Answer:
10√7
Step-by-step explanation:
[tex]4 \sqrt{7} + 3 \times 2 \sqrt{7} \\ 4 \sqrt{7} + 6 \sqrt{7} \\ 10 \sqrt{7} [/tex]
Answer:
10√7
Step-by-step explanation:
To combine the radicals, you must have the same number under both radicands. Luckily, you can simplify one of the radicands. This is done by separating the radicand (√28) into its common factors (√4 x √7) and taking the square root of one of the factors (√4 = 2).
4√7 + 3√28 <---- Original expression
4√7 + 3(√4 x √7) <---- Expand √28
4√7 + (3 x 2)√7 <----- Take √4
4√7 + 6√7 <---- Multiply coefficients
10√7 <---- Add both terms
solve w^2 + 7w - 18 = 0
with the steps pls
Answer:
w=2 w = -9
Step-by-step explanation:
w^2 + 7w - 18 = 0
We can factor this equation
What 2 numbers multiply to -18 and add to 7
9*-2 = -18
9+-2 = 7
(w-2) (w+9) = 0
Using the zero product property
w-2 = 0 w+9 =0
w=2 w = -9
Answer:
[tex]w_1=2\\w_2=-9[/tex]
Step-by-step explanation:
This is going to be solved using the quadratic formula.
1. Determine the quadratic equation’s coefficient [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex].
Use the standard form, [tex]ax^2+bx+c=0[/tex] , to find the coefficients of our equation,
[tex]w^2+7w-18=0[/tex]:
a = 1
b = 7
c = -18
2. Plug these coefficients into the quadratic formula
The quadratic formula gives us the roots for [tex]aw^2+bw+c=0[/tex] , in which [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are numbers (or coefficients), as follows:
[tex]w=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
7 additional steps:
a = 1
b = 7
c = -18
[tex]w=\frac{-7\pm\sqrt{7^2=4*1*-18} }{2*1}[/tex]
Simplify exponents and square roots
[tex]w=\frac{-7\pm\sqrt{49-4*1*-18} }{2*1}[/tex]
Perform any multiplication or division, from left to right:
[tex]w=\frac{-7\pm\sqrt{49-4*-18}}{2*1}\\w=\frac{-7\pm\sqrt{49--72}}{2*1}\\\\w=\frac{-7\pm\sqrt{49+72}}{2*1}\\w=\frac{-7\pm\sqrt{121}}{2*1}[/tex]
to get the result:
[tex]w=\frac{-7\pm\sqrt{49-4*-18}}{2}[/tex]
3. Simplify square root [tex]\sqrt{121}[/tex]
Simplify 121 by finding its prime factors:
121 ( 11 * 11)
The prime factorization of 121 is 11^2
Write the prime factors:
[tex]\sqrt{121}=\sqrt{11\cdot 11}[/tex]
Group the prime factors into pairs and rewrite them in exponent form:
'[tex]\sqrt{11\cdot 11}=\sqrt{11^2}[/tex]
Use the rule [tex]\sqrt{x^2=x}[/tex] to simplify further:
[tex]\sqrt{11^2}=11[/tex]
4. Solve the equation for w
[tex]w=\frac{-7\pm11}{2}[/tex]
The ± means two answers are possible.
Separate the equations:
[tex]w_1=\frac{(-7+11)}{2}[/tex] and [tex]w_2=\frac{-7-11}{2}[/tex]
[tex]w_1=\frac{-7+11}{2}[/tex]
[tex]w_1=\frac{4}{2}[/tex]
[tex]w_1=2[/tex]
[tex]w_2=\frac{-7-11}{2}[/tex]
[tex]w_2=\frac{-18}{2}[/tex]
[tex]w_2=-9[/tex]
---------------------
Why learn this
In their most basic function, quadratic equations define shapes like circles, ellipses and parabolas. These shapes can in turn be used to predict the curve of an object in motion, such as a ball kicked by football player or shot out of a cannon. When it comes to an object’s movement through space, what better place to start than space itself—with the revolution of planets around the sun in our solar system. The quadratic equation was used to establish that planets’ orbits are elliptical, not circular. Determining the path and speed an object travels through space is possible even after it has come to a stop: the quadratic equation can calculate how fast a vehicle was moving when it crashed. With information like this, the automotive industry can design brakes to prevent collisions in the future. Many industries use the quadratic equation to predict and thus improve their products’ lifespan and safety.---------------
Terms and topics
Solving quadratic equations using the quadratic formulaSimplifying radicalsFind prime factors-----------
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(x-5/6)^2=1/36
Answer:
x = [tex]\frac{2}{3}[/tex] , x = 1
Step-by-step explanation:
(x - [tex]\frac{5}{6}[/tex] )² = [tex]\frac{1}{36}[/tex] ( take square root of both sides )
x - [tex]\frac{5}{6}[/tex] = ± [tex]\sqrt{\frac{1}{36} }[/tex] = ± [tex]\frac{1}{6}[/tex] ( add [tex]\frac{5}{6}[/tex] to both sides )
x = [tex]\frac{5}{6}[/tex] ± [tex]\frac{1}{6}[/tex] , then
x = [tex]\frac{5}{6}[/tex] - [tex]\frac{1}{6}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]
x = [tex]\frac{5}{6}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{6}{6}[/tex] = 1
What does the word progressive mean in the sentence below
What is the sentence and what are the questions. Until I know I can't help. But I should be able to answer if you can tell me
A pre-school has 12 four-year old children and 11 three-year old children. What is the ratio of four-year old
children to three-year old children?
Answer:
12:11
Step-by-step explanation
Answer:
I think it would be 12:11
Step-by-step explanation:
This is because you can't down size the 11
The weight, w, that a horizontal beam can support varies inversely as the
length, l, of the beam. a beam measuring 5 meters in length can support
430 kilograms. how much weight can a beam measuring 2 meters
support?
A beam measuring 2 meters can support 172 kilograms
How to determine the weight?The variation is a direct variation.
So, we have:
w = kl
Where k is the constant of variation.
When l = 5, w = 430.
This means that:
430 = 5k
Divide both sides by 5
k = 86
So, we have:
w = 86l
When l = 2, we have:
w = 86 * 2
Evaluate
w = 172
Hence, a beam measuring 2 meters can support 172 kilograms
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The radius of a wheel on a toy truck is 4 inches. To the nearest foot, how far does the wheel
travel when it makes 7 revolutions?
what type of parent function is f(x) = |x|
Answer: Absolute value function
The type of parent function is f(x)= |x| is Absolute valued function
What is Absolute valued function?
An absolute value function is a function that contains an algebraic expression within absolute value symbols.
Given function:
f(x)= |x|
As, we know the modulus generally give the absolute value of any function and also the modulus always give the positive value.
The above property perfectly resemble the absolute valued function.
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A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 23 times, and the man is asked to predict the outcome in advance. He gets 20 out of 23 correct. What is the probability that he would have done at least this well if he had no ESP
The probability that he would have done at least this well if he had no ESP is 0.99979
What is the probability of determining that he would have done well with no ESP?To determine the probability, we need to first find the probability of doing well with ESP.
The probability of having 20 correct answers out of 23 coin flips is:
[tex]\mathbf{=(\dfrac{1}{2})^{20}}[/tex]
Since we have 20 correct answers, we also need to find the probability of getting 3 answers wrong, which is:
[tex]\mathbf{=(\dfrac{1}{2})^{3}}[/tex]
There are [tex](^{23}_{20})[/tex] = 1771 ways to get 20 correct answers out of 23.
Therefore, the probability of doing well with ESP is:
[tex]\mathbf{= 1771 \times (\dfrac{1}{2})^{20}} \times (\dfrac{1}{2})^{3}}[/tex]
= 0.00021
The probability that he would have at least done well if he had no ESP is:
= 1 - 0.00021
= 0.99979
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Multiply the following
(a) 2.7x4
(b) 0.79x32.4
(c)1.07 x 0.02
(d) 2.3x4.35
(e) 2.5x100
(f) 0.0008x100
g) 0.25x 10000
h)3x0.55
i)0.08x5
j)351.06x4
k)0.3x0.03
l) 21.7x0.1
m) 200.02 x 2.2
Kindly look into this and try to answer all of them this contains 30 points
liz wants to determine which sport students like to play the most at her school.which method will most likely produce a random example.
Answer:
Random sampling
Step-by-step explanation:
Random sampling is a method of choosing a sample of observations from a population to make assumptions about the population. It is also called probability sampling.
1. You need a parking for your food truck, so you purchased 26 “parking hours” that you can use over the next month to park your food truck at the fair. Weekday hours cost $2/hour and weekend hours cost $10/hour. You spent a total of $220. How many weekday hours did you purchase?
2.If the weekday hours tripled but your budget of $220 for 26 parking hours remain the same. How many weekend hours can you purchase now that the weekday hours have increased?
The weekday hours you purchased is 5 hours.
The number of weekend hours I can purchase if the weekday hours tripled is 11 hours.
What are the linear equations that represent the question?2a + 10b = 220 equation 1
a + b = 26 equation 2
Where:
a = number of hours for weekday parking b = number of hours for weekend parkingHow many weekday hours did you purchase?
Multiply equation 2 by 10
10a + 10b = 260 equation 3
Subtract equation 3 from equation 2
8a = 40
a = 5 hours
What is the weekend hours I can purchase?
(5 x 3) + b = 26
15 + b = 26
b = 26 - 15
b = 11 hours
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Dale has $1,000 to invest. He has a goal to have $2,600 in this investment in 8 years. At what annual rate compounded continuously will Dale reach his goal?
Answer:
11.94 %
Step-by-step explanation:
Compound interest formula FV = PV e^(it) i = decimal interest per year
t = time FV = future value
2600 = 1000e^(i * 8)
solve for i = 11.94 %
Decide whether quadrilateral ABCD with vertices 4(-3,0), B(-4,1), C(-1.4), and D(0,3) is a rectangle, rhombus, square, or parallelogram.
Answer: rectangle
Step-by-step explanation:
The options imply the figure is a parallelogram. Furthermore, we can tell that not all the sides are congruent, so we can rule out the possibility that it is a rhombus or a square.
To determine if it is a rectangle, we can use the slope formula to determine if there is a pair of perpendicular sides. If this is the case, then this will be a parallelogram with a right angle, making it a rectangle.
[tex]m_{\overline{AB}}=\frac{1-0}{-4-(-3)}=-1\\m_{\overline{BC}}=\frac{4-1}{-1-(-4)}=1\\\therefore \overline{AB} \perp \overline{BC}[/tex]
So, the most specific classification is a rectangle
There is a bag filled with 5 blue and 4 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 of the same colour?
5 blue, 4 red = 9 total
Probability (Blue, Blue) = 5/9 x 5/9 = 25/81 = 0.30864
Probability (Red, Red) = 4/9 x 4/9 = 16/81 = 0.19753
Probability (Blue,Blue) or (Red,Red) = 25/81 + 16/81 = 41/81 = 0.506173
Fraction answer = 41/81
Decimal answer = 0.506173 (round off as needed)
Which three side lengths best describe the triangle in the diagram?
A. 6 cm, 8 cm, and 10 cm
B. 3 cm, 4 cm, and 5 cm
C. 5 cm, 8 cm, and 10 cm
D. 6 cm, 8 cm, and 9 cm
Please help me
The three side length that describes the triangle in the image attached below are: 5 cm, 12 cm, and 13 cm.
What is a Triangle?A triangle is a shape that has three sides. The sides can be measured using a ruler.
The sides of the triangle in the image shown have side lengths as measured by the ruler beside each of the sides, which are 5 cm, 12 cm, and 13 cm.
Therefore, the three side lengths of the triangle in the diagram are: 5 cm, 12 cm, and 13 cm.
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please answer this !!
uhm i dont know sorry but i can't help you
What is 1 2/3 multiple 2/3
Answer:
[tex]1\frac{1}{9}[/tex]
Step-by-step explanation:
Given the following question:
[tex]1\frac{2}{3} \times\frac{2}{3}[/tex]
In order to multiply the two, we have to convert the mixed number into a improper fraction and then multiply the numerator by the numerator, the denominator by the denominator.
[tex]1\frac{2}{3} =3\times1=3+2=\frac{5}{3}[/tex]
[tex]\frac{5}{3} \times\frac{2}{3}[/tex]
[tex]5\times2=10[/tex]
[tex]3\times3=9[/tex]
[tex]=\frac{10}{9}[/tex]
Convert the improper fraction into a mixed number:
[tex]\frac{10}{9}[/tex]
[tex]\frac{10}{9} =10\div9=1\frac{1}{9}[/tex]
[tex]=1\frac{1}{9}[/tex]
Your answer is "1 1/9."
Hope this helps.
Brainliest if you give correct answer + explanation
Answer:
x = 8
Step-by-step explanation:
Perimeter :
2(Length + Width) = 44 2x + 3 + x - 5 = 22 3x - 2 = 22 3x = 24 x = 8Marc is trying to determine how many blue marbles are in a bag of `100` marbles. he can only fit `10` marbles in his hand at a time. he takes `11` samples of `10` marbles, returning the marbles to the bag each time. based on these results, how many of the `100` marbles do you expect are blue
Based on the result from the box plot, the number of blue marbles is equal to the median of the data set and this is equal to 40.
What is a boxplot?A boxplot is a type of chart that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread. Also, the five-number summary include the following:
MinimumFirst quartileMedianThird quartileMaximumFor this exercise, we would create a box plot (see attachment) for the marbles in a bag of 100 marbles. By critically observing the box plot, we can logically deduce that the number of blue marbles is equal to the median of the data set and this is given by:
Median = 4 × 10
Median = 40.
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Don’t know how to solve.
Answer:
$122.88
Step-by-step explanation:
the phone decreases by 20% each year , that is
(100 - 20)% = 80% = [tex]\frac{80}{100}[/tex] = 0.8
the phone reduces by a factor of 0.8 each year , then after 4 years
value = $300 × [tex](0.8)^{4}[/tex] = $122.88
Is y=2x-3 a funtion?
Answer:
yes
Step-by-step explanation:
Yes.
The graph of y = 2x - 2 is a straight line sloping up to the right.
It passes the vertical line test, so it is a function.
The histogram shows the results of a survey that asked people how many hours of sleep they get each night. Which
statements are true?
The true statements are
The mean is near the median.
The mean is the best measure of center.
The five-number summary is the best measure of variation
What is a histogram?
A histogram is used to represent data graphically. The histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval.
If the mean is greater than the median, the histogram would be skewed to the right. If the mean is less than the median, the histogram would be skewed to the left.
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Which lists all of the x-intercepts of the graphed
function?
O (0, 6)
O (1, 0) and (2, 0)
O (1, 0), (2, 0), and (-3, 0)
O (1, 0), (2, 0), (-3, 0), and (0, 6)
Answer:
(1, 0), (2, 0), and (-3, 0)
Step-by-step explanation:
The x intercepts are where it crosses the x axis. It crosses at (-3,0), (1,0) and (2,0)
Which polynomial function could be represented by the graph below?
A. [tex]f(x) = x^2 - 4x[/tex]
B. [tex]f(x) = x^2 + 4x[/tex]
C. [tex]f(x) = -x^2 - 4x[/tex]
D. [tex]f(x) = -x^2 + 4x[/tex]
Answer:
[tex]f(x) = {x}^{2} + 4x[/tex]
Step-by-step explanation:
The graph is concave up, this means that the leading term x^2 is positive.
[tex]f(x) = {x}^{2} + 4x[/tex]
[tex]y = {x}^{2} + 4x[/tex]
For the x intercept, let y = 0[tex] {x}^{2} + 4x = 0[/tex]
[tex]x(x + 4) = 0[/tex]
[tex]x = 0 \: \: \: or \: \: \: \: x = - 4[/tex]
The x intercepts are:
(0 , 0) and (-4 , 0)
For the y intercept, let x = 0
[tex]y = {0}^{2} + 4(0) = 0[/tex]
y intercept :(0, 0)
For the turning point:[tex]t.p = \frac{x1 + x2}{2} [/tex]
[tex]t.p = \frac{0 + ( - 4)}{2} = - 2[/tex]
[tex]f( - 2) = {( - 2)}^{2} + 4( - 2) = - 4[/tex]
Turning point:(-2 , -4)
If you connect all these coordinates you will get the parabola shown in the picture.
Look at the following sequence.
54, 36, 24, 16, . . .
If it is a geometric sequence, choose the common ratio. If it is not a geometric sequence, choose “not geometric.”
Answer:
[tex]r \: = \: \boxed{ \bold{\frac{2}{3} }}[/tex]
Step-by-step explanation:
Calculate the ratio of the progression by dividing a term of it by the immediately preceding one.[tex]r \: = \: \frac{36}{54} \\ \\ r \: = \: \frac{24}{36} \\ \\ r \: = \: \frac{16}{24} [/tex]
We simplify the fractions:[tex]r \: = \: \frac{2}{3} \\ \\ r \: = \: \frac{2}{3} \\ \\ r \: = \: \frac{2}{3} [/tex]
Since the ratio is the same, that is the common ratio.
MissSpanishI need help, please. I don’t understand
Answer:
60%
Step-by-step explanation:
So, this question is saying the bowls can be between a diameter of 6.95 and 7.05
Box 1, 3 and 5 are in this margin.
Box 2 and 4 are not.
3/5 boxes can be included.
3/5 is 6/10
6/10 is 60%
Anyone mind helping me solve this inequality? Step by step
By decomposing the figure in simpler shapes, we will see that the total area is:
a = 180 cm²
How to find the area of the composite figure?
Remember that the area of a rectangle of width W and length L is:
A = L*W
And the area of a triangle with base B and height H is:
A = B*H/2.
Then, the upper part can be seen as a rectangle of length of 6cm and width of 6 cm, with two triangles on the sides, such that each triangle has a base of 3cm and a height of 6cm.
So the area of that part is:
A = 6cm*6cm + 2*(3cm*6cm/2) = 54cm²
Now, the bottom triangle has a base of 12 cm, and a height of:
15cm - 6cm = 9cm
Then its area is:
A' = 12cm*9cm/2 = 54cm²
This means that the total area of the figure is:
total area = 54cm² + 54cm² = 108cm²
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9(w – 4) – 7w = 5(3w – 2)
Answer:
-2 =w
Step-by-step explanation:
9(w – 4) – 7w = 5(3w – 2)
The first step is to distribute
9w -36 - 7w = 15w -10
Combine like terms
2w -36 = 15w -10
Subtract 2w from each side
2w -36 -2w = 15w-10-2w
-36 = 13w -10
Add 10 to each side
-36+10 =13w-10+1-
-26 = 13w
Divide by 13
-26/13 =13w/13
-2 =w
Please help asap 25 points
Answer:
[tex]y = - 2 |x - 2| + 4[/tex]
Step-by-step explanation:
as the function moved to the right 2 steps, and up 4 steps
A cylinder has a radius of 12 m and a height of 9 m.
What is the exact volume of the cylinder?
108π m³
216π m³
972π m³
1296π m³
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=12\\ h=9 \end{cases}\implies V=\pi (12)^2(9)\implies V=1296\pi ~m^3[/tex]