Answer:
$2950
Step-by-step explanation:
Add together the following three items:
Materials: $2000 plus 15%, or 1.15($2000), or $2300
Labor: $500
Equipment Rental: $150
Total: $2300 + $500 + $150 = $2950
A jar has 15 marbles: 4 are green, 6 are red, and 5 are yellow. What is the probability that we will get a red marble or the green marble?
2/3
There are 4 green marbles and 6 red marbles, making 10 green or red marbles. The probability of drawing a red or a green marble is then 10/15 total marbles, which can be simplified to 2/3 by dividing the numerator and denominator each by 5.
Write one sine and one cosine equation for each graph below.
The numbers on the x-axis are -2π, -π, π and 2π.
The numbers on the y-axis are 2, 1, -1, and -2.
Explain.
Answer:
Q13. y = sin(2x – π/2); y = - 2cos2x
Q14. y = 2sin2x -1; y = -2cos(2x – π/2) -1
Step-by-step explanation:
Question 13
(A) Sine function
y = a sin[b(x - h)] + k
y = a sin(bx - bh) + k; bh = phase shift
(1) Amp = 1; a = 1
(2) The graph is symmetrical about the x-axis. k = 0.
(3) Per = π. b = 2
(4) Phase shift = π/2.
2h =π/2
h = π/4
The equation is
y = sin[2(x – π/4)} or
y = sin(2x – π/2)
B. Cosine function
y = a cos[b(x - h)] + k
y = a cos(bx - bh) + k; bh = phase shift
(1) Amp = 1; a = 1
(2) The graph is symmetrical about the x-axis. k = 0.
(3) Per = π. b = 2
(4) Reflected across x-axis, y ⟶ -y
The equation is y = - 2cos2x
Question 14
(A) Sine function
(1) Amp = 2; a = 2
(2) Shifted down 1; k = -1
(3) Per = π; b = 2
(4) Phase shift = 0; h = 0
The equation is y = 2sin2x -1
(B) Cosine function
a = 2, b = -1; b = 2
Phase shift = π/2; h = π/4
The equation is
y = -2cos[2(x – π/4)] – 1 or
y = -2cos(2x – π/2) - 1
Help!
Use the given conditions to write an equation for the line in point-slope form.
Passing through (-5, -7) and (-8, -6)
A) y− 7 = −13(x−5) or y −6 = −13(x−8)
B) y+7= −13(x+8) or y+6 = −13(x+5)
C) y+7 = −13(x+5) or y+6 = −13(x+8)
D) y+7 = −13(x+5) or y +6 = −13(x+7)
[tex]\bf (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-6}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-6-(-7)}{-8-(-5)}\implies \cfrac{-6+7}{-8+5}\implies \cfrac{1}{-3}\implies -\cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-7)=-\cfrac{1}{3}[x-(-5)]\implies y+7=-\cfrac{1}{3}(x+5)[/tex]
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_2=m(x-x_2) \\\\ \cline{1-1} \end{array}\implies y-(-6)=-\cfrac{1}{3}[x-(-8)]\implies y+6=-\cfrac{1}{3}(x+8)[/tex]
The image shows a geometric representation of the function f(x) = x^2 + 2x + 3 written in standard form. What is this function written in vertex form?
f(x) = (x + 2)^2 + 3
f(x) = (x^ + 2x)^2 + 3
f(x) = (x + 1)^2 + 2
f(x) = (x + 3)^2 + 2x
Answer:
f(x) = (x + 1)² + 2 in vertex form ⇒ 3rd answer
Step-by-step explanation:
* Lets revise how to find the vertex form the standard form
- Standard form ⇒ x² + bx + c, where a , b , c are constant
- Vertex form ⇒(x - h)² + k, where h , k are constant and (h , k) is the
vertex point (minimum or maximum) of the function
- At first we must find h and k
- By equating the two forms we can find the value of h and k
* Lets solve the problem
∵ f(x) = x² + 2x + 3 ⇒ standard form
∵ f(x) = (x - h)² + k ⇒ vertex form
- Put them equal each other
∴ x² + 2x + 3 = (x - h)² + k ⇒ open the bracket power 2
∴ x² + 2x + 3 = x² - 2hx + h² + k
- Now compare the like terms in both sides
∵ 2x = -2hx ⇒ cancel x from both sides
∴ 2 = -2h ⇒ divide both sides by -2
∴ -1 = h
∴ The value of h is -1
∵ 3 = h² + k
- Substitute the value of h
∴ 3 = (-1)² + k
∴ 3 = 1 + k ⇒ subtract 1 from both sides
∴ 2 = k
∴ The value of k = 2
- Lets substitute the value of h and k in the vertex form
∴ f(x) = (x - -1)² + 2
∴ f(x) = (x + 1)² + 2
* f(x) = (x + 1)² + 2 in vertex form
Evaluate the line integral c f · dr, where c is given by the vector function r(t). f(x, y) = xy i + 6y2 j r(t) = 14t4 i + t6 j, 0 ≤ t ≤ 1
[tex]\vec r(t)=14t^4\,\vec\imath+t^6\,\vec\jmath[/tex]
[tex]\mathrm d\vec r=(56t^3\,\vec\imath+6t^5\,\vec\jmath)\,\mathrm dt[/tex]
[tex]\vec f(x,y)=xy\,\vec\imath+6y^2\,\vec\jmath\implies\vec f(x(t),y(t))=14t^{10}\,\vec\imath+6t^{12}\,\vec\jmath[/tex]
Then the line integral is
[tex]\displaystyle\int_C\vec f\cdot\mathrm d\vec r=\int_0^1(14t^{10}\,\vec\imath+6t^{12}\,\vec\jmath)\cdot(56t^3\,\vec\imath+6t^5\,\vec\jmath)\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^1(36t^{17}+784t^{13})\,\mathrm dt=\boxed{58}[/tex]
The line integral c f dot dr for the given parameters can be calculated by substituting values of functions r(t) and f(x, y) into the line integral, then integrating over t from 0 to 1.
Explanation:To solve this problem, we start by writing the vector valued function r(t) and the vector field f(x, y) in component form. Given that r(t) = 14t4i + t6j and f(x, y) = xyi + 6y2j, the line integral c f dot dr becomes a definite interval where we integrate over t from 0 to 1.
In this case, we're essentially finding the work done by the vector field f as a particle moves along the path described by r(t). To calculate this, we need to find dr/dt which in our case evaluates to 56t3i + 6t5j.
Subsequent substitution of x = 14t4 and y = t6 into f will provide a new vector ft for f dot dr. Now we can find f dot dr by multiplying corresponding components of ft and dr/dt, add them up, and then integrate over t from 0 to 1.
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The amount of a sample remaining after t days is given by the equation p(t)=A(1/2)^t/h, where A is the initial amount of the sample and h is the half-life, in days, of the substance. A sample contains 18% of its original amount of Radon-222. The half-life of Radon-222 is about 3.8 days. Which is the best estimate for the age of the sample?
Answer:
9.4 days
Step-by-step explanation:
Filling in the given numbers, we can solve for t:
0.18 = 1·(1/2)^(t/3.8)
log(0.18) = (t/3.8)log(1/2)
t = 3.8·log(0.18)/log(0.50) ≈ 9.4 . . . . days
The best estimate of the age of the sample is 9.4 days.
Answer:
9.4 days
Step-by-step explanation:
Write the equation of the circle with center (3, 2) and with (9, 3) being a point on the circle. A) (x − 3)2 + (y − 2)2 = 13 B) (x − 3)2 + (y − 2)2 = 18 Eliminate C) (x − 3)2 + (y − 2)2 = 25 D) (x − 3)2 + (y − 2)2 = 37
Check the picture below.
so then, the distance from the center to that point is really the radius.
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{3}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{(9-3)^2+(3-2)^2}\implies r=\sqrt{36+1}\implies r=\sqrt{37} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{3}{ h},\stackrel{2}{ k})\qquad \qquad radius=\stackrel{\sqrt{37}}{ r} \\\\\\ (x-3)^2+(y-2)^2=(\sqrt{37})^2\implies (x-3)^2+(y-2)^2=37[/tex]
Anyone know the answer?
Answer:
2³² -1
Step-by-step explanation:
The sequence has a₁ = 1 and r = 2. Filling in the numbers for n=32, we have ...
S₃₂ = 1·(1 -2³²)/(1 -2)
S₃₂ = 2³² -1
Can you guys please help
if you add 3 to it it would be 6
Solve the system of equations given below
[tex]
y-15=3x \\
-2x+5y=-3 \\ \\
-2x+y-15=0 /\cdot2 \\
-2x+5y-3=0 /\cdot(-2) \\ \\
-4x+2y-30=0 \\
4x-10y+6=0 \\ \\
-8y-24=0 \\
\boxed{y=-3} \\ \\
-3-15=3x \\
\boxed{x=-6}
[/tex]
The answer is C. (-6, -3)
Hope this helps.
r3t40
For this case we have the following system of equations:
[tex]y-15 = 3x\\-2x + 5y = -3[/tex]
We multiply the first equation by -5:
[tex]-5y + 75 = -15x[/tex]
Now we add the equations:
[tex]-2x-5y + 5y + 75 = -3-15x\\-2x + 75 = -3-15x\\-2x + 15x = -75-3\\13x = -78\\x = \frac {-78} {13}\\x = -6[/tex]
We find the value of the variable "y" according to the first equation:
[tex]y = 3x + 15\\y = 3 (-6) +15\\y = -18 + 15\\y = -3[/tex]
The solution of the system is: (-6, -3)
Answer:
(-6, -3)
Option C
A triangle has an angle that measures 50°. The other two angles are in a ratio of 5:8. What are the measures of those two angles?
Answer:
Step-by-step explanation:
sum of angle of triangle is 180 degree
5x+8x+50degree =180 degree
13x= 180-50
13x= 130
x= 130/13
x=10
5x= 5*10=50degree
8x= 8*10 =80degree
The value of other two angles of triangle are 50 and 80 degrees.
Angles of triangle:Let us consider that other two angles of triangle are 5x and 8x.
Given that, one angle of triangle is 50 degree.
By property of triangle, sum of all three angles is equal to 180 degrees.
[tex]5x+8x+50=180\\\\13x=130\\\\x=130/13=10[/tex]
Other two angles of triangle are,
[tex]5x=5*10=50\\\\8x=8*10=80[/tex]
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A gym surveyed 100 female members. These members were chosen at random from the gym's membership database. Participants were asked the question, "Do you prefer to use the easy weight-lifting machines or the harder free weights?"
A report of the survey results stated that female members at the gym prefer the weight-lifting machines over the free weights.
Select ALL statements that correctly evaluate the report.
Answer:
Step-by-step explanation:
The sample is not biased. The members were selected at random from the gym's female population.
The question is biased. It described the weight lifting machines as "easy" and the free weights as "harder".
The second and third choices are correct.
Rhea is solving a math puzzle. To find the solution of the puzzle, she must find the product of two numbers. The first number is the sum of 23 and x, and the second number is 18 less than two times the first number. Which of the following functions represents the product of these two numbers?
First number = 23+x
Second number = 2(23+x)-18 = 46 +2x -18 = 2x +28
Now multiply each term by each term :
23 +x * 2x +28
23 * 2x + 23 * 28 + x *2x + x*28=
46x + 644 + 2x^2 + 28x =
Final answer = 2x^2 +74x +644
The answer is D.
Answer:
The product of two numbers is [tex]P(x)=2x^2+74x+644[/tex]
Step-by-step explanation:
We are given that The first number is the sum of 23 and x,
First number = 23+x
The second number is 18 less than two times the first number.
Second Number = [tex]2(23+x)-18[/tex]
The product of two numbers : [tex](23+x)(2(23+x)-18)[/tex]
[tex](23+x)(46+2x-18)[/tex]
[tex](23+x)(28+2x)[/tex]
[tex]2x^2+74x+644[/tex]
Let P(x) denotes the product
So, The product of two numbers is [tex]P(x)=2x^2+74x+644[/tex]
Hence Option D is true .
The product of two numbers is [tex]P(x)=2x^2+74x+644[/tex]
Find the volume of the basketball in terms of pi. The diameter across the circl is 28cm
Answer:
10976π/3 cm³
Step-by-step explanation:
Volume of a sphere is:
V = 4/3 π r³
where r is the radius (half the diameter).
The diameter is 28 cm, so the radius is 14 cm.
V = 4/3 π (14 cm)³
V = 10976π/3 cm³
Final answer:
The volume of a basketball with a diameter of 28 cm is 4,304π cm³ when expressed in terms of π.
Explanation:
To find the volume of a basketball in terms of π (pi), we start by noting that the formula for the volume of a sphere is V = ⅔πr³, where r is the radius of the sphere. Given that the diameter of the basketball is 28 cm, we will first find the radius by dividing the diameter by 2, which gives us a radius of 14 cm. We then plug this into the formula:
V = ⅔π(14 cm)³
After simplifying, we get:
V = ⅔π(2744 cm³)
And finally, the volume V in terms of π is:
V = 4,304π cm³
The z-statistic for a sample of delmar's practice times is 1.41. how should this statistic be interpreted in terms of the hypothesis test?
Answer:
Part 1: Answer C) There is not enough evidence to reject H0
Part 2: Answer C) There is not enough evidence to accept or reject his claim.
Step-by-step explanation:
Just did it on edge
The z-statistic of 1.41 means the sample mean is 1.41 standard deviations to the right of the population mean, if we assume the null hypothesis is true. The corresponding p-value is approximately 0.1587, which is greater than the commonly used threshold (0.05), leading us to not reject the null hypothesis.
Explanation:The z-statistic of 1.41 in the sample of Delmar's practice times can be used to draw conclusions about the sample's relationship to the population in a hypothesis test. It represents how many standard deviations an element (or group of elements, like a sample mean) falls from the mean or average of a population. A z-statistic of 1.41 means that the sample mean falls 1.41 standard deviations to the right of the population mean, assuming the null hypothesis to be true.
This information is useful in determining the p-value, which is the probability of observing a test statistic as extreme as the one calculated, assuming that the null hypothesis is true. If the p-value is smaller than the predetermined significance level (let's assume α=0.05), we would reject the null hypothesis. The p-value corresponding to z=1.41 in a two-tailed test is approximately 0.1587. Since this p-value is greater than 0.05, we would not reject the null hypothesis and state that we do not have enough evidence to suggest that Delmar's practice times are significantly different from the population.
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Which of the following are true statemetns about a 30-60-90 triangle?
I think it is a and b but I'm not sure
Answer:
Use the hyper link
Step-by-step explanation:
I took a picture on the unit.
Answer:
A.The longer leg is √3 times as long as the shorter
B. The hypotenuse is twice as long as the shorter leg
Step-by-step explanation:
The 30-60-90 is a special triangle with two acute angles 30° and 60°
The side across from the 30°= shorter leg
The side across from 60°=longer leg
The side across from 90°=hypotenuse
If we take the shorter side to be x and hypotenuse to be 2x then the longer leg will be;
Apply Pythagorean relationship
a² + b² =c²
c²-a²=b² where-----------c=2x and a=x
(2x)² - x² = b²
4x² - x² =b²
3x² = b²
√3x²=b
x√3 =b
Hence longer leg is √3 times longer than the shorter leg which is x and the hypothenuse 2x is twice the shorter leg which is x
You roll two dice numbered from one through six. What is the probability of rolling a dum greater than 11? Show your work either by drawing an area model for probability
Answer:
1/36 or 0.0277... or approximately a 3% chance of rolling a sum greater than 11 (i.e., a sum of 12)
Step-by-step explanation:
Create a 6 x 6 grid on a piece of graph paper. Number the 6 columns 1-6 at the top (for the value of the first die) and number the rows 1-6 on the side (for the value of the second die). You must imagine that you are rolling one die then the other (rather than how people "normally" roll both simultaneously). In the 36 empty boxes in your grid below the column numbers and to the right of the row numbers, put the sums of rolling the die at the top of the column + its corresponding die from the row (for example, use your fingers to match column number 4, say, with row 4 to get a sum of 8). When you've filled out the grid, you will see that a sum of 2 and sum of 12 have the same probability (there's only one way to get a sum of 2 or sum of 12, either 1 + 1 or 6 + 6). But there are many more ways, for example, to get a sum of 7
Which inequality statement best represents the graph?
f(x) > –x2 + x – 1
f(x) < x2 + x – 1
f(x) < –x2 + x – 1
f(x) > x2 + x – 1
Answer:
f(x) < –x2 + x – 1
Step-by-step explanation:
The graph is going down so we know that there is a maximum, therefore the A value has to be negative. This rules out f(x) < x2 + x – 1 and f(x) > x2 + x – 1 . The shaded area of the graph is below which indicates that f(x) has to be less than the function. This means the correct answer is f(x) < –x2 + x – 1 .
Answer:
[tex]y>-x^2 +x-1[/tex]
Step-by-step explanation:
Lets find the inequality that best describes the given statement
The graph of the parabola is upside down so the value of 'a' is -1
It means the equation for the parabola becomes [tex]y=-x^2 +x-1[/tex]
Now to get inequality , lets pick a point from the shaded part .
Lets pick (0,0), plug in 0 for x and 0 for y
[tex]y=-x^2 +x-1[/tex]
[tex]0=-(0)^2 +(0)-1[/tex]
[tex]0=-1[/tex]
0 is greater than -1
[tex]y>-x^2 +x-1[/tex]
A number generator was used to simulate the percentage of people in a town who ride a bike. The process simulates randomly selecting 100 people from the town and was repeated 20 times. The percentage of people who ride a bike is shown in the dot plot.
Which statement is true about the population of the town?
Answer:
Step-by-step explanation:
Of the 20 trials, 18 of them ended up between 60 and 75. So most likely, 60% to 75% of the town rides a bike.
The true statement about the dot plot is (c) Most likely, 60% to 75% of the town rides a bike.
How to interpret the dot plot?From the dot plot, we have the following sample between 60 and 75%
Sample = 3 + 4 + 6 + 5
Evaluate
Sample = 18
The above means that 18 out of the 20 trials fall between 60 and 75%
This means that between 60 and 75% of the town rides a bike
Hence, the true statement about the dot plot is (c)
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A sack of potato with 14 lbs. 9 oz. After Wendy makes potato salad for a picnic does sac wait 9 lbs. 14 oz. What is the week of the potato Wendy's use for the potato salad
Answer:
Your answer should be 4 pounds 6 ounces.
Step-by-step explanation:
If you subtract how much the potato sack was before she made the potato salad from how much it was after, this gives you how much the potato she used weighed.
The midpoint of AB =
Answer:
(-.5, 0)
Step-by-step explanation:
y ---- 2÷2=1, y-1= 1-1=0
x ---- 3÷2 =1.5, x-1.5= 1-1.5= -.5
Answer:
( -0.5, 0 )
Step-by-step explanation:
Add the 0 before 5, it matters if its right or wrong. The Answer is ( -0.5 , 0 ). ADD THE 0 !!!!!
In right △ABC, the altitude CH to the hypotenuse AB intersects angle bisector AL in point D. Find the sides of △ABC if AD = 8 cm and DH = 4 cm.
Answer:
[tex]AC=8\sqrt{3}\ cm\\ \\AB=16\sqrt{3}\ cm\\ \\BC=24\ cm[/tex]
Step-by-step explanation:
Consider right triangle ADH ( it is right triangle, because CH is the altitude). In this triangle, the hypotenuse AD = 8 cm and the leg DH = 4 cm. If the leg is half of the hypotenuse, then the opposite to this leg angle is equal to 30°.
By the Pythagorean theorem,
[tex]AD^2=AH^2+DH^2\\ \\8^2=AH^2+4^2\\ \\AH^2=64-16=48\\ \\AH=\sqrt{48}=4\sqrt{3}\ cm[/tex]
AL is angle A bisector, then angle A is 60°. Use the angle's bisector property:
[tex]\dfrac{CA}{CD}=\dfrac{AH}{HD}\\ \\\dfrac{CA}{CD}=\dfrac{4\sqrt{3}}{4}=\sqrt{3}\Rightarrow CA=\sqrt{3}CD[/tex]
Consider right triangle CAH.By the Pythagorean theorem,
[tex]CA^2=CH^2+AH^2\\ \\(\sqrt{3}CD)^2=(CD+4)^2+(4\sqrt{3})^2\\ \\3CD^2=CD^2+8CD+16+48\\ \\2CD^2-8CD-64=0\\ \\CD^2-4CD-32=0\\ \\D=(-4)^2-4\cdot 1\cdot (-32)=16+128=144\\ \\CD_{1,2}=\dfrac{-(-4)\pm\sqrt{144}}{2\cdot 1}=\dfrac{4\pm 12}{2}=-4,\ 8[/tex]
The length cannot be negative, so CD=8 cm and
[tex]CA=\sqrt{3}CD=8\sqrt{3}\ cm[/tex]
In right triangle ABC, angle B = 90° - 60° = 30°, leg AC is opposite to 30°, and the hypotenuse AB is twice the leg AC. Hence,
[tex]AB=2CA=16\sqrt{3}\ cm[/tex]
By the Pythagorean theorem,
[tex]BC^2=AB^2-AC^2\\ \\BC^2=(16\sqrt{3})^2-(8\sqrt{3})^2=256\cdot 3-64\cdot 3=576\\ \\BC=24\ cm[/tex]
How do you evaluate trig functions without a calculator
You can't in theory. Only a few "nice" values are known, because they lead to particular triangles. For example, we have
[tex]\sin(0)=0,\quad \cos(0)=1[/tex][tex]\sin(30)=\frac{1}{2},\quad \cos(30)=\frac{\sqrt{3}}{2}[/tex][tex]\sin(45)=\cos(45)=\frac{\sqrt{2}}{2}[/tex]You can add other angles using symmetries, for example, you can compute sin(60) using sin(90-x) = cos(x), or similar stuff.
You can also use the double/half angles identities to add another couple of angles in our list, but that's it.
Please help, picture of question included.
Answer:
b. [tex]\frac{p-1700}{10}[/tex]
Step-by-step explanation:
We have that the server's salary can be expressed as
[tex]p = $1700+$10t[/tex]
Counting the $ 1700 dollars as the fixed amount of your salary and contemplating the variable salary that would be $ 10 * t being t the number of overtime worked
from this expression we can clear the number of overtime worked by clearing t, so I finally have
[tex]p=$1700+$10t\\ $10t = p - $1700 \\ t= \frac{p-1700}{10}[/tex]
Done
I need help with this 50 points
Answer:
Step-by-step explanation:
Vertically stretched. The action of vertically stretched is accomplished by altering a in
y = a* abs(x)
What that means is that you make a > 1. In this case, a = 2
So far, what you have is
y = 2*abs(x)
Six units down. The action of 6 units down is accomplished by a number added or subtracted to/from absolute(x). down is minus, up is plus.
y = 2*abs(x) - b. Since we are moving down, b<0
y = 2*abs(x) - 6
Four Units Right. This is the tough one because it is anti intuitive. You would think you should be adding something somewhere to get a right hand movement.
Not true.
To move right you subtract something in the brackets.
y = 2*abs(x - 4) - 6
Graph
Just to make things complete, I have graphed this for you. Desmos is wonderful for this kind of problem.
red: y = abs(x)
blue: y = 2*abs(x - 4) - 6
Answer:
Step-by. step explanation:
Which function is equivalent to f(x) = e2x ?
Im pretty sure this is the answer F (x) = e^2x + 1
What’s the expression of 8y – 2(y + 4) anyone?
Answer:
The expression for 8y - 2(y+4) is 6y - 8
Step-by-step explanation:
An expression is a mathematical phrase which can contain symbols like a,b,c,x,y,z or numbers like 1,2,3,4,5, etc, or both. Expression is one sided where as equation in mathematics is a two sided expression. There is no left or right side in an Expression, there is always one side.
The given phrase is simplified as follows:
8y - 2(y+4)
8y -2y - 8
6y - 8
All of the following are equivalent, except _____.
2x + x
x(2 + 1)
2x²
3x
2x+x = 2x^2
X(2+1) = 2x^2
2x^2 stays the same
Therefore the answer is d 3x is not the same as the rest
Answer:
2x^2
Step-by-step explanation:
2x+x=3x
x(2+1)=2x+x=3x
3x
Evaluate 7 − (−1).
6
−6
8
−8
Simplify brackets
7 + 1
Simplify
8
Answer: C. 8
Answer:
minus and minus is plus
7+ 1 is 8 :)
Which of the following points is on a circle if its center is (-13,-12) and a point on the circumference is (-17, -12)?
A. (-17,-13)
B. (-9, -17)
C. (-12, 13)
D. (-9, -12)
Answer:
D
Step-by-step explanation:
Obtain the equation of the circle in standard form
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (- 13, - 12), thus
(x + 13)² + (y + 12)² = r²
The radius is the distance from the centre (- 13, - 12) to the point on the circumference (- 17, - 12)
Use the distance formula to calculate r
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 17, - 12) and (x₂, y₂ ) = (- 13, -12)
r = [tex]\sqrt{(-13+17)^2+(-12+12)^2}[/tex] = [tex]\sqrt{16}[/tex] = 4
Hence
(x + 13)² + (y + 12)² = 16 ← in standard form
Substitute the coordinates of each point into the left side of the equation and check
A (- 17, - 13) : (- 4)² + (- 1)² = 16 + 1 = 17 ≠ 16
B (- 9, - 17) : 4² + (- 5)² = 16 + 25 = 41 ≠ 16
C (- 12, 13) : 1² + 25² ≠ 16
D (- 9, - 12) : 4² + 0² = 16
Since (- 9, - 12) satisfies the equation, it is on the circle → D
Point D (-9, -12) is on the circumference of the circle centered at (-13,-12) with a radius of 4 units.
Explanation:To determine which point is on the circumference of a circle with the center at (-13,-12) and a known point on the circumference (-17, -12), we must first find the radius of the circle. The radius can be found by calculating the distance between the center and the known circumference point, which here is the horizontal distance between (-13,-12) and (-17, -12), equal to 4 units. Now, we have to check which of the given points is 4 units away from the center (-13,-12). After checking all options, the correct answer is D. (-9, -12).
To confirm, calculate the distance between the center and point D:
Distance = √((-9 - (-13))^2 + (-12 - (-12))^2)\
Distance = √((4)^2 + (0)^2)\
Distance = √(16)\
Distance = 4
Therefore, point D lies on the circumference of the circle as it is the same distance (radius) from the center as the known point (-17, -12).