about cylinders from
https://brainly.com/question/23935577
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write the linear equation that passes through the two given points (2,-2) and (0,-1)
Given the points:
(x1, y1) ==> (2, -2)
(x2, y2) ==> (0, -1)
To find the linear equation, use the form:
y = mx + b
where m is the slope.
To find the slope, use the formula below:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Thus, we have the slope as:
[tex]m=\frac{-1-(-2)}{0-2}=\frac{-1+2}{0-2}=\frac{1}{-2}=-\frac{1}{2}[/tex]Input 2 for x, -2 for y, and -1/2 for b to find b.
[tex]\begin{gathered} -2=-\frac{1}{2}(2)+b \\ \\ -2=-1+b \\ \\ -2+1=b \\ \\ -1=b \end{gathered}[/tex]Therefore, the linear equation is:
[tex]y=-\frac{1}{2}x-1[/tex]ANSWER:
[tex]y=-\frac{1}{2}x-1[/tex]4 students from a class of 15 are going to be chosen to be on the dance committee. Findthe number of different 4-person committees that can be made.
Answer:
[tex]C(15,4)=1365\text{ different committees}[/tex]Step-by-step explanation:
This situation can be approached using the formula for combinations:
[tex]\begin{gathered} C(n,r)=\frac{n!}{r!(n-r)!} \\ \text{where,} \\ n=\text{ number of possible items that can be }selected \\ r=\text{ number of items that were selected} \end{gathered}[/tex]Therefore, solve for n=15 and r=4.
[tex]\begin{gathered} C(15,4)=\frac{15!}{4!(15-4)!} \\ C(15,4)=1365\text{ different committees} \end{gathered}[/tex]Math help!!! Only a tutor that can give me answers to 9 and 10!!
9.
Alternative interior angles are congruent
Therefore;
5x + 42 = 18x -12
collect like term
5x - 18x = -12 - 42
-13 x = -54
Divide both-side of the equation by -13
x=4.15
find the measures of the angles of a right triangle where one of the acute angles is *3.5* times the other
Lets draw a picture of our problem:
where x denotes the measure of the base angle.
Since interior angles of any triangle add up to 180, we have
[tex]x+3.5x+90=180[/tex]which gives
[tex]4.5x+90=180[/tex]By subtracting 90 to both sides, we have
[tex]\begin{gathered} 4.5x=180-90 \\ 4.5x=90 \end{gathered}[/tex]Finally, by dividing both sides by 4.5, we get
[tex]\begin{gathered} x=\frac{90}{4.5} \\ x=20 \end{gathered}[/tex]Then, the base angle measures 20 degrees and the upper angle measure
[tex]3.5\times20=70[/tex]Therefore, the searched angles measure
[tex]20,70\text{ and 90}[/tex]in the sophomore class at Summit High School the number of students taking French is 2/3 of the number taking Spanish. how many students are studying each language if the total number of students in French and Spanish is 310 ?This is Homework
From the information given in the statement let be
[tex]\begin{gathered} f=\frac{2}{3}s\text{ (1)} \\ f+s=310\text{ (2)} \end{gathered}[/tex]Where
*f: number of students taking a French class
*s: number of students taking a Spanish class
So, you have a system of linear equations, which you can use the substitution method.
To do this, replace the value of the first equation in the second equation and solve for s
[tex]\begin{gathered} f+s=310\text{ (2)} \\ \frac{2}{3}s+s=310 \\ \frac{5}{3}s=310 \\ \text{ Multiply by }\frac{3}{5}\text{ on both sides of the equation} \\ \frac{3}{5}\cdot\frac{5}{3}s=310\cdot\frac{3}{5} \\ s=186 \end{gathered}[/tex]Now,
There are 4 options on the dessert menu at a restaurant. Bill and Laura like all of the choices equallyeach choose a dessert at random from the menu. What is the probability that Bill will choose apple pLaura will choose strawberry cheesecake for dessert? Express your answer as a decimal. If necessalyour answer to the nearest thousandth.0 0.938O 0.063O 0.25O 0.083
Solution
If we have 4 options and we want to find that Bill select one option and then Laura a different second option is:
1/2 * 1/2= 1/4= 0.25
Then the best answer is:
0.25
Triangle MNO has its vertices at the following coordinates:M(2, 2) N(-1,3) O(1,5)Give the coordinates of the image triangle M'N'O' after a 90° counterclockwise rotation about the origin.
The counter clockwise rotation of any point X(x,y) about origin results in change of coordinates as,
[tex]X(x,y)\rightarrow X^{\prime}(-y,x)[/tex]Determine the coordinates of the vertices of the triangle M'N'O'.
[tex]M(2,2)\rightarrow M^{\prime}(-2,2)[/tex][tex]N(-1,3)\rightarrow(-3,-1)[/tex][tex]O(1,5)\rightarrow(-5,1)[/tex]So coordinates of triangle M'N'O' are;
M'(-2,2)
N'(-3,-1)
O'(-5,1)
sandy made 8 friendship bracelets. she gave 1/8 to her best friend and 5/8 to her friends on the tennis team. write and solve an equation to find the fraction of her bracelets, b , sandy gave away1
Answer:
(3/4)b
Explanation:
• Fraction given to her best friend = 1/8
,• Fraction given to her friends on the tennis team = 5/8
To calculate the total proportion of the bracelet she gave away, we add:
[tex]\begin{gathered} (\frac{1}{8}+\frac{5}{8})b \\ =\frac{6}{8}b \\ =\frac{3\times2}{4\times2}b \end{gathered}[/tex]Reducing the fraction to its lowest form by canceling out 2 gives:
[tex]=\frac{3}{4}b[/tex]Which graph represents the solution of −2x≤4(x−6)?
Answer:
See attachments.
Step-by-step explanation:
Given inequality:
[tex]-2x\leq 4(x-6)[/tex]
Solve the inequality by first expanding the brackets:
[tex]\implies -2x\leq 4x-24[/tex]
Subtract 4x from both sides:
[tex]\implies -2x-4x\leq 4x-24-4x[/tex]
[tex]\implies -6x\leq -24[/tex]
Divide both sides by -6 (remembering to reverse the inequality sign as we are dividing by a negative number).
[tex]\implies \dfrac{-6x}{-6}\leq \dfrac{-24}{-6}[/tex]
[tex]\implies x\geq 4[/tex]
When graphing inequalities on a coordinate plane:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.Therefore, to graph the given inequality on a coordinate plane:
Draw a solid line at x = 4.Shade above the line (i.e. shade to the right of the line).(See attachment 1).
When graphing inequalities on a number line:
< or > : open circle.≤ or ≥ : closed circle.< or ≤ : shade to the left of the circle.> or ≥ : shade to the right of the circle..Therefore, to graph the given inequality on a number line:
Place a closed circle at 4.Shade to the right of the circle.(See attachment 2).
Set up the equation for the following word problem and solve the equation. Let y be the unknown number.81 times a number minus 77 is equal to - 77 less than the number.Step 1 of 2: Write out the equation,
The equation of the word is,
[tex]undefined[/tex]please help ………………. …………. ………… i already have the answer for part A but im having trouble with Parts B and C
In part B we must perform the following operation:
[tex](5a^3+4a^2-3a+2)+(a^3-3a^2+3a-9)[/tex]The key here is to group the terms according to the power of a they have:
[tex](5a^3+4a^2-3a+2)+(a^3-3a^2+3a-9)=(5a^3+a^3)+(4a^2-3a^2)+(-3a+3a)+(2-9)[/tex]Then, we can use the distributive property of the multiplication but in reverse:
[tex]b\cdot a+c\cdot a=(b+c)\cdot a[/tex]If we do this in each of the terms between parenthesis we get:
[tex]\begin{gathered} (5a^3+a^3)+(4a^2-3a^2)+(-3a+3a)+(2-9)= \\ =(5+1)a^3+(4-3)a^2+(-3+3)a-7 \\ (5+1)a^3+(4-3)a^2+(-3+3)a-7=6a^3+a^2-7 \end{gathered}[/tex]Then the answer for part B is:
[tex]6a^3+a^2-7[/tex]In part C we must simplify:
[tex](4y^3-2y+9)-(2y^3-3y^2+4y+7)[/tex]Here is important to remember that a negative sign before a parenthesis means that you have to change the sign of all the terms inside it. Then we have:
[tex](4y^3-2y+9)-(2y^3-3y^2+4y+7)=4y^3-2y+9-2y^3+3y^2-4y-7[/tex]Now we can do the same thing we did in part B, we group the terms according to the powers of y:
[tex]4y^3-2y+9-2y^3+3y^2-4y-7=(4y^3-2y^3)+3y^2+(-2y-4y)+(9-7)[/tex]Then we apply the distributive property in reverse:
[tex]\begin{gathered} (4y^3-2y^3)+3y^2+(-2y-4y)+(9-7)=(4-2)y^3+3y^2+(-2-4)y+2 \\ (4-2)y^3+3y^2+(-2-4)y+2=2y^3+3y^2-6y+2 \end{gathered}[/tex]Then the answer for part C is:
[tex]2y^3+3y^2-6y+2[/tex]Which is the equivalent of 6 14’ 48’’ written in decimal form Round to the nearest thousandth of a degree A. 6.145 B. 6.367 C. 6.247 D. 6.313
Answer
Step-by-step explanation
First, we need to convert the 48'' into minutes. Using the conversion factor: 1' = 60'', we get:
[tex]\begin{gathered} 48^{\prime}^{\prime}=48^{\prime}^{\prime}\cdot\frac{1^{\prime}}{60^{\prime}^{\prime}} \\ 48^{\prime\prime}=\frac{48}{60}^{\prime} \\ 48^{\prime}^{\prime}=0.8^{\prime} \end{gathered}[/tex]Then, 14 minutes and 48 seconds are equivalent to 14 + 0.8 = 14.8 minutes. To convert this amount of minutes into degrees we need to use the conversion factor 1° = 60', as follows:
[tex]\begin{gathered} 14.8^{\prime}=14.8^{\prime}\cdot\frac{1\degree}{60^{\prime}^{\prime}} \\ 14.8^{\prime}=\frac{14.8}{60}\degree \\ 14.8^{\prime}=0.247\operatorname{\degree} \end{gathered}[/tex]In consequence, 6° 14’ 48’’ is equivalent to 6 + 0.247 = 6.247°
Melina made a scale drawing of a building.She used a scale in which 0.5 inch represents 1 foot. Which graph represents this relationship?
From the graph, the y - axis 10 uints while the x - axis is 5 units
The x - axis is labeled inches and its half of the feet
For every half inch on x - axis you have 1 feet
The graph that displays the scale is graph D
The answer is OPTION D
The graph of F(x), shown below, resembles the graph of G(X) = x2, but it hasbeen changed somewhat. Which of the following could be the equation ofF(x)?600 = x2FUO = ?O. A. F(x) = 0.272 - 3B. F(x) = -x2 - 3C. F(x) = 2x2 - 3D. F(X) = 32 - 3
You have G(x) = x².
take into account that G(x) can be considered as an streched of the F(X), moreover, F(x) is a translation of G(x) downward 3 units. If G(x) is an strech of F(x), then, G(x) is multipled by a constant lower than 1.
Then, based on the previous considerations, you have that the form of F(x) is:
F(x) = 0.2x² - 3
while exploring a volcano zane heard somerumbling, so he decided to climb up out of there as quicklyas he could zane's elevation relative to the edge of the inside of the volcano (in meter) as a function time (in seconds) is graphed. PLEASE HELP ME WITH THIS How long did it take Zane to reach the edge of the volcano?
We have to find the time it took for Zane to be in the same elevation as the edge of the Volcano, that is, when his relative elevation is 0 on the graphic.
This happens at a time of 35 seconds. So:
It took Zane 35 seconds to reach the edge of the volcano.
A hot chocolate recipe calls for 2.5 gallons of milk. How many quarts of milk are needed for the recipe
Answer: 10
Step-by-step explanation: a gallon has 4 quarts, 4x2.5=10
10 quarts is 2.5 gallons.
Use Vocabulary in Writing 9. Explain how you can find the product 4 X 2 and the product 8 X 2 Use at least 3 terms from the Word List in your explanation.
Okay, here we have this:
The solution process is shown for any equation. Justify each step in the process with the appropriate property. Select the correct answer from each drop down menu.
Answer:
Explanation:
Here, we want to get the values in the segments
a) Here we would have to open up the brackets
Now, to do this, we are going to use the distributive property
By using the distributive property, we will be able to open up the brackets
Doing this, we can get the values in the brackets
So the answer here is distributive property
b) Here, we have
14 = -y after combining the like terms
The correct answer here is the subtraction property of equality
We simply subtract 3y from both sides of the equation to arrive at this answer
c) -14 = y
We have the multiplication property of equality
The reason for this is that we multiplied both sides by -1 to arrive at this answer
d) y = -14
This is the symmetric property of equality
We have this here because if two values are equal on both sides, we can switch each to the opposite sides and still retain the same equality values
5-74.The number of girls at Middle SchoolCyber Summer Camp was six morethan twice the number of boys. Therewere a total of 156 middle schoolstudents at the camp. Use the 5-DProcess to find the number of boysand the number of girls at camp.
We have the following:
Describe/Draw
The statement tells us that the number of girls was 6 plus twice the number of boys and that in total there are 156 students.
Define
Number of girls: y, y = 6 + 2x
Number of boys: x
Number of students: 154
Do
[tex]\begin{gathered} x+y=156 \\ x+6+2x=156 \\ 3x=156-6 \\ x=\frac{150}{3} \\ x=50 \end{gathered}[/tex]for y:
[tex]y=6+2\cdot50=6+100=106[/tex]Decide
The answer is correct because the sum of both is equal to 156 students
Declare
In total there are 50 boys and 106 girls
Solve the given equation:x = -8y + 9
We have to solve the equation.
[tex]x=-8y+9[/tex]We have 2 unknowns and one equation, so we can only express one in function of the other.
We already have x in function of y, so we will now express y in function of x:
[tex]\begin{gathered} x=-8y+9 \\ x-9=-8y+9-9 \\ \frac{x-9}{-8}=\frac{-8y}{-8} \\ \\ -\frac{x}{8}+\frac{9}{8}=y \\ \\ y=-\frac{x}{8}+\frac{9}{8} \end{gathered}[/tex]Answer:
y = -x/8 + 9/8
