We have to find the cleast common multiple of 3 and 5.
The least common multiple is the smallest number that has 3 and 5 as factors.
In this case, as 3 and 5 are prime numbers, the LCM is equal to the product of both factors:
[tex]\text{LCM}=3\cdot5=15[/tex]Answer: D. 15
Suppose the line through points (x,6) and (1,2) is parallel to the graph of 2x + y =3. Find the value of x.
SOLUTION:
Step 1:
In this question, we are given that:
Suppose the line through points (x,6) and (1,2) is parallel to the graph of 2x + y =3. Find the value of x.
Step 2:
Given the two points, (x,6) and (1,2), we need to find the slope.
[tex]\begin{gathered} slope,\text{ m =}\frac{y_2-y_1}{x_2-x_1} \\ (x_1,y_1)\text{ = ( x , 6 )} \\ (x_2,y_2)\text{ = ( 1, 2)} \end{gathered}[/tex][tex]m\text{ = }\frac{2-6}{1-x}=\frac{-4}{1-x}[/tex]Next, we find the slope of 2x+y = 3 ( Given y = mx + c )
( General Equation of a line)
[tex]\begin{gathered} y\text{ = -2x + 3} \\ \text{comparing with y = mx + c , we have that:} \\ \text{m = -2} \end{gathered}[/tex]Step 3:
Now, the two lines are parallel, which means that:
[tex]\begin{gathered} m_1=m_2 \\ \frac{-4}{1-x}=\text{ -2} \end{gathered}[/tex]So, we need to find x .
[tex]\begin{gathered} We\text{ cross-multiply, and we have that:} \\ -4\text{ = -2 ( 1-x)} \\ -4=-2+2x \\ -4\text{ + 2= 2x} \\ -2\text{ = 2x} \\ \text{Divide both sides by 2, we have that:} \\ \text{x =}\frac{-2}{2} \\ x\text{ = -1} \end{gathered}[/tex]Check:
Recall that the two points are: (x,6) and (1,2)
Now, x = -1
which means: ( -1, 6) and ( 1, 2)
[tex]undefined[/tex]Solve the equation. 7x = 3x2 - 1 a. 7+ V61 Or 6 7 √61 c. -7+ V6 X= 7- 761 X= 6 or 12 12 b. -7+ √61 7- √61 d. X= 7+ √61 7-V61 or 6 = 6 12 12
reordering
[tex]\begin{gathered} 7x=3x^2-1 \\ 7x-7x=3x^2-1-7x \\ 3x^2-7x-1=0 \end{gathered}[/tex]then solve
[tex]\begin{gathered} x_{1,\: 2}=\frac{-\left(-7\right)\pm\sqrt{\left(-7\right)^2-4\cdot\:3\left(-1\right)}}{2\cdot\:3} \\ x_{1,\: 2}=\frac{-\left(-7\right)\pm\sqrt{61}}{2\cdot\:3} \\ x_1=\frac{-\left(-7\right)+\sqrt{61}}{2\cdot\:3},\: x_2=\frac{-\left(-7\right)-\sqrt{61}}{2\cdot\:3} \\ for\text{ one} \\ x=\frac{-(-7)+\sqrt[]{61}}{2\cdot\: 3}=\frac{7+\sqrt[]{61}}{6} \\ or \\ x=\frac{-(-7)-\sqrt[]{61}}{2\cdot\: 3}=\frac{7-\sqrt[]{61}}{6} \end{gathered}[/tex]answer:
[tex]\begin{gathered} x=\frac{7+\sqrt{61}}{6} \\ or \\ x=\frac{7-\sqrt{61}}{6} \end{gathered}[/tex]Suppose that the funcation p and q are defined as follows
Given the functions p(x) and q(x) defined as:
[tex]\begin{gathered} p(x)=x^2+3 \\ q(x)=\sqrt[]{x+2} \end{gathered}[/tex]We can use the definition of composite functions:
[tex](f\circ g)(x)=f(g(x))[/tex]Then, to calculate (p o q)(2) = p(q(2)), we need to calculate q(2) first:
[tex]q(2)=\sqrt[]{2+2}=\sqrt[]{4}=2[/tex]Using this result on the composition:
[tex]\begin{gathered} (p\circ q)(2)=p(q(2))=p(2)=2^2+3=4+3 \\ \Rightarrow(p\circ q)(2)=7 \end{gathered}[/tex]Now, for (q o p)(2) = q(p(2)), we already calculate p(2) = 7. Then:
[tex]\begin{gathered} (q\circ p)(2)=q(p(2))=q(7)=\sqrt[]{7+2}=\sqrt[]{9} \\ \Rightarrow(q\circ p)(2)=3 \end{gathered}[/tex]Consider the steps to solve the equation. 2/5 ( 1/2 y + 20 ) − 4/5 = 9/20 (2y − 1) Distribute: 1/5 y + 8 − 4/5 = 9/ 10 y − 9/20 What is the next step after using the distributive property? Use the multiplication property of equality to isolate the variable term on one side of the equation. Use the multiplication property of equality to isolate the constant on one side of the equation. Combine the like terms on the right side of the equation. Combine the like terms on the left side of the equation. member to subscribe to my channel michadsen
The initial expression is:
[tex]\frac{2}{5}(\frac{1}{2}y+20)-\frac{4}{5}=\frac{9}{20}(2y-1)_{}[/tex]First we use the distibution propertie so:
[tex]\frac{1}{5}y+8-\frac{4}{5}=\frac{9}{10}y-\frac{9}{10}[/tex]Now we pass all term with y to the right and all constats to the left so:
[tex]\frac{8}{1}-\frac{4}{5}+\frac{9}{10}=\frac{9}{10}y-\frac{1}{5}y[/tex]now we operate so:
[tex]\begin{gathered} \frac{80}{10}-\frac{8}{10}+\frac{9}{10}=\frac{9}{10}y-\frac{2}{10}y \\ \frac{81}{10}=\frac{7}{10}y \end{gathered}[/tex]now we multiply by 10 and divide by 7 so:
[tex]\begin{gathered} \frac{10}{7}\cdot\frac{81}{10}=y \\ \frac{81}{7}=y \end{gathered}[/tex]Show/explain how to solve the formula forbhfinding the area of a triangle, A =2for h. Describe how you can use possibleunits associated with each of thevariables in this equation to guide yourthinking about solving this literalequation.
we need to solve h of the equation so
We do the oppisite operation for example, the 2 dividing is multipliying to the other side
[tex]2\times A=b\times h[/tex]and the same way for b
[tex]\frac{2\times A}{b}=h[/tex]Each of the Five cats and a pet strobe was weighed here are their weights in pounds 15, 9, 9, 11, 9. Find the median And mean weights of these cats if necessary round your answer to the nearest 10th
Hello there. To solve this question, we'll have to remember how to calculate the median and the mean of set of numbers.
Given the weight of the five cats:
15, 9, 9, 11, 9
We start by ordering the numbers:
9, 9, 9, 11, 15
Since this set has an odd number of entries, its median will be the center value:
9.
The mean of a set can be calculated by adding all the values and dividing it by the amount of numbers:
[tex]\frac{9+9+9+11+15}{5}[/tex]Adding the numbers
[tex]\frac{53}{5}[/tex]Calculating the fraction, we get:
[tex]10.6[/tex]This is the mean of the cats weights.
17. An equation for horizontal lines has the form: ___________ and is parallel to the ______ − axis.18. If you were to draw a horizontal line on the x−axis, the equation of the line would be y= 0. Explain why this equation is a logical conclusion?
Question 17:
An equation for horizontal lines has the form:
[tex]y=m[/tex]and is parallel to the x-axis
Question 18:
If you were to draw a horizontal line on the x−axis, the equation of the line would be y= 0. Explain why this equation is a logical conclusion?
Because it will represent the x-axis, all the points lying on the line will have
y-coordinates = 0
describe the transformation relating the graph of its has 1/2 x -3 2 to the graph of its mass of negative equals x squared
The parent function
[tex]f(x)=x^2[/tex]Write an equation for the line parallel to the given line that contains C.C(1,7) y = -3x + 4
Recall that the slope intercept equation of a line is of the form y=mx+b where m is the slope and b is the y intercept. In general, two lines are parallel if they look like this
This translates to the fact the the lines never touch each other. This also means that, in a way, the lines increase (or decrease) at the same rate. This notion of rate of increase/decrease is captured by the fact that if we have lines y=m1x+b1 and y=m2x+b2 they are parallel if they have the same slope. That is
[tex]m_1=m_2[/tex]We are given the line y=-3x+4 (with slope -3 and y intercept 4) and we want to find the equation y=mx+b. Since we want that both lines are parallel, based on our previous analysis, we should have
[tex]m=-3[/tex]So, so far, our equation looks like this
[tex]y=-3x+b[/tex]Now, we want this line to pass through the point (1,7), this means that whenever x=1, we must have y=7. So, we have the following equation
[tex]7=-3\cdot1+b[/tex]If we add 3 on both sides, we get
[tex]b=7+3=10[/tex]So our final result is the equation
[tex]y=-3x+10[/tex]We do not understand how to figure this out when part of the cone is missing.
we have that
the surface area of a truncated solid is equal to
[tex]SA=\pi\cdot\lbrack LR+Lr+R^2+r^2\rbrack[/tex]where
L is the slant heigh --------> L=6 cm
R=8 cm
r=4 cm
substitute
[tex]SA=\pi\cdot\lbrack6\cdot8+6\cdot4+8^2+4^2\rbrack[/tex][tex]\begin{gathered} SA=\pi\cdot\lbrack48+24+64+16\rbrack \\ SA=\pi(152) \\ SA=477.52cm2 \end{gathered}[/tex]Volume & Surface Area, Area of Sectors GH = 11
EXPLANATION
The area of the sector is given by the following relationship:
[tex]Area_{part\text{ of a circle}}=\frac{\text{degrees of the sector}}{360}_{}\cdot\pi\cdot r^2[/tex]Considering that the radius is r=11 and Replacing terms:
[tex]\text{Area}_{}=\frac{64}{360}\cdot\pi\cdot(11)^2[/tex]Computing the power and simplifying the fraction:
[tex]\text{Area}=\frac{8}{45}\cdot\pi\cdot121[/tex]Multiplying numbers:
[tex]\text{Area}=\frac{968}{45}\cdot\pi=21.51\cdot\pi=67.57\text{units}^2[/tex]The area of the sector is 67.57 squared units
What is an equation in point-slope form of the line shown?
we know that
The equation in point slope form is equal to
y-y1=m(x-x1)
step 1
Find the slope
we have the points (-4,1) and (4,-3)
m=(-3-1)/(4+4)
m=-4/8
m=-1/2
step 2
Find the equation
we have
m=-1/2
(x1,y1)=(-4,1)
substitute
y-1=-(1/2)(x+4) ------> equation in ponit slope form
with the point (4,-3)
the equation is
y+3=-(1/2)(x-4)Carla LaFong worked a 52 hr work week last week. She is paid 1 1 2 times her regular hourly rate for all hours over a 40 hr week. Her pay last week was $840. What is her hourly rate?
If she worked a 52 hours last week and paid [tex]1\frac{1}{2}[/tex] times her regular hourly rate for all hours over a 40 hours week, her last week pay was $840, then the hourly rate is $14.48
Total hours that she worked = 52 hours
Total payment of last week = $840
She paid [tex]1\frac{1}{2}[/tex] times her regular hourly rate for all hours over a 40 hours week.
Number of overtime hours = 52 - 40
= 12 hours
If the hourly rate is x then the over time pay is 1.5x
Then the equation will be
40x + 12×1.5x = 840
Solve the equation
40x + 18x = 840
58x = 840
x = 840/58
x = $14.48
Hence, if she worked a 52 hours work week last week and paid [tex]1\frac{1}{2}[/tex] times her regular hourly rate for all hours over a 40 hours week, her pay last week was $840, then the hourly rate is $14.48
Learn more about hourly rate here
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Name Run Sohwire intintie Algebra 2 Graphing Linear Inequalities Sketch the praph of euchlinear inecuality. Date 3/3/202) 1 x z-2x - 2 2) y sal 3) * 4) y < x-2
Explanation:
To graph the inequality, we first need to graph the line that separates the regions, so we will graph first:
y = x - 2
To graph the line, we need to give values to x and calculate the value of y. So:
If x = 0, then:
y = x - 2
y = 0 - 2
y = -2
If x = 2, then:
y = x - 2
y = 2 - 2
y = 0
Graph
So, we will use the points (0, -2) and (2, 0) to graph the region as:
Now, we can verify that the yellow region is the correct region because a point like (4, 0) that belongs to the region satisfies the inequality.
y < x - 2
0 < 4 - 2
0 < 2
You are preparing for a party and need to know how many cans of soda to buy. You know that you want four cans, and you estimate that each of your friends will drink three cans. You set up an arithmetic equation to calculate the number of cans of soda for n friends, c=4+(n-1)⋅3. Match each term in the sequence with the correct number of cans.
Solution:
Given the arithmetic equation below
[tex]\begin{gathered} c=4+(n-1)\cdot3 \\ Where \\ n\text{ is the of friends \lparen term\rparen} \\ c\text{ is the number of cans of soda} \end{gathered}[/tex]1) For term 6, i.e. n = 6,
Substitute 6 for n into the equation above
[tex]\begin{gathered} c=4+\left(6-1\right)\cdot \:3 \\ c=4+(5)(3)=4+15=19 \\ c=19 \end{gathered}[/tex]Hence, answer is b (19 cans)
2) For term 4, i.e. n = 4,
Substitute 4 for n into the equation above
[tex]\begin{gathered} c=4+\left(4-1\right)\cdot \:3 \\ c=4+(3)(3=4+9=13 \\ c=13 \end{gathered}[/tex]Hence, the answer is d (13 cans)
3) For term 2, i.e. n = 2,
Substitute 2 for n into the equation above
[tex]\begin{gathered} c=4+\left(2-1\right)\cdot \:3 \\ c=4+(1)(3)=4+3=7 \\ c=7 \end{gathered}[/tex]Hence, the answer is a (7 cans)
4) For term 1, i.e. n = 1
Substitute 1 for n into the equation above
[tex]\begin{gathered} c=4+\left(1-1\right)\cdot \:3 \\ c=4+(0)(3)=4+0=4 \\ c=4 \end{gathered}[/tex]Hence, the answer is c (4 cans)
Help with homework lesson for review to study for test.
We have the expression:
[tex]\frac{y^2-9}{y^2+y-12}[/tex]The restricted values of y are those values that make the denominator 0. This is the same as solving the equation:
[tex]y^2+y-12=0[/tex]This term can be factorized as:
[tex]\begin{gathered} y^2+y-12=(y+4)(y-3) \\ \Rightarrow(y+4)(y-3)=0 \end{gathered}[/tex]This is true for y = -4 and y = 3. So the restricted values for y are:
[tex]y\ne\mleft\lbrace-4,3\mright\rbrace[/tex]A customer at a pet store orders for "b" bags of birdseed and "m" bags of millet. If a bag of birdseed costs $4.09 and a bag of millet costs $26.00, find the expression representing the cost of the customer's order.4.09b + 26m30.09(b + m)30.09*b*m30.09*b/m
The number of bags of birdseed is "b" and each costs 4.09, then the cost of the "b" birdseed is 4.09b.
Next, the bags of millet is "m" and each cost 26, then the cost for "m" bags of millet is 26m.
Finally, the total of the order is obtained adding both:
[tex]4.09b+26m[/tex]Hence the answer is the first option, 4.09b+26m
The temperature is 60F if the temperature will decrease by 3F each hour let H be the number of hours when will the temperature be below 32F
The temperature of the given environment starts at 60ºF and decreases at a constant rate of 3ºF/h. We can write a linear equation for the room temperature as
[tex]T=-3H+60[/tex]Where H is the number of hours that passed. We want to know when the temperature will be below 32ºF, in another words
[tex]T<32[/tex]If we substitute the expression for the temperature on the inequality, we're going to have
[tex]-3H+60<32[/tex]Solving for H:
[tex]\begin{gathered} -3H+60<32 \\ -3H<32-60 \\ -3H<-28 \\ 3H>28 \\ H>\frac{28}{3} \end{gathered}[/tex]Triangle LMN ~ Triangle PON. What is the value of x?
SOLUTION:
Step 1 :
In this question, we can see clearly that:
[tex]\text{Triangle LMN }\approx\text{ Triangle PON}[/tex]Step 2:
From the diagram, we can see that :
[tex]\frac{MN}{LM}\text{ = }\frac{ON}{OP}[/tex]where MN = x,
LM = 42,
ON = 12,
OP = 14.
Step 3:
Substituting the values, we have that:
[tex]\begin{gathered} \frac{x}{42}\text{ = }\frac{12}{14} \\ \text{cross - multiply, we have that:} \\ 14\text{ x = 12 ( 42 )} \\ \text{Divide both sides by 14 , we have that:} \end{gathered}[/tex][tex]\begin{gathered} x\text{ = }\frac{12(\text{ 42 )}}{14} \\ x\text{ = 12 x 3} \\ \text{x = 36 - OPTION D} \end{gathered}[/tex]CONCLUSION :
The value of x = 36 -- OPTION D .
Help there are 3 more parts to this one question
Given the functions:
f(x) = 8x - 6
g(x) = (x + 6)/8
The expression (g ∘ f)(x) means replacing the "x" value in the g(x) function with the f(x) value.
Therefore, we have:
[tex]\begin{gathered} g(x)=\frac{x+6}{8} \\ \text{Substitute x with f(x).} \\ g(x)=\frac{(8x-6)+6}{8} \\ \text{Simplify the function.} \\ g(x)=\frac{8x}{8} \\ g(x)=x \end{gathered}[/tex]9. Choose the equivalent fraction for 0.625
2(3x-7)+4(3x+2)=6(5x+9)+3
We will simplify each side at first then, solve to find x
[tex]\begin{gathered} 2(3x-7)+4(3x+2)=6(5x+9)+3 \\ 2(3x)-2(7)+4(3x)+4(2)=6(5x)+6(9)+3 \end{gathered}[/tex]Now multiply and add the like terms
[tex]\begin{gathered} 6x-14+12x+8=30x+54+3 \\ (6x+12x)+(-14+8)=30x+(54+3) \end{gathered}[/tex]Add 6 from both sides
[tex]\begin{gathered} 18x+6-6=30x+57+6 \\ 18x=30x+63 \end{gathered}[/tex]Subtract 30x from both sides
[tex]18x-30x=30x-30x+63[/tex][tex]-12x=63[/tex]Divide both sides by -12 to find x
[tex]\begin{gathered} \frac{-12x}{-12}=\frac{63}{-12} \\ x=-5.25 \end{gathered}[/tex]The value of x is -5.25
on a scale drawing a building is 5 1/2 in. tall. if the scale of the drawing is 1 in. : 8 ft how tall is the building
Since each inch on the drawing is equal to 8 ft on the real life, then multiply the size of the building in the drawing times 8 to find its actual size:
[tex]\begin{gathered} 5\frac{1}{2}\times8=5\times8+\frac{1}{2}\times8 \\ =40+\frac{8}{2} \\ =40+4 \\ =44 \end{gathered}[/tex]Therefore, the building is 44 feet tall.
1. Quadrilateral ZYXW has vertices at the following ordered pairs: Z(1,0), Y(6, -3), X(1, -6), and W(-4, -3). What type of quadrilateral is ZYXW?
1. From the picture, it can be seen that quadrilateral ZYXW is a rhombus (all sides are equal and opposite sides are parallel)
4.Identify each sequence as arithmetic or geometric AND find the common ratio or difference: -6,-3,0,3,6,…A. Arithmetic or GeometricB. Common ratio/rate: 5,20,80,320,1280,…A. Arithmetic or GeometricB. Common rate/ratio:
In order to check if the sequence is arithmetic, we can subtract each term by the term before. If result is always the same, the sequence is arithmetic and the difference between terms is the common rate.
The geometric sequence is similar, but we need to divide by the term before instead of subtracting.
So we have:
[tex]\begin{gathered} A\text{.} \\ -3-(-6)=-3+6=3 \\ 0-(-3)=0+3=3 \\ 3-0=3 \\ 6-3=3 \end{gathered}[/tex]So the first sequence is arithmetic, with the common rate equal to 3.
[tex]\begin{gathered} B\text{.} \\ 20-5=15 \\ 80-20=60 \\ 320-80=240 \\ \ldots \end{gathered}[/tex]The differences are not the same, so let's try dividing them now:
[tex]\begin{gathered} \frac{20}{5}=4 \\ \frac{80}{20}=4 \\ \frac{320}{80}=4 \\ \frac{1280}{320}=4 \end{gathered}[/tex]So the second sequence is geometric, and the common ratio is equal to 4.
could you help me out
we have that
In the right triangle of the figure
cos(x)=5/9 ------> adjacent side divided by the hypotenuse
so
using a calculator
x=cos^-1(5/9)
x=56.25 degrees
therefore
answer is option Fa forest covers a area of 3100 km^2. suppose that each year this area decreases by 3% . what will the area be after 7 years
Use f(x) and g(x) to answer the question. f(x)=x−1g(x)=x2+3x−9 What is the product (f⋅g)(x)?
Answer:
x³ + 2x² - 12x + 9
Explanation:
The functions are
f(x) = x - 1
g(x) = x² + 3x - 9
Then, the product (f·g)(x) = f(x)g(x), so replacing the expressions above, we get
(f·g)(x) = (x - 1)(x² + 3x - 9)
(f·g)(x) = x(x²) + x(3x) + x(-9) - 1(x²) - 1(3x) - 1(-9)
(f·g)(x) = x³ + 3x² - 9x - x² - 3x + 9
(f·g)(x) = x³ + 2x² - 12x + 9
Therefore, the answer is
x³ + 2x² - 12x + 9
In triangle ABC, with right angle at C, if c=6 and a=4, the CosA=
ANSWER
cos A = √20/6 ≈ 0.75
EXPLANATION
Triangle ABC is:
Since this is a right triangle we can use the trigonometric ratios to find cosA:
[tex]\cos A=\frac{\text{adjacent side}}{hypotenuse}[/tex]the hypotenuse of this triangle is side c, and the adjacent side is side b. We don't have side b, but we have two sides and again, as this is a right triangle, we can use the Pythagorean theorem to find the missing side:
[tex]\begin{gathered} c^2=a^2+b^2 \\ b=\sqrt[]{c^2-a^2} \\ b=\sqrt[]{6^2-4^2} \\ b=\sqrt[]{36-16} \\ b=\sqrt[]{20} \end{gathered}[/tex]The cosine of A is then:
[tex]\cos A=\frac{b}{c}=\frac{\sqrt[]{20}}{6}[/tex]Rounded to the nearest hundredth:
[tex]\cos A\approx0.75[/tex]Problem 218. A family orders 3 large pizzas. The teenager in the familyeats 1/4 of the family's order. How much pizza does he eat?
According to the given data we have the following:
family orders 3 large pizzas
The teenager in the family eats 1/4 of the family's order
Therefore, in order to calculate the amount of pizza he eat we would make the following calculation:
amount of pizza he eat=quantity of pizza the teenage eat*total pizzas
amount of pizza he eat=1/4*3
amount of pizza he eat=3/4
Therefore he will eat 3/4 of a large pizza.