Answer:
(-4, -4)
Step-by-step explanation:
You have to put this in vertex form by completing the square in order to determine the vertex. Begin by setting the quadratic equal to 0 then moving the 12 over by subtraction:
[tex]x^2+8x=-12[/tex]
The rules are to take half the linear term, square it, and add it to both sides. Our linear term is 8. Half of 8 is 4, and 4 squared is 16. So we add 16 to both sides:
[tex](x^2+8x+16)=-12+16[/tex]
During this process we have created a perfect square biomial on the left. We will state that, along with simplifying on the right:
[tex](x+4)^2=4[/tex]
Now we will move the 4 back over and set it back to equal y:
[tex](x+4)^2-4=y[/tex]
And from this you can see that the coordinates of the vertex are (-4, -4)
The volume of a cylinder, given by the formula V= pie ^2 h, is 539 cubics inches. In the formula, r represents the radius and h represents the height of the cylinder. What equation represents the value of r in terms of h
Answer:
[tex]\displaystyle r=\sqrt{\frac{539}{\pi\cdot h}}[/tex]
Step-by-step explanation:
Fill in the value of the volume and solve for r.
[tex]539=\pi\cdot r^2\cdot h\\\\\dfrac{539}{\pi\cdot h}=r^2 \quad\text{divide by the coefficient of $r^2$}\\\\r=\sqrt{\dfrac{539}{\pi\cdot h}} \quad\text{take the square root}[/tex]
The row-reduced form of a system of three linear equations in three variables is given by this matrix. How many solutions does the system have?
Answer:
B. infinite solutions along a line
Step-by-step explanation:
The matrix is equivalent to the equations ...
x = 2
y = 9
0z = 0 . . . . . . true for any z
This tells you the solutions are ...
(x, y, z) = (2, 9, z)
This defines a line parallel to the z-axis.
Points A(-2, 4), B(1, 3), C(4, -1) and D form a parallelogram. What are the coordinates of D?
Answer:
D (1,0)
Step-by-step explanation:
Let the coordinates of D be (a,b).
The diagonals of a parallelogram bisect each other.
The midpoint of AC should be the same as the midpoint of BD.
[tex](\frac{-2+4}{2},\frac{4+-1}{2}) =(\frac{1+a}{2} ,\frac{3+b}{2})[/tex]
[tex](\frac{2}{2},\frac{3}{2}) =(\frac{1+a}{2} ,\frac{3+b}{2})[/tex]
Compare corresponding coordinates
This implies that:
[tex]1+a=2[/tex], [tex]3+b=3[/tex]
[tex]a=2-1[/tex], [tex]b=3-3[/tex]
[tex]a=1[/tex], [tex]b=0[/tex]
Therefore the coordinates of D are: (1,0)
Answer:
Option D for plato users
Step-by-step explanation:
D. (1, 0)
PLEASE HELP ASAP 35 PTS + BRAINLIEST TO RIGHT/BEST ANSWER.
Im pretty sure its b or d, but cant figure out which; please only answer if you’re positive!
Answer:
b
Step-by-step explanation:
(625x¹²y⁸)^¼
(5⁴x¹²y⁸)^½
5×x³×y²
5x³y²
5|x³|y²
For it to be positive,
x³ should be positive because 5 and y² already are positive.
Need help with reflection
Answer:
(1,6)
Step-by-step explanation:
In this question, the point (1,2) is first reflected on the line y=0 then followed by line y=2
In the first reflection, y=0, the line is the x-axis, so the point (1,2) is reflected on the x-axis. The law here is that reflection of a point (x,y) on the x-axis, will result to an image of (x,-y)
The point is (1,2), its image will be (1,-2)
The new image (1, -2) is then reflected on the line y=2 but you should be aware that the x-coordinate will remain the same, but the y-coordinate will change. This is to say that the y coordinate value will shift the same number of units above the line y=2 as it is below the line y=2
Point (1,-2) reflected on line y=2 will result to an image (1,6). The x-coordinate value has remained the same, where as the y coordinate value has shifted 4 units above the line y=2 because it was 4 units below the line y=2.
Final image will be (1,6)
What is the selling cost of a jacket that the store buys for $60 if the markup is 12%?
$52.80
$67.20
$76.80
$132.00
Answer: $67.20
Step-by-step explanation:
store buys jacket at 60 dollars and marks it up 12%
$60 x .12% = $7.20
$60 + $7.20 = $67.20
Is your received a $15,000 loan from the bank after six years she owes the bank 5000 in interest what was Angie’s interest-rate
Answer:
it would be 3.33%
Step-by-step explanation:
Answer:
about 5.55%
Step-by-step explanation:
The interest formula is ...
i = Prt
where i is the interest earned, P is the principal amount, r is the annual rate, and t is the number of years. Fill in the given information and solve for the remaining variable.
5000 = 15000·r·6
5000/90000 = r = 1/18 ≈ 5.55% . . . . . divide by the coefficient of r
____
Comment on the answer
The decimal value of 1/18 is 0.0555555... repeating indefinitely. Rounded to 3 digits, it would be 5.56%. The offered answer choices seem to give more attention to the repeating digits than to proper rounding.
PLEASE HELP BRAINLIEST
Answer:
there is a 25% chance that Tim takes 2 red sweets.
Step-by-step explanation:
P (2 red sweets)= 2/8
2/8 ÷ 2= 1/4
1/4= .25
.25= 25%
PLEASE HELP!! WILL MARK BRAINLEST?!
-Estimate the line of best fit using two points on the line.
Answer: I think is A
Step-by-step explanation:
You do y2-y1/x2-x1 and get a slope of 3 and according to the graph when the x is 3 the y is about 2 hope this help
Answer:
A
Step-by-step explanation:
if you do all the math will see that A is correct and the other guy said its A so its defently A
What is the probability of an event that is impossible? Suppose that a probability is approximated to be zero based on empirical results. Does this mean that the event is impossible?
Answer:
The probability of an event that is impossible is zero (0)No, a probability approximated to be zero based on empirical results does not mean that the event is impossible.Explanation:
For the first question, the mathematical (statistical, to be more precise) definition of a event that is impossible is that its probability is zero.
There are two extremes when you talk about probability: 0 and 1. 0 means that the event cannot occur in any way, while 1 is that the event is certain (it cannot not happen).
An example of an event with probability 0 is: men born in the Sun. This is an impossible event, and so there is no chance (probability 0) to find a man born in the Sun.
For the second question, when you deal with empirical results, this is with an experiment, the fact of having a probability zero as result of approximations does not make that an event be impossible; the event is unlikely (if the experiments were carried out properly) but yet it can happen.
For example, say you put 1,000 ballots in a bag with the number 3, together with 1 ballot with the number 9. Then, you perform the experiment of drawing a ballot 2,000 times. Suppose you draw the ballot with the number 9 two times. In that case, your approximated experimental probability of drawing a 9 will be 2 /2,000 = 0.001. Which you could round to 0.00. That may be valid but it cannot be taken as that the event of drawing the ballot with the number 9 is impossible, it is just unlikely.
Answer:
0
Step-by-step explanation:
.21875 as a fraction
Answer:
7/32
Step-by-step explanation:
0.21875 can be expressed as the fraction 7/32.
To express the decimal number 0.21875 as a fraction, we can follow these steps:
Step 1: Write the decimal number as a fraction with the same value as the original decimal number.
In this case, 0.21875 can be written as 21875/100000.
Step 2: Simplify the fraction if possible by finding the greatest common divisor (GCD) of the numerator and denominator.
The GCD of 21875 and 100000 is 625.
By dividing both the numerator and denominator by 625, we get:
21875/100000
= (21875 ÷ 625) / (100000 ÷ 625)
= 35/160.
Step 3: Further simplify the fraction if possible.
In this case, we can divide both the numerator and denominator by 5 to simplify the fraction:
35/160 = (35 ÷ 5) / (160 ÷ 5) = 7/32.
Therefore, 0.21875 can be expressed as the fraction 7/32.
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Please help, question above
Answer:
a + b - c - d
Step-by-step explanation:
The rules of exponents are ...
(x^a)(x^b) = x^(a+b)
(x^a)/(x^b) = x^(a-b)
Using these rules on your expression, we can simplify it to ...
(3^a) · (3^b) ÷ (3^c) ÷ (3^d)
= 3^(a+b) ÷ (3^c) ÷ (3^d)
= 3^(a+b-c) ÷ (3^d)
= 3^(a+b-c-d)
_____
The Order of Operations requires multiplication and division be evaluated left-to-right in order of appearance. The ÷ symbol means the same thing as the / symbol in this context: whatever is on its immediate left is divided by whatever is on its immediate right.
PLEASE HELP
Is there any sort of calculator or problem solver online that can let me input problems like these? I have absolutely no idea how to solve them, I have a ton of them, and I'm low on time to solve them. :(
First you must know that the sides 2x and x + 8 are equal to each other and sides x and 3x - 16 are equal to each other.
This means you can make a formula like so:
2x = x + 8
and
x = 3x - 16
Now you may solve for x for both of them (you should get the same answer for both x's)
2x - x = (x - x) + 8
x = 8
and
x - 3x = (3x - 3x) - 16
-2x = -16
-2x/-2 = -16/-2
x = 8
To find the length of each side just replace x with 8!
Hope this helped!
~Just a girl in love with Shawn Mendes
what is the total weight in pounds of 56 notebooks if each notebook weighs 5/8 lb? please show work
Answer:
Multiply the number of notebooks by the weight of one notebook.
When multiplying a whole number by a fraction, multiply the whole number by the top number of the fraction, and then divide that by the bottom number of the fraction.
56 x 5 = 280
280 / 8 = 35
The 56 notebooks weigh 35 pounds.
If $190 is invested at an interest rate of 11% per year and is compounded continuously, how much will the investment be worth in 4 years? Use the continuous compound interest formula: A = Pert
Answer:
$295.01
Step-by-step explanation:
Using the compounding continuously formula, we are looking for A. We have that P = 190; r = .11 (always use the decimal form of the rate!); and t = 4. Filling in we have:
[tex]A=190e^{(.11)(4)}[/tex]
Simplifying that multiplication:
[tex]A=190e^{.44}[/tex].
On your calculator, raise e to the .44 power to get
A = 190(1.552707219) and
A = $295.01
The investment should be worth in 4 years is $295.01.
Given that,
If $190 is invested at an interest rate of 11% per year and there is 4 years.Based on the above information, the calculation is as follows:
[tex]A = 190e^{0.11 \times 4}\\\\= 190e^{-44}\\\\= 190\times 1.55\\\\[/tex]
= $295.01
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Prehistoric cave paintings were discovered in a cave in france. the paint contained 24 %24% of the original carbon-14. use the exponential decay model for carbon-14, upper a equals upper a 0 e superscript negative 0.000121 ta=a0e−0.000121t, to estimate the age of the paintings. the paintings are approximately 1179411794 years old. (round to the nearest integer.) question is complete.
Answer:
t = 11,794 years
Step-by-step explanation:
If you are looking for a confirmation that your answer is correct, it is.
Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations. 9x-4y+z=-4. -x+2y-3z=20. 4x+4y-z=43
Answer:
d. (3, 7, -3)
Step-by-step explanation:
The reduced row-echelon form of the augmented matrix has 1s on the diagonal and zeros off-diagonal, except for the answer in the last column. It can be convenient to start by writing the augmented matrix using the second equation first:
[tex]\left[\begin{array}{ccc|c}-1&2&-3&20\\9&-4&1&-4\\4&4&-1&43\end{array}\right] \\\\\text{Add 9 times the first row to the second, and 4 times the first row to the third}\\\\\left[\begin{array}{ccc|c}-1&2&-3&20\\0&14&-26&176\\0&12&-13&123\end{array}\right][/tex]
[tex]\text{Subtract 2 times the third row from the second}\\\\\left[\begin{array}{ccc|c}-1&2&-3&20\\0&-10&0&-70\\0&12&-13&123\end{array}\right] \\\\\text{Divide the second row by -10}\\\\\left[\begin{array}{ccc|c}-1&2&-3&20\\0&1&0&7\\0&12&-13&123\end{array}\right][/tex]
[tex]\text{Subtract 2 times the second row from the first, and}\\\text{subtract 12 times the second row from the third}\\\\\left[\begin{array}{ccc|c}-1&0&-3&6\\0&1&0&7\\0&0&-13&39\end{array}\right] \\\\\text{Divide the third row by -13}\\\\\left[\begin{array}{ccc|c}-1&0&-3&6\\0&1&0&7\\0&0&1&-3\end{array}\right][/tex]
[tex]\text{Add 3 times the third row to the first, then multiply the result by -1}\\\\\left[\begin{array}{ccc|c}1&0&0&3\\0&1&0&7\\0&0&1&-3\end{array}\right][/tex]
The method may not be strictly according to some algorithm, but it avoids fractions and gives the correct result: (x, y, z) = (3, 7, -3).
Answer:
The answer is d. (3, 7, -3)
Step-by-step explanation:
100% sure I got a 100 on review exam
Through which angle of rotation does the image of a regular pentagon coincide with its preimage?
A 90 degrees
B 72 degrees
C 60 degrees
D 45 degrees
E 30 degrees
Answer:
Step-by-step explanation:
e
Answer: B- 72
Step-by-step explanation:
You take a random token from a bag that contains 44? red, 1414? green, and 66? blue tokens. What is the probability your token is red?
Answer:
11/381
Step-by-step explanation:
Not sure what the ? after each number means but I'm going to assume they aren't there
so we need find the number of tokens in all which is
44+1414+66=1524
P(red)=44/1524 now reduce giving P(red)=11/381
Moderators please delete this answer.
If I=PRT and P=$49,236.45, R=105% and T=2 years, estimate I
Answer:I=103395.6
Step-by-step explanation:
Using the formula for calculating interest (I) which is PRT, you substitute the given values for principal (P), rate (R), and time (T) respectively. First, calculate the product of principal P and rate R, then multiply this result by the time (T). Hence, the estimated interest is $103,396.54.
Explanation:The formula for calculating interest (I) is I = PRT. In your case, the principal (P) is $49,236.45, the rate (R) is 105% or 1.05 (we use decimal form for this calculation), and the time (T) is 2 years. To calculate interest, we substitute these values into the formula as follows:
I = $49,236.45 * 1.05 * 2
First, calculate the product of principal and rate: $49,236.45 * 1.05 = $51,698.27
Next, multiply this result by the time: $51,698.27 * 2 = $103,396.54
Therefore, the estimated interest is $103,396.54
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If A⊥Y and X || Y, then _____
In the context of mathematical geometry, if 'A⊥Y and X || Y', it means that A is perpendicular to Y and X is parallel to Y. In such a scenario, A would also be perpendicular to X.
Explanation:In mathematical terms, the symbols used in this question represent geometric relationships. Here, 'A⊥Y' means that A is perpendicular to Y, meaning A intersects with Y at a right angle (90 degrees). 'X || Y' signifies that X and Y are parallel, meaning they are in the same plane never intersect or meet, regardless of how far extended.
When it is given 'A⊥Y and X || Y', this suggests a specific geometric condition. In such a case, the vector A (or line/segment) is perpendicular to the vector Y. Also, the Vector X is parallel to Y. From these conditions, if one line is perpendicular to a second line, and a third line is parallel to the second line, then the first and third lines are also perpendicular to each other. Therefore, the conclusion in this case would be 'A is perpendicular to X' or 'A⊥X'.
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A photo of a painting measured 13 x 17 inches the scale of the photo to the original painting is 1 inch to 3 inches. What is the size of this painting
Answer:
29 × 51 inches
Step-by-step explanation:
If the scale is ...
photo : painting = 1 : 3
then each dimension of the painting is 3 times the corresponding dimension of the photo. The painting is (3×13) by (3×17) inches, or 39 × 51 inches.
Subtract (2x3 + 9x − 8) − (4x2 − 15x + 7).
Answer:
[tex]2x^{3}-4x^{2}+24x-15[/tex]
Step-by-step explanation:
we have
[tex](2x^{3}+9x-8)-(4x^{2}-15x+7)[/tex]
step 1
Eliminate the parenthesis
[tex]2x^{3}+9x-8-4x^{2}+15x-7[/tex]
step 2
group terms that contain the same variable
[tex]2x^{3}-4x^{2}+(9x+15x)+(-8-7)[/tex]
step 3
Combine like terms
[tex]2x^{3}-4x^{2}+24x-15[/tex]
1. Monica cashed her paycheck at Ready Cash. The fee at
Ready Cash to cash a check is 10% of the amount of the
check. Her paycheck was $538. How much was the fee
for Monica to cash her paycheck?
show my work like this
One of every 20 customers reports poor customer service on your company’s customer satisfaction survey. You have just created a new process that should cut the number of poor customer service complaints in half. What percentage of customers would you expect to report poor service after this process is implemented?
1.) 5%
2.) 10%
3.) 2%
4.) 2.5%
Answer:
4.) 2.5%
Step-by-step explanation:
1/20 = 5/100 = 5%
If that value is cut in half, it becomes ...
(1/2)×5% = 2.5%
Answer:
The correct option is 4) 2.5%
Step-by-step explanation:
Consider the provided information.
One of every 20 customers reports poor customer service on your company’s customer satisfaction survey.
First find the 1 is how much percent of 20.
[tex]\frac{1}{20}\times 100=1\times 5=5\%[/tex]
That means 5% of customers reports for poor customer services.
It is given that, You have just created a new process that should cut the number of poor customer service complaints in half.
Previously 5% of customers was not satisfy with the customer services, now only half of it not satisfy the customer service.
[tex]\frac{1}{2}\times 5\%=2.5\%[/tex]
Hence, the correct option is 4) 2.5%
Plz help :/
A mystery spinner is 50% RED and WHITE, while the rest is BLUE and GREEN. If 1/6 of the spinner is GREEN, how much is BLUE? (Show your work or explain completely.)
Answer:
1\2
Step-by-step explanation:
draw a circle split it where there are 6 slices color half red and white now color one of the slices green and the rest blue there are 2 slices out of 6 colored blue. Hope it helped! make sure to reduce
Final answer:
The spinner is half RED and WHITE, and the other half is BLUE and GREEN. With 1/6 of it being GREEN, the remaining fraction 1/3 of the spinner is BLUE.
Explanation:
To determine how much is BLUE on the mystery spinner, we must calculate the portions of each color. We know that the spinner is 50% RED and WHITE combined and the remainder is BLUE and GREEN. Since 1/6 of the spinner is GREEN, we have to find out what fraction is left for BLUE.
Firstly, we calculate what 50% is in fraction form, which is 1/2 of the spinner. Now, knowing that 1/6 of the spinner is GREEN, we subtract the GREEN fraction from the half not covered by RED and WHITE:
1/2 (portion of BLUE and GREEN) - 1/6 (portion of GREEN) = (3/6 - 1/6) = 2/6, which simplifies to 1/3.
Therefore, 1/3 of the spinner is BLUE.
When the graph of a quadratic function crosses the x-axis twice, the x-coordinate of the vertex lies ______ the two x-intercepts.
Answer:
"halfway between"
Step-by-step explanation:
The zero crossings are symmetrical about the line of symmetry, which is a vertical line through the vertex. The x-coordinate of the vertex s the average of the two x-intercepts, so lies between them--exactly halfway between them.
Answer:
Between
Step-by-step explanation:
The Vertex is a point where two or more curve meets. In the case of a quadratic equation, the vertex is at the minimum point (if a is positive) or at the maximum point (if a is negative).
When the graph of a quadratic function crosses the x-axis twice, the x-coordinate of the vertex lies between the two x-intercepts.
Note that the two x-intercepts are the roots of the quadratic function.
Find the area of this rhombus
The answer is:
The area of the rhombus is equal to 64 squared inches.
[tex]area=64in^{2}[/tex]
Why?Since we already know half of the length of the diagonals of the rhombus, we can calculate the area of the rhombus using the following formula:
[tex]area=\frac{diagonal_{1}*diagonal_{2}}{2}[/tex]
From the image we can see that:
[tex]diagonal_{1}=8in+8in=16in[/tex]
[tex]diagonal_{2}=4in+4in=8in[/tex]
So, substituting, we have:
[tex]area=\frac{16in*8in}{2}=\frac{128in^{2} }{2}=64in^{2}[/tex]
Hence, we have that the area of the rhombus is equal to 64 square inches.
Have a nice day!
Answer: SECOND OPTION.
Step-by-step explanation:
You can calculate the area of the rhombus with this formula:
[tex]A=\frac{d_1*d_2}{2}[/tex]
Where [tex]d_1[/tex] and [tex]d_2[/tex] are the lengths of the diagonals.
You can observe in the figure that the length of each diagonal is:
[tex]d_1=4in+4in=8in\\d_2=8in+8in=16in[/tex]
Now you can substitute the lenghts of the diagonals into the formula. Therefore, the area of this rhombus is:
[tex]A=\frac{(8in)(16in)}{2}[/tex]
[tex]A=\frac{128}{2}[/tex]
[tex]A=64in^2[/tex]
The owner of a small manufacturing plant employs six people. As part of their personnel file, the owner asked each employee to record the distance they travel one way from home to work. The six distances (in miles) are listed below. What is the range of the data? 2.4 5.2 1.8 4.9 6.4 3.5
Answer:
4.6
Step-by-step explanation:
Formula: Range = highest value - lowest value
Step 1: List all the data in ascending order
1.8, 2.4, 3.5, 4.9, 5.2, 6.4
Step 2: Identify the lowest and highest number
Lowest number : 1.8
Highest number : 6.4
Step 3 : Substitute the values in the formula
Range = highest value - lowest value
6.4 - 1.8 = 4.6
!!
All points to the of zero on a horizontal number line are negative. True or False
TRUE IT IS REALLY TRUEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
True, all points to the of zero on a horizontal number line are negative.
Step-by-step explanation:
Detailed explanation is as follows:
* All points to the left of zero on a horizontal number line are negative.
* A number line is a picture of a graduated straight line that serves as abstraction for real numbers.
* This number line can be extended to the left to represent numbers which are smaller than 0.
Tags: horizontal number line, points to the zero