Use completing the square to solve for x in the equation (x - 12)(x + 4) = 9.
A. x = -1 or 15
B. x = 1 or 7
C. x (plus sign over minus sign) square root of 41.
D. x (plus sign over minus sign) square root of 73.
Please help! This is timed!
Answer:
It is D.x=4+√73
Step-by-step explanation:
Got it right on edg.2022 :))
A circle has an area of 75 square centimeters. Which answer is closest to the measure of its radius?
A) 2.75 centimeters
B) 4.9 centimeters
C) 9.8 centimeters
D) 23.9 centimeters
Answer:
4.9
Step-by-step explanation:
Find complete factorization of the expression 32xy-56xyz
Leticia charges $8 per hour to babysit. She babysat Friday night for 4 hours, and then she babysat again on Saturday. She earned a total of $72. How many hours did Leticia babysit on Saturday? Choose two answers: one for the equation that models this situation and one for the correct answer.
First, we have to look at the equation that models this situation. We learn that the price per hour of babysitting is $8. On Friday, Leticia babysat for 4 hours, and on Saturday, she babysat an unknown amount of time. In total, she earned $72. Therefore:
8 ( 4 + x ) = 72
( 4 + x ) = 72 / 8
4 + x = 9
x = 9 - 4
x = 5
Leticia babysat 5 hours on Saturday.
A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or .
Since the area of the circle is the area of the square, the volume of the cylinder equals
the volume of the prism or (2r)(h) or πrh.
the volume of the prism or (4r2)(h) or 2πrh.
the volume of the prism or (2r)(h) or r2h.
the volume of the prism or (4r2)(h) or r2h.
The ratio of the area of the cross sectional circle and area of the cross sectional square is π : 4
What is the ratio of two quantities?Suppose that we've got two quantities with measurements as 'a' and 'b'
Then, their ratio(ratio of a to b) a:b or [tex]\dfrac{a}{b}[/tex]
We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).
Suppose that we've got a = 6, and b= 4, then:
[tex]a:b = 6:2 = \dfrac{6}{2} = \dfrac{2 \times 3}{2 \times 1} = \dfrac{3}{1} = 3\\or\\a : b = 3 : 1 = 3/1 = 3[/tex]
Remember that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unitless(no units) quantity.
For this case, we're specified that:
Radius of the circle of the cross section of the cylinder = r unitsSide length of the square cross section of the square prism = 2r unitsThen, the area of the circle is:
[tex]\pi r^2 \: \rm unit^2[/tex]
and the area of the square is: [tex]\rm side^2 = (2r)^2= 4r^2 \: \rm unit^2[/tex]
The ratio of the area of the circle to the area of the square is:
[tex]\dfrac{\pi r^2}{4r^2} = \dfrac{\pi}{4} = \pi : 4[/tex]
Thus, the ratio of the area of the cross sectional circle and area of the cross sectional square is π : 4
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A pair of vertical angles has measures
(2z+43)°
and
(−10z+25)°
.
What is the value of z? Vertical angles = each other
(2z+43)°
=
(−10z+25)°
−
3
2
−
11
4
−31
Answer:
The answer is Z equals negative 3/2
Step-by-step explanation:
Rewrite the equation of the parabola in vertex form. y= x2 + 8x - 21
Answer:
[tex]y=(x+4)^{2}-37[/tex]
Step-by-step explanation:
we know that
The equation of a vertical parabola into vertex form is equal to
[tex]y=a(x-h)^{2}+k[/tex]
where
(h,k) is the vertex of the parabola
if a> 0 then the parabola open upward (vertex is a minimum)
if a< 0 then the parabola open downward (vertex is a maximum)
In this problem we have
[tex]y=x^{2}+8x-21[/tex]
Convert to vertex form
Complete the square
[tex]y+21=x^{2}+8x[/tex]
[tex]y+21+16=(x^{2}+8x+16)[/tex]
[tex]y+37=(x^{2}+8x+16)[/tex]
[tex]y+37=(x+4)^{2}[/tex]
[tex]y=(x+4)^{2}-37[/tex] --------> equation in vertex form
The vertex is the point [tex](-4,-37)[/tex]
the parabola open upward (vertex is a minimum)
Answer:
the answer is y=(x+4)^2-37
Step-by-step explanation:
5÷4×6+e=5what does this equal ?
Identify the first step in solving the equation below. 2003-05-04-00-00_files/i0420000.jpg A. Subtract 2w from each side. B. Multiply each side by w. C. Add 2w to each side. D. Divide each side by 2.
Let v be the vector from initial point P1 to terminal point P2. Write v in terms of i and j. 2) P1 = (0, 0); P2 = (3, -4)
The vector [tex]\( \mathbf{v} = 6\mathbf{i} - 3\mathbf{j} \)[/tex].
Its magnitude is [tex]\( \sqrt{45} \)[/tex] in reduced radical form.
To find vector [tex]\( \mathbf{v} \)[/tex] from point [tex]\( P_1 \)[/tex] to point [tex]\( P_2 \)[/tex], we subtract the coordinates of [tex]\( P_1 \)[/tex] from the coordinates of [tex]\( P_2 \)[/tex]:
[tex]\[\mathbf{v} = \begin{pmatrix} x_2 - x_1 \\ y_2 - y_1 \end{pmatrix}\][/tex]
Given [tex]\( P_1 = (-2, 5) \) and \( P_2 = (4, 2) \), we can calculate \( \mathbf{v} \):[/tex]
[tex]\[\mathbf{v} = \begin{pmatrix} 4 - (-2) \\ 2 - 5 \end{pmatrix} = \begin{pmatrix} 6 \\ -3 \end{pmatrix}\][/tex]
So, [tex]\( \mathbf{v} = 6\mathbf{i} - 3\mathbf{j} \)[/tex].
To find the magnitude of [tex]\( \mathbf{v} \)[/tex], we use the formula:
[tex]\[|\mathbf{v}| = \sqrt{v_x^2 + v_y^2}\][/tex]
Where [tex]\( v_x \)[/tex] and [tex]\( v_y \)[/tex] are the components of [tex]\( \mathbf{v} \)[/tex]
For [tex]\( \mathbf{v} = 6\mathbf{i} - 3\mathbf{j} \), \( v_x = 6 \) and \( v_y = -3 \)[/tex]:
[tex]\[|\mathbf{v}| = \sqrt{(6)^2 + (-3)^2} = \sqrt{36 + 9} = \sqrt{45}\[/tex]
Thus, the magnitude of vector [tex]\( \mathbf{v} \) is \( \sqrt{45} \)[/tex] in reduced radical form.
Correct question is:
Let v be the vector from initial point P1 to terminal point P2.
Write v in terms of i and j, and find the magnitude of vector v.
Leave the magnitude in reduced radical form.
P1 = (-2,5) , P2 = (4,2)
Two circles have the same radius. Complete the description for whether the combined area of the two circles is the same as the area of a circle with twice the radius. The combined area of two circles with the same radius is ___πr2. The area of a circle with twice the radius is ___πr2. The combined area of two circles is as the area of a circle with twice the radius.
The circumference of a circle is 18.84 kilometers. What is the circle's radius? C=18.84 km Use 3.14 for . kilometers
The Circle's radius is roughly 3 kilometers.
To find the compass of a circle when given the circumference, we can use the formula
C = 2πr
where C is the circumference, and r is the compass.
Given that the circumference is18.84 kilometers, we can substitute these values into the formula and break for the compass
18.84 = 2 x3.14 x r
Dividing both sides of the equation by 2 x 3.14
18.84 /( 2 x 3.14) = r
Simplifying the right side
r ≈18.84/6.28
r ≈ 3 kilometers.
Thus, the circle's radius is roughly 3 kilometers.
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for a standard normal distribution whats the probability of getting a positive number
In a standard normal distribution, the probability of getting a positive number is 0.5.
Explanation:Probability of Getting a Positive Number in a Standard Normal Distribution
In a standard normal distribution, the probability of getting a positive number is 0.5. This is because the standard normal distribution is symmetric around 0, and half of the distribution lies to the right of 0, which corresponds to positive numbers.
To the nearest hundredth, what is the length of line segment AB ? Drag your answer into the box. The length of line segment AB is approximately units
9.54
10.44
13.00
13.15
Answer:
B. 10.44 units.
Step-by-step explanation:
We are asked to find the length of line segment AB.
To find the length of line segment AB we will use distance formula.
[tex]\text{Distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Upon substituting the coordinates of point A and B in distance formula we will get,
[tex]\text{Distance between point A and point B}=\sqrt{(1--9)^2+(-1--4)^2}[/tex]
[tex]\text{Distance between point A and point B}=\sqrt{(1+9)^2+(-1+4)^2}[/tex]
[tex]\text{Distance between point A and point B}=\sqrt{(10)^2+(3)^2}[/tex]
[tex]\text{Distance between point A and point B}=\sqrt{100+9}[/tex]
[tex]\text{Distance between point A and point B}=\sqrt{109}[/tex]
[tex]\text{Distance between point A and point B}=10.4403065089105502\approx 10.44[/tex]
Therefore, the length of line segment AB is 10.44 units and option B is the correct choice.
Answer:
I'm a nooby so 10.44.
Step-by-step explanation:
find the domain of the function f(x)=24/x^2-20x+96
what is the 4Th rule of probability in statistics?
Final answer:
The fourth rule of probability in statistics is the sum rule, which states that the probability of the occurrence of one event or the other event, of two mutually exclusive events, is the sum of their individual probabilities.
Explanation:
The fourth rule of probability in statistics is the sum rule. The sum rule is used when considering two mutually exclusive outcomes that can come about by more than one pathway. It states that the probability of the occurrence of one event or the other event, of two mutually exclusive events, is the sum of their individual probabilities.
For example, if we flip a penny (P) and a quarter (Q), the probability of getting one coin coming up heads and one coin coming up tails can be calculated as [(PH) (QT)] + [(QH) × (PT)]
=( [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] ) + ( [tex]\frac{1}{2}[/tex] ×[tex]\frac{1}{2}[/tex] )
[tex]= \frac{1}{2}[/tex]
it takes Joanna 15 minutes to complete 4 puzzles. At that rate, how many puzzles can she complete in 1 hour 45 minutes
A bag contains 15 green, 18 yellow, and 16 orange balls. One ball is randomly selected. To the nearest percent, what is the probability of the event? Drag and drop the correct value into the box. P(yellow)=
Since the bag contains 15 green, 18 yellow, and 16 orange balls, the total number of balls in the bag are 15+18+16=49.
Therefore, the probability of the event that the drawn ball is yellow is given by:
P(yellow)=[tex] \frac{Number of Yellow Balls}{Total Number of Balls} [/tex]
[tex] \therefore P(Yellow)=\frac{18}{49}\times 100\approx36.73\approx37 [/tex]%
Thus, the the probability of the event, to the nearest percent, that the drawn ball is yellow is 37%.
what is 6 ×2/3 in simplest form
Which fraction is between 0 and 1/2?
A. 2/3
B. 7/10
C. 3/5
D. 3/8
8,321/100 is equal to which number?
The percents of different drinks sold at a snack shop are shown in the circle graph. What percent of the drinks sold were colas?
cade road 1 3/5th miles on Saturday and 1 3/4th on Sunday. how far did he ride on the two days?
how many liters of a 60% acid solution must be mixed with a 75% acid solution to obtain 20L of a 72% solution
the expression below is scientific notation for what number??
NEED answer fast, please hurry. If events A and B are independent, and the probability that event A occurs is 83%, what must be true?
The probability that event B occurs is 17%.
The probability that event B occurs is 83%.
The probability that event A occurs, given that event B occurs, is 83%.
The probability that event B occurs, given that event A occurs, is 83%.
Answer:
the answer is C.
Step-by-step explanation:
83%
The true statement about the given conditional Probability is; The probability that event A occurs, given that event B occurs, is 83%.
How to Solve Conditional Probability?
We are told that If events A and B are independent, and the probability that event A occurs is 83%.
Now, Conditional probability like p(A|B) is the probability of event A occurring, given that event B occurs. Thus, applying that to our question means we can denote that;
The probability that event A occurs, given that event B occurs, is 83%.
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Find the inverse of the function. y = 2x2 –4
Answer:
The inverse function is [tex]y=\sqrt{\frac{x+4}{2}}[/tex]
Step-by-step explanation:
The given function is [tex]y=2x^2-4[/tex].
This function is only invertible on the interval, [tex]x\ge 0[/tex].
To find the inverse on this interval, we interchange [tex]x[/tex] and [tex]y[/tex].
[tex]x=2y^2-4[/tex]
We now make [tex]y[/tex] the subject to get,
[tex]x+4=2y^2[/tex]
[tex]\Rightarrow \frac{x+4}{2}=y^2[/tex]
[tex]\Rightarrow \pm \sqrt{\frac{x+4}{2}}=y[/tex]
But the given interval is [tex]x\geq 0[/tex], This implies that, [tex]y\geq 0[/tex].
[tex]y=\sqrt{\frac{x+4}{2}}[/tex]
A certain mixture of nuts contains cashews, almonds, and macadamia nuts. Each container must include three times as many almonds as cashews and twice as many cashews as macadamia nuts. If there are a total of 24 ounces in each container, how many ounces of cashews must be included?
can someone please help me
Which of the quadratic functions has the narrowest graph? Y = 1/6x^2, y = 2x^2, y = -x^2, y = 1/8x^2
Answer:
[tex]y=2x^2[/tex]
B is correct
Step-by-step explanation:
Given: We are given equation of parabola ans to choose narrowest graph.
[tex]y=ax^2[/tex]
Parabola form narrowest and widest.
Larger value of a most narrowest graph.
Smaller value of a most widest graph.
Now, we will see the coefficient of x²
[tex]y=\dfrac{1}{6}x^2,\ \ \ a=\dfrac{1}{6}[/tex]
[tex]y=2x^2,\ \ \ a=2[/tex]
[tex]y=-x^2,\ \ \ a=-1[/tex]
[tex]y=\dfrac{1}{8}x^2,\ \ \ a=\dfrac{1}{8}[/tex]
Now, we arrange the value of a in descending order.
[tex]2>1>\dfrac{1}{6}>\dfrac{1}{8}[/tex]
2 is largest value of these.
Hence, The narrowest graph is [tex]y=2x^2[/tex]