Examine the following system of inequalities.
{y <−1/4x+4 and y>(x+4)^2
Which option shows the graph of the system?
Dotted linear inequality shaded above passes through (0, 4) & (4,5). Dotted parabolic inequality shaded below passes through (negative 6,4), (negative 4, 0) & (negative 2, 4).
Dotted linear inequality shaded below passes through (0, 4) & (4,3). Dotted parabolic inequality shaded above passes through points (negative 6,4), (negative 4, 0) & (negative 2, 4).
Dotted linear inequality shaded below passes through (0, 4) & (4,5). Dotted parabolic inequality shaded above passes through points (negative 6,4), (negative 4, 0) & (negative 2, 4).
Dotted linear inequality shaded above passes through (0, 4) & (4,3). Dotted parabolic inequality shaded below passes through (negative 6,4), (negative 4, 0) & (negative 2, 4).
Answers
Dotted linear inequality shaded below passes through (0, 4) & (4,3). Dotted parabolic inequality shaded above passes through points (negative 6,4), (negative 4, 0) & (negative 2, 4).
Step-by-step explanation:Hello! Let me help you to find the correct option to this problem. First of all, we have the following system of inequalities:
[tex]\left\{ \begin{array}{c}y< -\frac{1}{4}x+4\\y>(x+4)^{2}\end{array}\right.[/tex]
To solve this, let's write the following equations:
FIRST:[tex]y=-\frac{1}{4}x+4[/tex]
This is a linear function written in slope-intercept form as [tex]y=mx+b[/tex]. So, the slope [tex]m=-\frac{1}{4}[/tex] and the y-intercept is [tex]b=4[/tex]. Since in the inequality we have the symbol < then the graph of the line must be dotted. To get the shaded region, let's take a point, say, [tex](0, 0)[/tex] and let's test whether the region is above or below the graph. So:
[tex]y< -\frac{1}{4}x+4 \\ \\ Let \ x=y=0 \\ \\ 0<-\frac{1}{4}(0)+4 \\ \\ 0<4 \ True![/tex]
Since the expression is true, then the region is the one including point [tex](0, 0)[/tex], that is, it's shaded below.
SECOND:[tex]y=(x+4)^{2}[/tex]
This is a parabola that opens upward and whose vertex is [tex](-4,0)[/tex]. Since in the inequality we have the symbol > then the graph of the parabola must be dotted. Let's take the same point [tex](0, 0)[/tex] to test whether the region is above or below the graph. So:
[tex]y>(x+4)^{2} \\ \\ Let \ x=y=0 \\ \\ 0>(0+4)^2\\ \\ 0>16 \ False![/tex]
Since the expression is false, then the region is the one that doesn't include point [tex](0, 0)[/tex], that is, it's shaded above
____________________
On the other hand, testing points (0, 4) and (4,3) on the linear function:[tex]y=-\frac{1}{4}x+4 \\ \\ \\ \bullet \ (0,4): \\ \\ y=-\frac{1}{4}(0)+4 \therefore y=4 \\ \\ \\ \bullet \ (4,3): \\ \\ y=-\frac{1}{4}(4)+4 \therefore y=3[/tex]
So the line passes through these two points.
Now, testing points (negative 6,4), (negative 4, 0) & (negative 2, 4) on the parabola:[tex]y=(x+4)^2 \\ \\ \\ \bullet \ (-6,4): \\ \\ y=(-6+4)^2 \therefore y=(-2)^2 \therefore y=4 \\ \\ \\ \bullet \ (-4,0): \\ \\ y=(-4+4)^2 \therefore y=0 \\ \\ \\ \bullet \ (-2,4): \\ \\ y=(-2+4)^2 \therefore y=(2)^2 \therefore y=4[/tex]
So the line passes through these three points.
Finally, the shaded region is shown below.
Related Questions
Which is the equation of a line with a slope
of 1 and a y-intercept of 2?
(1) y + x = 2 (3) y - x + 2 = 0
2) y - x = 2 (4) y + x - 2 = 0
Please help
Answers
Answer:
2) y-x=2
Add x on both sides:
y =x+2
The slope is 1 and the y-intercept is 2.
Step-by-step explanation:
So a linear equation in slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.
Let's put all of these in that form:
1) y+x=2
Subtract x on both sides:
y =-x+2
The slope is -1 and the y-intercept is 2.
2) y-x=2
Add x on both sides:
y =x+2
The slope is 1 and the y-intercept is 2.
3) y-x+2=0
Add x on both sides:
y +2=x
Subtract 2 on both sides:
y =x-2
The slope is 1 and the y-intercept is -2.
4) y+x-2=0
Add 2 on both sides:
y +x =2
Subtract x on both sides:
y =-x+2
The slope is -1 and and the y-intercept is 2.
Maria earns $60.00 for 8 hours of work and Marc earns $46.50 for 6 hours of work. Which person earns the most per hour? A. Maria. B. Marc. C. They earn the same amount. D. It cannot be determined.
Answers
Answer:
C. Marc
Step-by-step explanation:
to get the amount they earn in an hour divide the amount they earn by the amount of hours they worked for.
Maria: 60 divided by 8 = 7.50
Marc: 46.50 divided by 6 = 7.75
Which equations could be used to solve for the unknown lengths of △ABC? Check all that apply.
sin(45°) = 
sin(45°) = 
9 tan(45°) = AC
(AC)sin(45°) = BC
cos(45°) = 
Answers
Answer:
sin(45°)= AC/9
cos(45°)= BC/9
Step-by-step explanation:
This is a right angle triangle:
∠ABC =∠CAB = 45°
Now
AC= CB
AB = 9 units.
We will apply sines:
sine(45°)= AC/AB
We know that AB = 9 units.
So substitute the value of side AB
sin(45°)= AC/9
Now apply cos(45°)
cos(45°)= BC/AB
Again substitute the value of AB:
cos(45°)= BC/9
Thus the answer is
sin(45°)= AC/9
cos(45°)= BC/9 ....
Answer:
A
E
Step-by-step explanation:
Which of the following sequences is an arithmetic sequence?
A. {-10,5,-2.5,1.25,...}
B. {100,20,4,0.8,...}
C. {1,4,16,48,...}
D. {-10,-3.5,3,9.5,...}
Answers
Answer:
D
Step-by-step explanation:
For a sequence to be an arithmetic sequence, it must have a common difference. In other words, it must either go down by the same number or up by the same number.
Let's look at the choices:
A. {-10,5,-2.5,1.25,...}
-10 to 5, that went up by 15. It has to keep going up by 15 to be arithmetic. However 5+15 is not -2.5 so it isn't arithmetic.
B. {100,20,4,0.8,...}
100 to 20, that went down by 80. Since 20-80 is not 4, then this sequence is not arithmetic.
C. {1,4,16,48,...}
1 to 4, that went up by 3. 4+3 is not 16 so this is not arithmetic.
D. {-10,-3.5,3,9.5,...}
-10 to -3.5, that went up 6.5.
-3.5+6.5=3
3+6.5=9.5
This is arithmetic. It keeps going up by 6.5.
What is 1(y), when y = -5/8
Answers
Final answer:
The expression 1(y), when y = -5/8, is calculated by multiplying 1 by -5/8, which simply yields -5/8.
Explanation:
The task is to find the value of the expression 1(y) when y is given as -5/8. The expression 1(y) can be interpreted as simply '1 times y'. Therefore, we need to multiply the number 1 by -5/8 to find the answer.
1(y) = 1 * (-5/8) = -5/8
This is a basic arithmetic operation, specifically multiplication, commonly encountered in mathematics. When we multiply any number by 1, the result is the number itself, which in this case applies to the negative fraction -5/8.
n 1917 the cost of a first-class postage stamp was 3¢. In 1974 the cost for a first-class postage stamp was 10¢. What is the percent of increase in the cost of a first-class postage stamp?
Answers
Answer:
233.33 %.
Step-by-step explanation:
The increase is 10 - 3 = 7c.
Percentage increase = 100 * 7 / 3.
= 700 / 3
= 233.33 %.
The cost of a first-class postage stamp increased approximately 233.33% from 1917 to 1974.
To calculate the percent increase in the cost of a first-class postage stamp from 1917 to 1974, follow these steps:
Determine the initial price in 1917: 3¢.Determine the final price in 1974: 10¢.Calculate the increase: 10¢ - 3¢ = 7¢.Divide the increase by the initial price: 7¢ / 3¢ ≈ 2.3333.Convert the result into a percentage: 2.3333 × 100 ≈ 233.33%.Thus, the percent increase in the cost of a first-class postage stamp from 1917 to 1974 is approximately 233.33%.
Multiply. Express your answer in simplest form. 1/8 × 5/6
5/12
5/48
5/32
3/20
Answers
Answer:
5/48
Step-by-step explanation:
1x5=5
8x6=48
which give u
5/48
Answer:
[tex]\large\boxed{\dfrac{5}{48}}[/tex]
Step-by-step explanation:
[tex]\dfrac{1}{8}\times\dfrac{5}{6}=\dfrac{1\times5}{8\times6}=\dfrac{5}{48}\leftarrow\text{this is the simplest form}[/tex]
If you subtract my number from 300, or if you add my number to 220, you will get the same result. What is my number?
Answers
Answer:
40
Step-by-step explanation:
Subtracting a number k from 300 looks like this 300-k.
Adding a number k to 220 looks like this 220+k.
They are saying for some number k that we have 300-k and 220+k is the same value.
That is, 300-k=220+k.
This is the equation we are going to solve for your number.
300-k=220+k
Add k on both sides:
300=220+2k
Subtract 220 on both sides;
80=2k
Divide both sides by 2:
40=k
k=40.
So the number is 40.
Check: 300-40=260 while 220+40=260.
If a polynomial function f(x) has roots 3 and square root of 7, what must also be a root of f(x)
Answers
Answer:
x = - [tex]\sqrt{7}[/tex]
Step-by-step explanation:
Radical roots occur in pairs, that is
x = [tex]\sqrt{7}[/tex] is a root then so is x = - [tex]\sqrt{7}[/tex]
Answer:
-√7 = -2.64
Step-by-step explanation:
The polynomial function has roots. The first root is 3 and the second is √7.
When we have a square root that means that we get two roots from the same number but one is negative and the other is positive. For example, if we have:
√x² = ±x
Because we can have:
(-x)² = x², or
(x)²=x².
So a square root always gives us two answers, one negative and the other positive.
Which of these is the quadratic parent function?
Answers
Answer:
C) f(x) = x2
Step-by-step explanation:
PLEASE ANSWER
All books in a store are being discounted by 40%.
Let x represent the regular price of any book in the store. Write an expression that can be used to find the sale price of any book in the store.
Answers
Answer:
x(1 - .4)
Step-by-step explanation:
x = regular price.
1 - .4 = .6 = 60%
The sale price is equal to the full price (aka x) minus the discounted price (40% of x = 40/100 times x = .4x)
Therefore sale price = x - .4x or x(1 - .4)
A recipe says it takes 2&1/2 cups of flour to make a batch of cookies. How many cups of flour are needed to make 3&3/4 batches of cookies?
I got 9&3/8, is that correct?
Answers
Step-by-step explanation:
Write a proportion:
2½ cups / 1 batch = x cups / 3¾ batches
Cross multiply:
x × 1 = 2½ × 3¾
To multiply the fractions, first write them in improper form:
x = (5/2) × (15/4)
x = 75/8
Now write in proper form:
x = 9⅜
Your answer is correct! Well done!
Suppose your car has h liters of engine oil in the morning. During the day, some oil may have leaked, you may have added more oil, or both. The oil level in the evening is g liters.
Answers
Oil added or consumed during the day equals evening oil level minus morning oil level (g - h).
To calculate how much oil was consumed or added during the day, you can use the formula:
Change in oil = g - h
If the value is positive, it means oil was added.
If the value is negative, it means oil was consumed (leaked or used).
For example, if in the morning your car had 5 liters of oil (h = 5) and in the evening it had 7 liters (g = 7):
Change in oil = 7 - 5 = 2 liters
This means 2 liters of oil were added during the day.
he function f(x) = x^2 + 10x - 3 written in vertex form is fx) = (x+5)^2– 28. What are the coordinates of the vertex?
0 (-5, -28)
O (-5, 28)
O (5.-28)
O (5, 28)
Answers
Answer:
(- 5, - 28 )
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
f(x) = (x + 5)² - 28 ← is in vertex form
with vertex (h, k) = (- 5, - 28)
What is a counter example for: If the name of the month begins with a J, then it is a summer month.
Answers
Answer:
January
Step-by-step explanation:
January is a counter-example of the name of the month begins with a January then it's a winter month by a season.
The counter example is : January since it begins with the letter J and is a winter month, which is not summer.
What is a counter example?An example that disproves a statement (shows that it is false) is called a counter example.
How to find the counter example for the given examples?According to the problem, the given statement is : If the name of the month begins with a J, then it is a summer month.The counter example will be : January since January is a month that starts with J that is not a summer month
January is the only month that fits this criteria.
Find more about "Counter Examples" here: https://brainly.com/question/17784562
#SPJ2
The best fitting straight line for a data set of X-values plotted against y-values is
called
a. a correlation matrix
b. polynomial expansion
c. varimax rotation
d. a regression equation
Answers
Answer:
a. a correlation matrix
Step-by-step explanation:
The best fitting straight line for a data set of X-values plotted against y-values is called a correlation matrix.
Vector G is 40.3 m long in a
-35.0° direction. Vector His
63.3 m long in a 270° direction.
Find the magnitude of their
vector sum.
magnitude (m)
Enter
Answers
Answer:
Approximately 92.51.
Not sure what the desired rounding is since it isn't listed.
Step-by-step explanation:
So the first vector G is 40.3 m long in a -35 degree direction.
Lat's find the components of G.
[tex]G_x=40.3\cos(-35)=33.0118[/tex].
[tex]G_y=40.3\sin(-35)=-23.1151[/tex].
The second vector H is 63.3 m long in a 270 degree direction.
[tex]H_x=63.3\cos(270)=0[/tex].
[tex]H_y=63.3\sin(270)=-63.3[/tex].
The resultant vector can be found by adding the corresponding components:
[tex]R_x=G_x+H_x=33.0118+0=33.0118[/tex]
[tex]R_y=G_y+H_y=-23.1151+(-63.3)=-86.4151[/tex]
Now we are asked to find the magnitude of [tex](R_x,R_y)[/tex] which is given by the formula [tex]\sqrt{R_x^2+R_y^2}[/tex].
Since [tex](R_x,R_y)=(33.0118,-86.4151)[/tex] then the magnitude is [tex]\sqrt{(33.0118)^2+(-86.4151)^2}=\sqrt{8557.34844}=92.51[/tex].
The magnitude of the sum of vector G (40.3m, -35°) and vector H (63.3m, 270°) is found by breaking each vector into its components, summing these components, and using the Pythagorean theorem. The magnitude of the sum of these vectors is approximately 92.1 m.
Explanation:Given that vector G has a magnitude of 40.3 m and is in a -35.0° direction, and vector H has a magnitude of 63.3 m and is in a 270° direction, the sum of these vectors can be determined. This sum is found by breaking each vector into its component forms, adding the components together, and then using the Pythagorean theorem to find the magnitude of the result.
For vector G: Gx = 40.3m * cos(-35) = 33m and Gy = 40.3m * sin(-35) = -23.14m. For vector H: Hx = 0 (as sin(270) equals 0) and Hy = -63.3m (as sin(270) equals -1). The sum vector S = (Gx+Hx, Gy+Hy) = (33m+0 , -23.14m-63.3m) = (33m, -86.44m). Thus, to find the magnitude of the sum of the vectors, we use the Pythagorean theorem: |S| = sqrt((33m)² + (-86.44m)²) = 92.1 m (rounded to 1 decimal place).
Learn more about Sum of Vectors here:https://brainly.com/question/36920213
#SPJ11
Transformations were performed on pentagon H as shown in the graph. What types of transformations were performed? Do those transformations result in congruent shapes?
A. Translation and dilation, yes
B. Translation and reflection, no
C. Translation and rotation, yes
D. Translation and dilation, no
Answers
You know it’s a translation because first it’s not in the same spot and second it is an answer choice in all the answer
You know it’s not a reflection because the shape looks the same and every point faces the same direction
So that is means it’s a dilation.
You also know that it’s a dilation because there is a size difference between the two.
Lastly because of the size difference, they aren’t congruent because congruent means the same and they aren’t the same size
which function has a removable discontinuity
x-2/x^2-x-2,
x^2-x+2/x+1,
5x/1-x^2,
2x-1/x
Answers
Answer:
[tex]\frac{x-2}{x^2-x-2}[/tex]
Step-by-step explanation:
A removable discontinuity is when there is a hole in your graph. This is usually because one X value has been canceled out. Most of the time, it takes factoring to figure out if there is a removable discontinuity when looking at an equation.
First, look at the numerator [tex]x-2[/tex] . This can't be factored any further. However, [tex]x^2-x-2[/tex] can be factored since it is a trinomial (has three terms) .
For the purposes of this example, you may want to think about it as
[tex]1x^2 -1x-2[/tex]
To factor, multiply the the outside coefficients
1 x -2 = -2
Now take the middle coefficient (-1) and ask yourself what two numbers multiply to make -2, but still add to be -1.
-2 x 1 = -2
-2 + 1 = -1
So in factored form, the equation is
[tex]\frac{x-2}{(x-2)(x+1)}[/tex]
Since you have x-2 on both top and bottom, that can be canceled out. x - 2 would be your removable discontinuity in this situation.
A removable discontinuity can occur in a function if there are common factors in both the numerator and denominator that can be canceled out.
Explanation:A function has a removable discontinuity at a particular point if the function is undefined at that point but can be made continuous by redefining the value at that point. To identify the removable discontinuity, we need to factor both the numerator and denominator of the function. By factoring, we can determine if any common factors exist that can be canceled out, resulting in a removable discontinuity.
Let's consider the given functions:
x-2/x^2-x-2: The denominator can be factored as (x-2)(x+1). We can cancel out the common factor x-2, resulting in a removable discontinuity at x=2.x^2-x+2/x+1: The numerator cannot be factored, so there are no removable discontinuities in this function.5x/1-x^2: The numerator and the denominator have no common factors to cancel out, so there are no removable discontinuities in this function.Learn more about Removable Discontinuity here:https://brainly.com/question/24162698
#SPJ2
Simplify the expression 43 + 2(3 − 2).
14
16
66
68
Answers
Final answer:
To simplify the expression 43 + 2(3 - 2), first solve inside the parentheses (3 - 2 = 1), then multiply by 2 (2 × 1 = 2), and finally add to 43 to get 45.
Explanation:
The question asks to simplify the expression 43 + 2(3 − 2). To simplify, follow the order of operations, often remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). First, solve the expression within the parentheses, which is 3 − 2 = 1. Next, multiply the result by 2 (2 × 1 = 2). Lastly, add this result to 43 to get the final answer, 43 + 2 = 45. This process demonstrates how to approach and simplify mathematical expressions using proper order of operations.
VERY EASY WILL GIVE BRAINLEST THANK YOU AND FRIEND YOU How can the Associative Property be used to mentally fine 48 + 82?
Answers
Answer:
You can use teh associative property to split 48 and 82 each into 2 peices
(40+8)(80+2) then you can move the parenthesis around. 40+(8+80)+2
40+(88+2)
40+90=130
Like: 40+80=120
8+2=10
120+10=130
So the answer is: 130
Pls help !!!!!!!!!! I need to get this question right
Answers
Answer:
B
Step-by-step explanation:
Answer:
He didn't change the direction of the inequality when he divided both sides by -2.
Step-by-step explanation:
Let's go through each step and see.
First step: They distribute and they did so correctly. -4(x+8)=-4x-32.
Second step: They added 2x on both sides.
Third step: They added 32 on both sides.
Fourth step: The divide both sides by -2 correctly but since this is inequality you must flip the sign.
For example 3>2 but if you multiply both sides by -1 or divide both sides by -1 you get -3<-2.
You have to flip the sign whenever you multiply or divide both sides of inequality by negative number.
Which of the following sets could be the sides of a right triangle?{2, 3, square root of 13} {5, 5, 2, square root of 10} { 5, 12, 15 }
Answers
Answer:
{2, 3, √13}
Step-by-step explanation:
In a right triangle, the sum of the squares of the two shorter sides equals the square of the third side (Pythagoras).
Let's check each set of sides in turn.
A. {2, 3, √13}
2² + 3² = 4 + 9 = 13
(√13)² = 13
This is a right triangle.
B. {5, 5, 2, √10}
This is a quadrilateral (four sides).
C. {5, 12, 15}
5² + 12² = 25 +144 = 169
15² = 225
This is not a right triangle.
which shows 3x^2-18x=21 as a perfect square equation? what are the solution(s)?
a. (x-3)^2=0; -3
b. (x-3)^2=16; -1 and 7
c. x^2-6x+9; -3
d. 3x^2-18x-21=0, -1 and 7
Answers
Answer:
b
Step-by-step explanation:
Given
3x² - 18x = 21 ( divide all terms by 3 )
x² - 6x = 7
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 3)x + 9 = 7 + 9
(x - 3)² = 16 ( take the square root of both sides )
x - 3 = ± [tex]\sqrt{16}[/tex] = ± 4 ( add 3 to both sides )
x = 3 ± 4, hence
x = 3 - 4 = - 1 and x = 3 + 4 = 7
The correct option is b. [tex]\((x-3)^2=16\); -1 and 7.[/tex]
To solve the given quadratic equation [tex]\(3x^2 - 18x = 21\),[/tex] we first divide the entire equation by 3 to simplify it:
[tex]\[ x^2 - 6x = 7 \]\[ x^2 - 6x + 9 - 9 = 7 \] \[ (x - 3)^2 - 9 = 7 \][/tex]
Now, we isolate the perfect square on one side:
[tex]\[ (x - 3)^2 = 7 + 9 \] \[ (x - 3)^2 = 16 \][/tex]
This is the perfect square equation. To find the solutions, we take the square root of both sides:
[tex]\[ x - 3 = \pm4 \][/tex]
Now, we solve for \(x\) by adding 3 to both sides:
[tex]\[ x = 3 \pm 4 \][/tex]
This gives us two solutions:
[tex]\[ x = 3 + 4 = 7 \] \[ x = 3 - 4 = -1 \][/tex]
Therefore, the solutions to the equation are [tex]\(x = -1\) and \(x = 7\),[/tex] which corresponds to option b. [tex]\((x-3)^2=16\); -1 and 7.[/tex]
PLZ HELP
Pre-calculus
Answers
[tex]\bf \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad a^{log_a x}=x \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_6(\sqrt[3]{6})\implies \log_6(6^{\frac{1}{3}})\implies \cfrac{1}{3} \\\\[-0.35em] ~\dotfill\\\\ \log_2(64)\implies \log_2(2^6)\implies 6 \\\\[-0.35em] ~\dotfill\\\\ -3\log_5(25)\implies -3\log_5(5^2)\implies -3(2)\implies -6 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \log_2(\sqrt[4]{8})\implies \log_2(\sqrt[4]{2^3})\implies \log_2(2^{\frac{3}{4}})\implies \cfrac{3}{4} \\\\[-0.35em] ~\dotfill\\\\ \log_3\left( \frac{1}{81} \right)\implies \log_3\left( \frac{1}{3^4} \right)\implies \log_3(3^{-4})\implies -4[/tex]
Answer:
3/4 goes with [tex]\log_2(8^\frac{1}{4})[/tex]
-4 goes with [tex]\log_3(\frac{1}{81})[/tex]
-6 goes with [tex]-3\log_5(25)[/tex]
1/3 goes with [tex]\log_6(6^\frac{1}{3})[/tex]
Step-by-step explanation:
[tex]\log_6(6^\frac{1}{3})=\frac{1}{3}\log_6(6)=\frac{1}{3}\cdot 1=\frac{1}{3}[/tex]
[tex]\log_2(64)=6 \text{ since } 2^6=64[/tex]
[tex]-3\log_5(25)=-3(2)=-6 \text{ since } 5^2=25[/tex]
[tex]\log_2(8^\frac{1}{4})=\frac{1}{4}\log_2(8)=\frac{1}{4}\log_2(2^3)=\frac{1}{4}\cdot (3)\log_2(2)=\frac{1}{4} \cdot 3 \cdot 1=\frac{3}{4} [/tex]
[tex] \log_3(\frac{1}{81})=\log_3(\frac{1}{3^4})=\log_3(3^{-4})=-4\log_3(3)=-4(1)=-4[/tex]
Here are few rules I used:
[tex]\log_a(b)=x \text{ means } a^x=b[/tex]
[tex]\log_a(a)=1 [/tex]
[tex]\log_a(b^r)=r \log_a(b)[/tex]
A ; 1/2. B ; 1/3. C ; 2/3 D ; 4/9
Answers
Option B, 1/3
Since pepper topping can be in any size pizza, it remains as a 1/3 probability, since there are three toppings per size.
e equation 2x + 3y = 36, when y = 6?
Answers
Answer:
x=9
Step-by-step explanation:
Since y=18
The new equation is [tex]2x+3*6=36[/tex]
Moving some terms, it stays like the following:
[tex]2x=36-18[/tex]
solving for x, give us that x=9
On a particular day, the wind added 4 miles per hour to Jaime's rate when she was rowing with the wind and subtracted 4 miles per hour from her rate on her return trip. Jaime found that in the same amount of time she could row 48 miles with the wind, she could go only 24 miles against the wind. What is her normal rowing speed with no wind?
Answers
Answer:
12 miles per hour
Step-by-step explanation:
Let her normal rowing speed be x
Also note the formula D = RT, where d is distance, R is rate(speed) and T is time
On windy day, her speed is x + 4
On against wind return, her speed is x - 4
With wind, she can go 48 miles in same amount of time when she goes 24 miles against wind. This can be written as:
48 = (x+4)T
24 = (x-4)T
We can write each equation in terms of T and equate both. So we have:
48/x+4 = T
24/x-4 = T
Thus,
[tex]\frac{48}{x+4}=\frac{24}{x-4}\\48(x-4)=24(x+4)\\48x-192=24x+96\\24x=288\\x=\frac{288}{24}\\x=12[/tex]
Thus, Jaime's normal rowing speed is 12 miles per hour
which expression gives the distance between points (1,-2) and (2,4)
Answers
Answer:
[tex]\sqrt{37}[/tex]
Step-by-step explanation:
Distance formula
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
[tex]d = \sqrt {\left( {1 - 2 } \right)^2 + \left( {-2 - 4 } \right)^2 }[/tex]
Simplify
[tex]d = \sqrt {\left( {-1 } \right)^2 + \left( {-6 } \right)^2 }[/tex]
Simplify
[tex]d = \sqrt {\left 1 + \left 36}[/tex]
[tex]d = \sqrt{37}[/tex]
Answer
[tex]d = \sqrt{37}[/tex]
Point T is reflected over the y-axis. Determine the coordinates of its image. T (2, 5)
a(2, -5)
b(2, 5)
c(-2, -5)
d(-2, 5)
Answers
Answer:
d. (-2, 5)
Step-by-step explanation:
Point T is reflected over the y-axis.
Therefore, the coordinates are (-2, 5).
Answer:
T' is (-2,5)
Step-by-step explanation:
To reflect a point across the y-axis, you will note the following:
1- the sign x-coordinate of the point is flipped while the value remains the same
2- both the sign and the value of the y-coordinate remain the same
We are given that:
point T is (2,5)
Applying the above:
sign of x-coordinate is flipped and value is the same :
x- coordinate of T' is -2
both sign and value of y-coordinate are the same:
y-coordinate of T' is 5
Based on the above:
T' would be (-2,5)
Hope this helps :)