Answer:
[tex]-\frac{1}{3}[/tex]Explanation:
Here, we want to get the gradient of the line L3
The equation of a straight line can be expressed as:
[tex]y\text{ = mx + b}[/tex]where m is the gradient (slope) and b is the y-intercept (the y-value when x = 0)
Now,let us write the equation of the first line in the slope-intercept form
Mathematically, we have this as:
[tex]\begin{gathered} 3x-y\text{ + 2 = 0} \\ y\text{ = 3x + 2} \end{gathered}[/tex]The gradient of the first line is 3
Now,let us get the gradient of the second line L3
Mathematically, when two lines ae perpendicular, the product of their gradients (slopes) equal -1
Thus, we have it that:
[tex]\begin{gathered} m_1\text{ }\times m_2\text{ = -1} \\ 3\text{ }\times m_2\text{ = -1} \\ m_2\text{ = -}\frac{1}{3} \end{gathered}[/tex]A house addition is in the shape of a semicircle (a half-circle) with a radius of 9 ft. What is itsarea?
We find its area as follows:
[tex]A=\frac{1}{2}\pi r^2[/tex][This is the equation for the area of a circle divided by 2] Now, we replace the radius:
[tex]A=\frac{1}{2}\pi(9)^2\Rightarrow A=\frac{81}{2}\pi\Rightarrow A\approx127.23[/tex]So, the area of the semi-circle is approximately 127.23 squared feet.
Type the correct answer in each box. Use numerals instead of words. If necessary, use/ for the fraction bar(s).The equation of a circle is given.2+ y²+6x+10y+18=0Determine the center and radius of the circle.) and the radius of the circle isunits.The center of the circle is at (ResetNext
ANSWER
[tex]\begin{gathered} center=(-3,-5) \\ r=4 \end{gathered}[/tex]EXPLANATION
Given;
[tex]x^2+y^2+6x+10y+18=0[/tex]The standard equation of circle of a circle centered at (h,k) with radius r is;
[tex](x-h)^2+(y-k)^2=r^2[/tex]Re-write the given equation in the standard form, we have;
[tex]\begin{gathered} x^{2}+y^{2}+6x+10y+18=0 \\ x^{2}-6x+(\frac{6}{2})^{2}+y^{2}+10y+(\frac{10}{2})^{2}=-18+9+25 \\ (x-3)^2+(y-5)^2=4^2 \end{gathered}[/tex]Hence, h=-3, k=-5, radius is 4
?What is the factored form of x6 - 9?O(x + 3)(x – 3)(x5 + 3)(x – 3)o(x3 + 3)(x2 - 3)o(x3 + 3)(x3 - 3)+DONE
Answer:
[tex]\lparen x^3+3)\left(x^3-3\right)[/tex]Explanation:
Given the expression
[tex]x^6-9[/tex]It can be rewritten as
[tex]x^{2\cdot3}-3^2=\lparen x^3)^2-3^2[/tex]Use the formula
[tex]a^2-b^2=\left(a+b\right)\left(a-b\right)[/tex]to get
[tex]\lparen x^3+3)\left(x^3-3\right)[/tex]which is the factored form of the given expression.
Answer:
It's Option D
Step-by-step explanation:
edge
a chemical company makes two brands of antifreeze. the first brand is 45% pure antifreeze and the second brand is 70% pure antifreeze. in order to obtain 170 gallon of a mixture that contains 65% pure antifreeze how many gallons of each brand of antifreeze mudt be used
Answer:
The first brand is 34 gallons
The second brand is 136 gallons
Explanation:
Let x represent the first brand, and
y represent the second brand
The total number of gallons of mixture to be obtained is 170, so
x + y = 170 .................................................................................(1)
And
45% of x + 70% of y = 65% of (x + y)
0.45x + 0.7y = 0.65(x + y)
0.45x - 0.65x = 0.65y - 0.7y
0.2x = 0.05y
Divide both sides by 0.05
4x = y ...........................................................................................(2)
Solving (1) and (2) simultaneously
Using (2) in (1)
x + 4x = 170
5x = 170
Divide both sides by 5
x = 170/5 = 34
Put x = 34 in (2)
4(34) = y
y = 136
What plus Ten equals thirty two
What plus Ten equals thirty two is equivalent to
x + 10 = 32
10 is adding on the left, then it will subtract on the right
x = 32 - 10
x = 22
Hi I just need a quick and easy explanation for this question I’m having a bit of trouble
Using the properties of parallel lines and transversal we can calculate the value of ∠5 as 64° .
The two lines are parallel to one another and the intersecting line is the transversal to the parallel lines.
the two given angles whose values are given are
∠4 = 106-y
∠6 = 3y-10
Now we can clearly see that these two angles ∠4 and ∠6 are co-interior angles.
We know that co-interior angles are supplementary.
Hence ∠4 + ∠6 = 180°
now we will put the values in the equation:
or , 106-y + 3y-10 = 180 °
or , 96 + 2y = 180 °
or, 2y = 84 °
or, y = 42°
Therefore ∠4 = 106 - y = 106° - 42° = 64°
Now from the properties of parallel lines we can see that ∠4 and ∠5 are alternate angles.
Hence ∠4 = ∠5 = 64°
therefore the value of ∠5 is 64° .
to learn more about parallel lines visit:
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how does a to the 4 b to -5 over c to -3 d to the 6th get simplified?
Given the expression
[tex]\frac{a^4b^{-5}}{c^{-3}d^6}[/tex]To simplify the expression above, we convert all negative indices to positive indices
Applying the rule of indices
[tex]a^{-x}=\frac{1}{a^x}[/tex]Applying the rule to the given expression gives
[tex]\begin{gathered} \text{Where b}^{-5}=\frac{1}{b^5}\text{ and} \\ c^{-3}=\frac{1}{c^3} \end{gathered}[/tex]Substitute the above deduction into the given expression
[tex]\begin{gathered} \frac{a^4b^{-5}}{c^{-3}d^6}=a^4\times\frac{1}{b^5}\times\frac{1}{\frac{1}{c^3}}\times\frac{1}{d^6} \\ \text{Where }\frac{1}{\frac{1}{c^3}}=c^3 \\ =a^4\times\frac{1}{b^5}\times\frac{1}{\frac{1}{c^3}}\times\frac{1}{d^6}=a^4\times\frac{1}{b^5}\times c^3\times\frac{1}{d^6} \\ =\frac{a^4c^3}{b^5d^6} \\ \frac{a^4b^{-5}}{c^{-3}d^6}=\frac{a^4c^3}{b^5d^6} \end{gathered}[/tex]Hence, the simplified form is
[tex]\frac{a^4c^3}{b^5d^6}[/tex]change these to decimals. 7%, 200%, .3%
the 7% means
7/100 = 0.07
[tex]7\text{ \% =}\frac{7}{100}=0.07[/tex]200 % means
200/100 = 2
and 0.3 % means
0.3/100 = 0.003
complete the function table for the given domain and plot the points on the graph f(x)=2^x-7x. 0. 1. 2. 3. 4. f(x) . . . . graph
we have the following:
[tex]f(x)=2^x-7[/tex]replacing:
[tex]\begin{gathered} f(0)=2^0-7=1-7=-6;(0,-6)^{} \\ f\mleft(1\mright)=2^1-7=2-7=-5;(1,-5) \\ f\mleft(2\mright)=2^2-7=4-7=-3;(2,-3) \\ f(3)=2^3-7=8-7=1;(3,1) \\ f(4)=2^4-7=16-7=9;(4,9) \end{gathered}[/tex]x 0 1 2 3 4
f(x) -6 -5 -3 1 9
Edward deposited 9,000 into a savings account 2years ago tthe simple interest is 2% how much money did edward earn in intrest
We just need to use the simple interest formula:
[tex]I=PV\cdot r\cdot t[/tex]Where:
I = Interest
PV = Principal or initial investment = 9000
r = interest rate = 0.02
t = time = 2
[tex]\begin{gathered} I=9000\times0.02\times2 \\ I=360 \end{gathered}[/tex]$360
For the data shown in the plot below identify a point apart from the main cluster
(8, 7) or (8.5, 7.5)
See explanation below
Explanation:From the graph, there are two points away from the main clusters.
This is because their distance compared to other points is far apart. The main cluster is where most of the points are located
The two points are (x, y): (8, 7) and (8.5, 7.5)
In the absence of options, you can pick any of the points as the point that is apart from the cluster.
identify the correct trigonometry formula to use to solve for the given anglea. sin-¹(1.41)b. cos-¹(1.41)c. sin-¹(.71)d. tan-¹(.71)
The definition of arctan is opposit side by adjesent side.
[tex]\begin{gathered} \text{Angle}=tan^{-1}(\frac{Oppos\text{ side}}{\text{Adjesent side}}) \\ =\tan ^{-1}(\frac{34}{48}) \\ =\tan ^{-1}(0.71) \end{gathered}[/tex]Thus, the correct option is option d.
I'm confused about how to solve this using the special right triangles method
ANSWER:
[tex]x=4\sqrt[]{2}[/tex]STEP-BY-STEP EXPLANATION:
We can calculate the value of x, by means of the trigonometric function sine
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \text{opposite = }4 \\ \theta\text{ =60\degree} \\ \text{hypotenuse = x} \end{gathered}[/tex]Replacing:
[tex]\begin{gathered} \sin 45=\frac{4}{x} \\ x=\frac{4}{\sin45} \\ \sin 45=\frac{\sqrt[]{2}}{2} \\ x=\frac{4}{\frac{\sqrt[]{2}}{2}} \\ x=\frac{8}{\sqrt[]{2}}\cdot\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ x=\frac{8\sqrt[]{2}}{2} \\ x=4\sqrt[]{2} \end{gathered}[/tex]One sample t for means You want to know if the average customer rating fro your store is about a 7.0 on a 1-10 scale. Your collect a sample of 100 customers. Their average rating was 7.3, with a standard deviation of 2.0.
Given:
A sample of 100 customers.
CWhich of the following is the inverse of F(x)=2x+3?COAa 4520-19B.0 с.OD.103765PREVIOUSG Search or type URI(3,0)(15,0)3YSUBMIT
We have to find the inverse of the function f(x) = 2x + 3.
We can find the inverse function as:
[tex]\begin{gathered} f(f^{-1}(x))=x \\ 2f^{-1}(x)+3=x \\ 2f^{-1}(x)=x-3 \\ f^{-1}(x)=\frac{1}{2}x-\frac{3}{2} \end{gathered}[/tex]From the options we can see that the slope has to be positive, so we can discard optiosn B and C.
Then, we can check option A:
- It has a y-intercept of -1.5, which is equal to -3/2.
- The x-intercept is (3,0), what indicates that it increases 0.5 units of y per unit increase in x. This corresponds to a slope of 0.5 or 1/2.
Then, as both characteristics match with the equation of the inverse, the right representation is option A.
Answer:
The inverse is f^-1(x) = 1/2*x - 3/2 [Option A]
The school band brought cheese and pepperoni pizzas in ratio represented in the tape diagram for their end of year party.
ANSWER
2 pepperoni pizzas
EXPLANATION
From the tape diagram, the ratio of cheese pizzas to pepperoni pizzas is:
3 : 1.
They bought 6 cheese pizzas.
Let the number of pepperoni pizzas be x.
So, by comparison, we have that:
3 : 1 = 6 : x
or
[tex]\begin{gathered} \frac{3}{1}\text{ = }\frac{6}{x} \\ \text{Cross multiply to find x:} \\ 3\cdot\text{ x = 6 }\cdot\text{ 1} \\ \text{Divide through by 3:} \\ x\text{ = }\frac{6}{3} \\ x\text{ = 2} \end{gathered}[/tex]Therefore, they bought 2 pepperoni pizzas.
Dan is a software salesman. His base salary is $2200, and he makes an additional $120 for every copy of History is Fun he sells.Let P represent his total pay (in dollars), and let N represent the number of copies of History is Fun he sells. Write an equation relating P to N. Then use this equation to find his total pay if he sells 23 copies of History is Fun.
We will have the following:
The equation in this case is:
[tex]P=120N+2200[/tex]So, if he sells 23 copies, he will make:
[tex]P(23)=120(23)+2200\Rightarrow P(23)=4960[/tex]So, he would make $4960.
A car company charges $42.50 per day to rent a car in 10 since for every mile driven Lydia wants to rent a car knowing that she plans to drive 225 miles and she has at most a $150 to spend
Explanation:
d: number of days.
m: number of miles.
The total cost of the car 'y' is:
[tex]y=42.5d+0.1m[/tex]Lydia plans to drive 225 miles, this is m = 225. And she has $150 to spend, so we have to solve y ≤ 150.
The inequality to solve is:
[tex]\begin{gathered} y\le150 \\ 42.5d+0.1\cdot225\le150 \\ 42.5d+22.5\le150 \end{gathered}[/tex]Solving the inequality:
[tex]\begin{gathered} 42.5d+22.5\le150 \\ 42.5d\le150-22.5 \\ 42.5d\le127.5 \\ d\le\frac{127.5}{42.5} \\ d\le3 \end{gathered}[/tex]Lydia can afford 3 days at most.
Answers:
• Inequality: ,42.5d + 22.5 ≤ 150
,• d ≤ 3
wich statement explain how Andy could prove what kind of quadrilateral this is ?
The first step is to locate the points to find what kind of quadrilateral this is.
The next step is to find the lengths of the diagonals, if both have the same length then the quadrilateral is a rectangle, if the don't the quadrilateral is a parallelogram.
When looking at the picture is easy to determine that the quadrilateral is a parallelogram, but the statement that could prove what kind of quadrilateral this is is C. Find the lengths of the diagonals to show that the quadrilateral is a parallelogram.
solve y=f(x) for x. then find the inputs when the output is -3
Answer:
Given that,
[tex]f(x)=-7x-2[/tex]To find the inputs when the output is -3
that is, when f(x)=-3, to find the value of x
Put f(x)=-3 in the above equation we get,
[tex]-3=-7x-2[/tex][tex]-7x=-3+2[/tex][tex]\begin{gathered} -7x=-1 \\ x=\frac{1}{7} \end{gathered}[/tex]Answer is: x=1/7.
7-Which beans are the better deal? O Kidney Beans $1.18 per Ib Lima Beans $2.13 for 2 lbs 7b-What is the Unit Price for the better deal? Round to the nearest hundredth) Put your answer in the form 0.00 07 00, so if answer is 43 cents, its 043 or 43, if there is a dollar amount ke 1.50, do not add zeros in front) Your answer
Kidney $1.18 per 500g
Lima. $ 2.13. Per 2 lbs= 1000g
Then
Kidney = 1.18 x 1 lb
Lima = 2.13/2= 1.065 x 1 lb
So ANSWER IS :Better deal Is LIMA BEANS
Part 7b
UNIT PRICE for better deal is
LIMA BEANS , At $1.065 per lb
which equation doesn't represent a linear function? [tex]a. \: y = \frac{1}{2}x \: + 2[/tex][tex]b . \: y = {x}^{2} \\ c . \: y = 2x \\ d. \: y = x - 2[/tex]
The general equation for linear equation is,
[tex]y=mx+b[/tex]The equation y = x^2, consist of power term on the variable x. So this equation does not follow the linear equation and is a quadratic equation.
Thus, equation y = x^2 is not a linear function. Option B is correct answer.
13. You have $19.50 to buy subs for a party. Each sub costs $5.10. Estimate how many subs you can buy. Is your estimate too little or too much?
Let N be the number of subs, then we can write the following relationship:
[tex]5.10\cdot N=19.5[/tex]That is, this equality gives us the number of subs we can buy. If we move 5.10 to the right hand side, we have
[tex]\begin{gathered} N=\frac{19.50}{5.10} \\ N=3.82 \end{gathered}[/tex]this means that we can buy 4 subs approximately.
What is the value of t? 76 T
Those are vertical angles, which are two non-adjacent angles formed by intersecting two lines. The intersection forms two pair of vertical angles. So:
[tex]m\angle t=76[/tex]Give the slope and the Y intercept of the line represented by y-7=-7x
Answer:
• m=-7
,• b=7
Explanation:
Given the line:
[tex]y-7=-7x[/tex]To determine the slope and y-intercept, first, express the line in the slope-intercept form (y=mx+b).
[tex]\implies y=-7x+7[/tex]You can then compare:
• Slope, m = -7
,• y-intercept, b =7
The slope of the line is -7 and the y-intercept is 7.
The circle is inscribed in the square. Find the area of the shaded region.
We can solve this by calculating the area of the square and subtracting the area of the inscribed circle. The area of the square is:
[tex]Square=10\cdot10=100cm^2[/tex]The formula for the area of a circle is:
[tex]A=\pi r^2[/tex]The radius of the inscribed circle is half the length of the side of the square, then, the radius is r = 5 cm
[tex]Circle=\pi5^2=25\pi\text{ }cm^2[/tex]Now, we rest:
[tex]Square-Circle=100cm^2-25\pi cm^2\approx21.46cm^2[/tex]The answer is 21.46cm²
For which graph is the parent function y = x2
Answer:
Answer d
Step-by-step explanation:
Make sure to get another answer + can you make sure if there is answer choices, please and thx
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The problem is:The area of a square picture frame is 55 square inches. Find the length of one side of the frame. explain.Part A. Part B To the nearest whole inch. To the nearest 10th of an inch
Part A
area = 55 in²
The area of a square is given by:
area = side x side
So
55 in² = side x side
55 in² = side²
Taking the square root of both sides of the equation we get:
√55 in² = side
7 in = side
Part B
side = 7.4 in
Are the pair of lines y = 1/3x - 1 and y = 3x parallel, perpendicular, or neither?
A line with slope m and y-intercept b has the following slope-intercept form equation:
[tex]y=mx+b[/tex]If two lines have the same slope, they are parallel. If they have slopes that are the negative reciprocal of each other, then they are perpendicular.
If none of the above cases happen, then they are neither parallel nor perpendicular.
The line y = (1/3)x - 1 has slope 1/3.
The line y = 3x has slope 3.
As we see, the slopes are different, so the lines are not parallel. Also, the negative reciprocal of 3 is -1/3, not 1/3.
Therefore, the given lines are neither parallel nor perpendicular.
Solve the following quadratic equation using the quadratic formula in the picture: Problem: -3y^2 - 2y - 6 = 0
The given equation is,
[tex]-3y^2-2y-6=0[/tex]Here, a = -3, b = -2, c = -6. Therefore, y can be calculated as,
[tex]\begin{gathered} y=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}=\frac{2\pm\sqrt[]{4-(4)(-3)(-6)}}{-6}=-\frac{1\pm\sqrt[]{-68}}{3} \\ =\frac{-1+\sqrt[]{68}}{3},\frac{-1-\sqrt[]{68}}{3} \end{gathered}[/tex]