First, let's find the slope of the line that passes through the points (-4,3) and (6,2):
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow m=\frac{2-3}{6-(-4)}=\frac{-1}{6+4}=-\frac{1}{10} \end{gathered}[/tex]Now we can use the first point to get the equation of the line:
[tex]\begin{gathered} (x_1,y_1)=(-4,3) \\ y-y_1=m(x-x_1) \\ \Rightarrow y-3=-\frac{1}{10}(x-(-4))=-\frac{1}{10}(x+4)=-\frac{1}{10}x-\frac{4}{10}=-\frac{1}{10}x-\frac{2}{5} \\ \Rightarrow y=-\frac{1}{10}x-\frac{2}{5}+3=-\frac{1}{10}x-\frac{2}{5}+\frac{15}{5}=-\frac{1}{10}x+\frac{13}{5} \\ y=-\frac{1}{10}x+\frac{13}{5} \end{gathered}[/tex]therefore, the equation of the line is y=-1/10x+13/5
To raise money for charity, Bob and some friends are hiking across the continent of Asia. While out on the trail one day, one of his Jordian friends asks Bob for the temperature. He glances at his precision sports watch and sees that the temperature is -12.9 F. What is this temperature in degrees C Celsius ()?
ANSWER
[tex]-24.9[/tex]EXPLANATION
Given;
[tex]-12.9F[/tex]To convert to degree Celsius, we use the formula;
[tex]\begin{gathered} \frac{5}{9}(F-32) \\ \\ \end{gathered}[/tex]Substituting F;
[tex]\begin{gathered} \frac{5}{9}(-12.9-32) \\ =\frac{5}{9}\times-44.9 \\ =-\frac{224.5}{9} \\ =-24.94 \\ \cong-24.9 \end{gathered}[/tex]I find an awesome pair of red Jimmy Choo ‘Romy 100’ heels for 35% off. If the sale price is $812.50, what was the original price before the markdown?
812.50 ------------------------ 65%
x ----------------------- 100%
x = (100 x 812.50) / 65
x = 81250 / 65
x = $1250
The original price was $1250.00
What value of x makes this equation true?3 - 2x = 8 - 13
First we have to solve the substraction on the right side of the equation:
[tex]3-2x=-5[/tex]Now we add 2x on both sides:
[tex]\begin{gathered} 3-2x+2x=-5+2x \\ 3=-5+2x \end{gathered}[/tex]Now add 5 on both sides:
[tex]\begin{gathered} 3+5=-5+5+2x \\ 8=2x \end{gathered}[/tex]And divide both sides by 2:
[tex]\begin{gathered} \frac{8}{2}=\frac{2x}{2} \\ 4=x \end{gathered}[/tex]The value of x that makes the equation true is 4
Madelyn incorrectly followed the set of directions when she transformed pentagon PENTA.The directions are listed below the coordinate plane. What was the error Madelyn made?A. She rotated, but not 180°B. She reflected over the x-axis instead of the y-axisC. She translated 4 units to the left instead of the rightD. She did not make a mistake
Solution:
Given the transformation below:
Given the directions:
[tex]\begin{gathered} Rotate\text{ 180 degrees} \\ Reflect\text{ over the y-axis} \\ Translate\text{ 4 unnts to the right} \end{gathered}[/tex]Step 1: Give the coordinates of the vertices of pentagon PENTA.
Thus,
[tex]\begin{gathered} P(-5,5) \\ E(-3,\text{ 5\rparen} \\ N(-4,\text{ 4\rparen} \\ T(-3,\text{ 2\rparen} \\ A(-5,\text{ 2\rparen} \end{gathered}[/tex]step 2: Rotate the pentagon 180 degrees.
For 180 degrees rotation, we have
[tex]\begin{gathered} A(x,y)\to A^{\prime}(-x,\text{ -y\rparen} \\ where \\ A^{\prime}\text{ is an image of A} \end{gathered}[/tex]Thus, the coordinates of pentagon becomes
[tex]\begin{gathered} P(5,\text{ -5\rparen} \\ E(3,\text{ -5\rparen} \\ N(4,\text{ -4\rparen} \\ T(3,\text{ -2\rparen} \\ A(5,\text{ -2\rparen} \end{gathered}[/tex]The image is shown below:
step 3: Reflect over the y-axis.
For reflection over the y-axis, we have
[tex](x,y)\to(-x,y)[/tex]This, we have the image to be
step 4: Translate 4 units to the right.
For translation by 4 units to the right, we have
[tex](x,y)\to(x+4,\text{ y\rparen}[/tex]This gives
Hence, the mistake Madelyn made was that she reflected over the x-axis instead of the y-axis.
The correct option is B.
Points A, B, and C are collinear and point B lies in between points A and C. If AB = 3x + 1, BC = 15, and AC = 7x + 1, find AC. Show work please
Answer:
AC = AB + BC + AC
AC= 3×+1+15+7×+1
AC= 3x+7×+1+15+1
AC=10×+17
Find the angle of elevation from the base of one tower to the top of the second
This system can be represented by a triangle with base 350 m length and height 100 m length
The angle of elevation is given by:
[tex]\tan ^{-1}(\frac{100}{350})=\tan ^{-1}(\frac{2}{7})\approx0.28\text{ rad }\approx\text{ 16\degree}[/tex]Which of these equations has infinitely many solutions? 3(1-2x + 1) = -6x + 2. 4 + 2(x - 5) = 1/2 {(4x - 12) (5x + 15) 3x - 5 = 5= 1/(5x () which statement explains a way you can tell the equation has infinitely many solutions? It is equivalent to an equation that has the same variable terms but different constant terms on either side of the equal sign. It is equivalent to an equation that has the same variable terms and the same constant terms on either side of the equal sign. It is equivalent to an equation that has different variable terms on either side of the equation.
Answer
The equation with infinite solutions is Option B
4 + 2 (x - 5) = ½ (4x - 12)
The key way to know if an equation has infinite solutions is shown in Option B
It is equivalent to an equation that has the same variable terms and the same constant terms on either side of the equal sign.
Explanation
The key way to know if an equation has infinite solutions is when
It is equivalent to an equation that has the same variable terms and the same constant terms on either side of the equal sign.
So, we will check each of the equations to know which one satisfies that condition.
2x + 1 = -6x + 2
2x + 6x = 2 - 1
8x = 1
Divide both sides by 8
(8x/8) = (1/8)
x = (1/8)
This is not the equation with infinite solutions.
4 + 2 (x - 5) = ½ (4x - 12)
4 + 2x - 10 = 2x - 6
2x - 6 = 2x - 6
2x - 2x = 6 - 6
0 = 0
This is the equation with infinite solutions.
3x - 5 = (1/5) (5x + 15)
3x - 5 = x + 3
3x - x = 3 + 5
2x = 8
Divide both sides by 2
(2x/2) = (8/2)
x = 4
This is not the equation with infinite solutions.
Hope this Helps!!!
Find the derivative :f(x) = 6x⁴ -7x³ + 2x + √2
We need to find the derivative of the function
[tex]f\mleft(x\mright)=6x^{4}-7x^{3}+2x+\sqrt{2}[/tex]The derivative of a polynomial equals the sum of the derivatives of each of its terms.
And the derivative of each term axⁿ, where a is the constant multiplying the nth power of x, is given by:
[tex](ax^n)^{\prime}=n\cdot a\cdot x^{n-1}[/tex]Step 1
Find the derivatives of each term:
[tex]\begin{gathered} (6x^4)^{\prime}=4\cdot6\cdot x^{4-1}=24x^{3} \\ \\ (-7x^3)^{\prime}=3\cdot(-7)\cdot x^{3-1}=-21x^{2} \\ \\ (2x)^{\prime}=1\cdot2\cdot x^{1-1}=2x^0=2\cdot1=2 \\ \\ (\sqrt[]{2})^{\prime}=0,\text{ (since this term doesn't depend on x, its derivative is 0)} \end{gathered}[/tex]Step 2
Add the previous results to find the derivative of f(x):
[tex]f^{\prime}(x)=24x^{3}-21x^{2}+2[/tex]Answer
Therefore, the derivative of the given function is
[tex]24x^3-21x^2+2[/tex](3 x 10–6) x (7.07 x 1011)
we have
(3 x10^-6)x(7.07x10^11)
remmeber that adds the exponents
so
(3x7.07)x10^(-6+11)
(21.21)x10^5 ---------> 21.21)x10^5x(10/10)
2.121x10^6
whats the length of RS,UW,UVwhat is the value of x and y
In the given triangle,
it is given that,
U is the midpoint of RS, V is the midpoint of ST and W is the midpoint of RT
so,
UR = US
VT = VS
WT = WR
put the values,
UR = US
12 = US
so, RS = 2 x UR = 2 x 12 = 24
VT = VS
11 = 2x
x = 11/2
x = 5.5
so, TS = 2 x 11 = 22
WT = WR
3y = 15.9
y = 15.9/3
y = 5.3
so, RT = 2 x 15.9 = 31.8
also, UV = 1/2 RT
UV = 1/2 x 31.8 = 15.9
UW = 1/2x TS
UW = 1/2 x 22 = 11
VW = 1/2 RS
VW = 1/2 x 24 = 12
There were two candidates in a student government election for 7th gradeTreasurer, Kaya and Jay. Out of 322 total votes, Jay received 112 votes andKaya received 210. What percentage of the students voted for Kaya? Roundto the nearest tenth, if necessary.53.3%O 187.5%O 34.8%0 65.2%
Given:
There were the two candidate in the students governement election : kaya and jay.
Total votes=322
jay received 112 votes and Kaya received 210 votes.
To calculate the percetage of votes for kaya,
[tex]\begin{gathered} P=\frac{parts}{\text{whole}}\times100 \\ P=\frac{210}{322}\times100 \\ P=65.2 \end{gathered}[/tex]Answer: 65.2% of the students voted for Kaya.
I got the top part of my homework right, I’m just not sure how to do the bottom one. Thank you!
The graph of a function and its inverse are always symmetrical across the line defined by:
[tex]y=x[/tex]This is true for any function and its inverse.
which is higher? -32 or 36?
36 is higher
positive numbers are higher than negative numbers
Hence 36 is higher than -32
Find the missing sides of the following without using calculator
The missing sides are 3 and 3√3
Explanation:Let the opposite sides be represented by x, and the other missing side be y, then
[tex]\sin \theta=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]Using the above, we have:
[tex]\begin{gathered} \sin 60=\frac{x}{6} \\ \\ x=6\sin 60 \\ =6\times\frac{\sqrt[]{3}}{2} \\ \\ =3\sqrt[]{3} \end{gathered}[/tex]And
[tex]\begin{gathered} \cos \theta=\frac{\text{adjacent}}{\text{hypotenuse}} \\ \\ \cos 60=\frac{y}{6} \\ \\ y=6\cos 60 \\ =6\times\frac{1}{2} \\ \\ =3 \end{gathered}[/tex]The missing sides are 3 and 3√3
Find a degree 3 polynomial that has zeros -3,3, and 5 and in which the coefficient of x^2 is -10.The polynomial is: _____
Given the polynomial has zeros = -3, 3, 5
so, the factors are:
[tex](x+3),(x-3),(x-5)[/tex]Multiplying the factors to find the equation of the polynomial:
So,
[tex]\begin{gathered} y=(x-3)(x+3)(x-5) \\ y=(x^2-9)(x-5) \\ y=x^2(x-5)-9(x-5) \\ y=x^3-5x^2-9x+45 \end{gathered}[/tex]But the coefficient of x^2 is -10.
So, Multiply all the coefficients by 2
So, the answer will be:
The polynomial is:
[tex]2x^3-10x^2-18x+90[/tex]5 1/8 divided by 10
Find the quotient. If possible, rename the quotient as a mixed number or a whole number. Write your answer in simplest form, using only the blanks needed.
If [tex]5\frac{1}{8}[/tex] is divided by 10, 41/80 is the quotient.
What are fractions?Fractions are used to depict the components of a whole or group of items. Two components make up a fraction. The numerator is the number that appears at the top of the line. It specifies how many identically sized pieces of the entire event or collection were collected. The denominator is the quantity listed below the line.
The total number of identical objects in a collection or the total number of equal sections that the whole is divided into are both displayed. A fraction can be expressed in one of three different ways: as a fraction, a percentage, or a decimal. The first and most popular way to express a fraction is in the form of the letter ab. Here, a and b are referred to as the numerator and denominator, respectively.
The given expressions are
[tex]5\frac{1}{8}[/tex] / 10
41/ 8 ÷10
= 41/8 × 1/10
= 41/80
This is the quotient.
To know more about fractions, visit:
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Which of the following equations represents the line that passes throught the points (2, -6) and(-4,3)?A.y= -3/2x - 7B.y= -2/3x - 3C.y= -2/3x + 1/3D.y= -3/2x - 3
Given two points (x1, y1) and (x2, y2), the slope (m) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing with points (2, -6) and (-4, 3), we get:
[tex]m\text{ = }\frac{3-(-6)}{-4-2}=\frac{9}{-6}=-\frac{3}{2}[/tex]slope-intercept form of a line:
y = mx + b
where m is the slope and b is the y-intercept.
Replacing with point (2, -6) and m = -3/2, we get:
-6 = -3/2(2) + b
-6 = -3 + b
-6 + 3 = b
-3 = b
Finally, the equation is:
y = -3/2x - 3
A text book store sold a combined total of 347 history and physics textbooks in a week. The number of history textbooks sold was 79 more than the number of physics textbooks sold. How many textbooks of each type were sold?
Let the number of history textbooks be h and the number of physics textbooks be p.
It was given that the bookstore sells a combined total of 347 books. Thus we have:
[tex]h+p=347[/tex]It is also given that the number of history textbooks sold was 79 more than the number of physics textbooks. This gives:
[tex]h=p+79[/tex]We can substitute for h into the first equation:
[tex]p+79+p=347[/tex]Solving, we have:
[tex]\begin{gathered} 2p+79=347 \\ 2p=347-79 \\ 2p=268 \\ p=\frac{268}{2} \\ p=134 \end{gathered}[/tex]Substitute for p in the second equation, we have:
[tex]\begin{gathered} h=p+79 \\ h=134+79 \\ h=213 \end{gathered}[/tex]Therefore, there were 134 physics textbooks and 213 history textbooks.
Robert is selling his bulldozer at a heavy equipment auction. The auction company receives a commission of 5%of the selling price. If Robert owes $122,230 on the bulldozer, then what must the bulldozer sell for in order forhim to be able to pay it off?Select one:a.123,000b. 122,230C. 128,664d. 130,786
Answer:
Explanation:
The auction company receives a commission of 5% of the selling price.
Let the sale price of the bulldozer = x
[tex]\begin{gathered} \text{ Sale Price}=\text{ The amount Robert owes + Commision} \\ x=122,230+0.05x \end{gathered}[/tex]The equation is then solved for x:
[tex]\begin{gathered} x-0.05x=122230 \\ 0.95x=122230 \\ \text{ Divide both sides by 0.95} \\ \frac{0.95x}{0.95}=\frac{122,230}{0.95} \\ x=128663.20 \\ \text{ Round up} \\ x\approx128,664 \end{gathered}[/tex]The bulldozer must sell for $128,664 n order for him to be able to pay off the a
The water trough shown in the figure to the right is constructed with semicircular ends. Calculate its volume in gallons if thediameter of the end is 19 in. and the length of the trough is 5 ft. (Hint: Be careful of units.)(Round to the nearest tenth as needed.)
Solution
For this case we can use the following formula:
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]The perimeter of the triangle PQR is 94cm. What is the length of PQ?
the length of PQ is 33 cm
Explanation:The perimeter of the triangle = 94 cm
The triangle is an isosceles triangle as two of its sides are equal
From the diagram:
PQ = RQ
Perimeter of triangle = PQ + PR + RQ
PR = 28 cm
94 = PQ + 28 + RQ
94 = 2PQ + 28
94 - 28 = 2PQ
66 = 2PQ
divide both sides by 2:
66/2 = 2PQ/2
PQ = 33
Hence, the length of PQ is 33 cm
Frustratingly this is the third time I’m asking this question that two tutors got wrong. Please help?
To answer this question, we need to translate each of the expressions into algebraic form. Then we have:
1. We have that one number is 2 less than a second number.
In this case, let x be one of the numbers, and y the second number. Now, we can write the expression as follows:
[tex]x=y-2[/tex]2. We also have that twice the second number is 2 less than 3 times the first:
[tex]2y=3x-2[/tex]3. And now, we have the following system of equations:
[tex]\begin{cases}x=y-2 \\ 2y=3x-2\end{cases}[/tex]4. And we can solve by substitution as follows:
[tex]\begin{gathered} x=y-2\text{ then we have:} \\ \\ 2y=3(y-2)-2 \\ \\ 2y=3(y)+(3)(-2)-2 \\ \\ 2y=3y-6-2 \\ \\ 2y=3y-8 \end{gathered}[/tex]5. To solve this equation, we can subtract 2y from both sides, and add 8 from both sides too:
[tex]\begin{gathered} 2y-2y=3y-2y-8 \\ 0=y-8 \\ 8=y-8+8 \\ 8=y \\ y=8 \end{gathered}[/tex]6. Since y = 8, then we can use one of the original equations to find x as follows:
[tex]\begin{gathered} x=y-2\Rightarrow y=8 \\ x=8-2 \\ x=6 \end{gathered}[/tex]Therefore, we have that both numbers are x = 6, and y = 8.
In summary, we have that:
• The smaller number is 6.
,• The larger number is 8.
Which of the following names the figure in the diagram below?
O A. Triangle
O B. Prism
O C. Polygon
O D. Pyramid
O E. Cylinder
O F. Cube
Step 1
A triangular prism is a 3D shape that looks like an elongated pyramid. It has two bases and three rectangular faces.
Step 2:
A triangular prism has two triangular bases and three rectangular sides and is a pentahedron because it has five faces. Camping tents, triangular roofs and "Toblerone" wrappers -- chocolate candy bars -- are examples of triangular prisms.
Final answer
B. Prism
solve by substitution x+2y-z = 4 3x – y +z = 5 2x + 3y + 2z = 7
You have the following system of equations:
ExplanationCheckX3(a) Move the cubes so that each stack has the same number of cubes.Then give the number of cubes in each stack.(b) What is the mean of 8, 6, 8, 4, and 9?(These are the numbers of cubes in the original stacks.)0(c) Are the values you found in parts (a) and (b) the same? Why or why not?No. But it didn't have to turn out that way. When the stacks are made equal,the number of cubes in each stack may be the mean of the original stacks.I need help with this math problem.
a. After moving the cubes so that each stack has the same number of cubes, we got 7 cubes in each stack.
Explanation:
In total, there are 35 cubes. Since there are 5 stacks, we divide 35 by 5 and got 7. Hence, there must be 7 cubes in each stack.
b. To determine the mean, simply do the same process above. Add the given numbers and divide the sum by the total numbers given.
[tex]8+6+8+4+9=35[/tex]Since there are 5 numbers, divide 35 by 5.
[tex]35\div5=7[/tex]Hence, the mean is 7.
c. Yes, the values in parts a and b are equal. When we make the stacks equal, the number of cubes in each stack must be the mean of the original stacks because the mean is the average of the number of stacks. (Option 3)
I have to find the least common denominator and the domain, but i’m lost
Explanation:
[tex]\frac{2x\text{ - 3}}{x^2+6x+8}\text{ + }\frac{10}{x^2+x\text{ - 12}}[/tex]Finding the LCM:
[tex]\begin{gathered} =\frac{(2x-3)(x^2+x-12)+10(x^2+6x+8)}{(x^2+6x+8)(x^2+x-12)} \\ =\frac{(2x)(x^2+x-12)-3(x^2+x-12)+10(x^2+6x+8)}{(x^2+6x+8)(x^2+x-12)} \\ =\frac{(2x^3+2x^2-24x)-3x^2-3x+36+10x^2+60x+80}{(x^2+6x+8)(x^2+x-12)} \end{gathered}[/tex][tex]undefined[/tex]Can you please help me out with a question
What is the value of xin the product of powers below? 6^9 * 6^x = 6^2 -11 -7 7 11
Given:
[tex]6^{9\text{ }}\ast6^x=6^2[/tex]To find the value of x, first apply exponential property which is:
[tex]a^m\text{ }\ast a^{n\text{ }}=a^{m+n}[/tex]Now we have:
[tex]6^{9+x\text{ }}=6^2[/tex]Since both bases are equal, let's remove both bases, take the exponent and find x:
[tex]9\text{ + x = 2}[/tex]Now subtract from both sides:
[tex]9\text{ - 9 + x = 2 - }9[/tex][tex]0\text{ + x }=\text{ -7}[/tex][tex]x\text{ = -7}[/tex]The value of x is -7
Heads= 24Tails= 21Based on the table, what is the experimental probability that the coin lands on heads? Express your answer as a fraction
ok
Total number of results = 24 + 21
= 45
Probability that the coins lands on heads = 24/45
= 8/15
Result = 8/15
What is (4x ^ 2 + 14x + 6) ÷ (x+3)
Hello!
We have the expression:
[tex]\frac{4x^2+14x+6}{x+3}[/tex]Note that all numbers in the numerator are even. So, we can put 2 in evidence, look:
[tex]\frac{2(2x^2+7x+3)}{x+3}[/tex]Now, let's rewrite 7x as 6x+x:
[tex]\frac{2(2x^2+6x+x+3)}{x+3}[/tex]The first and second terms are multiples of 2x, so let's rewrite it putting it in evidence too:
[tex]\frac{2(2x(x+3)+x+3)}{x+3}[/tex]Another term appears twice: (x+3). So, we'll have:
[tex]\frac{2(x+3)(2x+1)}{x+3}[/tex]Canceling the common factors:
[tex]\frac{2\cancel{x+3}(2x+1)}{\cancel{x+3}}=2(2x+1)=\boxed{4x+2}[/tex]Answer:4x +2.