Answer:
-14
Step-by-step explanation:
Observe first that $x=0$ is not a solution to the equation since it makes the denominator of $\frac{1}{2x}$ equal to 0. For $x\neq 0$, we may multiply both sides by both denominators and move all the resulting terms to the left-hand side to get $2x^2-2rx+7=0$. Observe that there are two ways the original equation could have exactly one solution. Either $2x^2-2rx+7=0$ has two solutions and one of them is 0, or else $2x^2-2rx+7=0$ has exactly one nonzero solution. By trying $x=0$, we rule out the first possibility.
Considering the expression $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ for the solutions of $ax^2+bx+c=0$, we find that there is exactly one solution if and only if the discriminant $b^2-4ac$ is zero. Setting $(-2r)^2-4(2)(7)$ equal to 0 gives $4r^2-4(14) = 0$. Add 4(14) and divide by 4 to find $r^2=14$. The two solutions of this equation are $\sqrt{14}$ and $-\sqrt{14}$, and their product is $\boxed{-14}$.
The value of r from the given equation is r=(2x²+7)/2x.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is [tex]\frac{1}{2x}=\frac{r-x}{7}[/tex].
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
By cross multiplication, we get
7=2x(r-x)
7=2rx-2x²
2rx=7+2x²
r=(2x²+7)/2x
Therefore, the value of r from the given equation is r=(2x²+7)/2x.
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Is 100.1 rational or irrational
Answer:
It's rational number
Step-by-step explanation:
if a number is non stop it is irrational
it a number stops as it stopped here at 1 so it's a rational number
Answer:
Rational
Step-by-step explanation:
It's a decimal with no recurring digits:)
For how many positive integer values of N is the expression 36/N + 2 an integer?
Answer:
Step-by-step explanation:
36=2×2×3×3
factors of 36 are 2,3,4,6,9,12,18,36
when N+2=2,N=0 (0 is neither positive nor negative.)
N+2=3,N=3-2=1
N+2=4,N=4-2=2
N+2=6,N+6-2=4
N+2=9,N=9-2=7
N+2=12
N=12-2=10
N+2=18,N=18-2=16
N+2=36,N=36-2=34
so for 7 positive integer values of N,36/(N+2)is a positive integer.
Since there are 8 factors of 36 hence 8 positive integers are possible for the expression 36/N + 2 to be an integer
The total number of positive integers needed will be equivalent to all the factors of 36 as shown;The factors of 36 are 1, 2, 3, 6, 9, 12, 18, 36. Since there are 8 factors of 36 hence 8 positive integers are possible for the expression 36/N + 2 to be an integerLearn more on factors here: https://brainly.com/question/25829061
You are selling lemonade for $1.50, a bag of kettle corn for $3, and a hot dog for $2.50 at a fair. Write and simplify an expression for the amount of money you receive when p people buy one of each item
Answer:
1.5p + 3p + 2.5p
Step-by-step explanation:
This expression, 1.5p + 3p + 2.5p, will represent the amount of money received when p people buy one of each food item.
Since the price of each is the coefficient for p, this will represent how much money will be gained from each food item. All 3 terms will be added together to represent the total amount of money gained from selling all 3 items.
PLEASE HELP 46 POINTS!!!
Answer:
Step-by-step explanation:
a) Input = -9 ⇒ x = -9
y = x² + 3
Plugin x = (-9),
y = (-9)² + 3
= 81 + 3 {(-9)² = -9 * (-9) = 81}
y = 84 ---> Output
y = √x - 2
= √-9 - 2 { i² = -1}
[tex]= \sqrt{3*3 * i^{2}}-2\\\\=3i -2[/tex]
y = 3i - 2 ------> Output
b) Output = 0
y = x² + 3
x² + 3 = 0
x² = -3
[tex]x = \sqrt{-3}=\sqrt{3i^{2}}\\\\x = i \sqrt{3}[/tex]
y = √x -2
0 = √x - 2
√x = 2
Take square,
[tex](\sqrt{x})^{2}=2^{2}\\\x = 4[/tex]
The interquartile range is determined by the formula _________.
A. Third quartile - First quartile
B. Third quartile + first quartile
C. First quartile - third quartile
D. Maximum - minimum
Answer:
A)
Step-by-step explanation:
The inter quartile range is determined by the formula Third quartile - first quartile.
In a set, an inter quartile range is a measure of where the bulk of the data's lie
1. What property could you use to show that triangles ACT and ODG are congruent?
Answer:
SSS
Step-by-step explanation:
We do not know any of the angles, and we also do not know if the triangles are right triangles. Thus, SSS is the only option left. We know that all three sides are congruent anyway.
Answer:
SSS
Step-by-step explanation:
AC = OD
AT = OG
CT = DG
You have three congruent sides making ΔACT & ΔODG congruent by SSS.
please solve this ASAP. I need this done but I can't figure it out
Answer:
x = 61
Step-by-step explanation:
Supplementary angles add up to 180 degrees. We can create an equation and solve for x.
(2x + 6) + (x - 9)= 180
~Combine like terms
3x - 3 = 180
~Add 3 to both sides
3x = 183
~Divide 3 to both sides
x = 61
Best of Luck!
I need help on this question pls
56/64 = 7/8
7/8 x 120
105.
the function h(x) is a transformation of the square root parent function
Answer:
h(x)=\sqrt(x+6)
Step-by-step explanation:
I just did the test for a p e x
Write each of the following in the simplest exponential form please help
Answer:
Step-by-step explanation:
[tex]a^{m}*a^{n} =a^{m+n}\\\\\\2^{3}*2^{5} = 2^{3+5} =2^{8}\\\\\\3^{2}*3^{4}=3^{2+4} = 3^{6}\\\\\\a^{2}*a^{5}=a^{2+5}=a^{7}[/tex]
solve this it attached
[tex]\\ \sf\longmapsto \dfrac{15}{k}[/tex]
k=3Put the value
[tex]\\ \sf\longmapsto \dfrac{15}{3}[/tex]
[tex]\\ \sf\longmapsto 5[/tex]
[tex]\large\bf{\orange{ \implies}} \tt \: \frac{15}{k} \\ [/tex]
Value of k is 3
[tex]\large\bf{\purple{ \implies}} \tt \: \cancel\frac{15}{3} \: = \: 5 \: \\ [/tex]
In a recent Super Bowl, a TV network predicted that 53 % of the audience would express an interest in seeing one of its forthcoming television shows. The network ran commercials for these shows during the Super Bowl. The day after the Super Bowl, and Advertising Group sampled 79 people who saw the commercials and found that 41 of them said they would watch one of the television shows.Suppose you have the following null and alternative hypotheses for a test you are running:H0:p=0.53H0:p=0.53Ha:p≠0.53Ha:p≠0.53Calculate the test statistic, rounded to 3 decimal places
======================================================
Explanation:
We're conducting a one proportion Z test.
The hypothesized population proportion is p = 0.53, which is not to be confused with the p-value (unfortunately statistics textbooks seem to overuse the letter 'p'). Luckily this problem is not asking for the p-value.
The sample population proportion is
phat = x/n = 41/79 = 0.518987 approximately
The standard error (SE) is
SE = sqrt(p*(1-p)/n)
SE = sqrt(0.53*(1-0.53)/79)
SE = 0.056153 approximately
Making the test statistic to be
z = (phat - p)/(SE)
z = (0.518987 - 0.53)/0.056153
z = -0.19612487311452
z = -0.196
Which is approximate and rounded to 3 decimal places.
anyone know how to solve a functions equation such as x^2-x-x <0
Answer:
Step-by-step explanation:
[tex]x^{2} -x-x<[/tex] 0
[tex]x^{2} -2x[/tex] < 0
x^2-2x+1<1
(x-1）^2<1
-1<x-1<1
0<x<2
[tex](x-1)^{2}[/tex][tex](x-1)^{2}[/tex]
find the extrema of the function y=cos2x
Answer:
Step-by-step explanation:
Find derivative of the function:
y' = -2·sin(2·x)
-2·sin(2·x) = 0
x1 = 0
x2 = 3.142
f(0) = 1
f(3.142) = 1
Answer
fmin = 1, fmax = 1
6) By which least number should each of the following numbers be divided to make them perfect squares? b) 45125
45125|5
9025|5
1805|5
361|19
19|19
1
[tex]45125=5^3\cdot 19^2=5^2\cdot 5\cdot19^2[/tex]
It's 5
FOR EASY BRAINLIEST ANSWER THESE QUESTIONS:
1.
2.
3.
4.
5.
Step-by-step explanation:
all answers and steps are in picture
Evaluate the expression 5^-2
Answer:
[tex]\boxed{\frac{1}{25} \text { OR } 0.04}}[/tex]
Step-by-step explanation:
[tex]5^{-2}\\\\\text {Apply Negative Exponent Rule: } a^{-b}=\frac{1}{a^b}\\\\5^{-2}=\frac{1}{5^2}=\boxed{{\frac{1}{25}} \text { OR } 0.04}[/tex]
Helena builds a shed in her backyard. There is a larger section for large tools, like her lawn mower, and a smaller section for small tools. What is the length of the entire shed? What type of number is the length? List as many types of numbers for the length as you can.
Answer:
4+5[tex]\sqrt{2}[/tex] ft
Step-by-step explanation:
The type o the length of the shed will be a real number and a rational number. Then the correct option is B and E.
What is a number system?The continuous portrayal of numerals using digits and perhaps other marks is known as a number system.
If the value of a numerical expression is terminating then they are the rational number then they are called the rational number.
Helena builds a shed in her backyard.
There is a larger section for large tools, like her lawn mower, and a smaller section for small tools.
The type o the length of the shed will be a real number and a rational number.
Then the correct option is B and E.
The complete question is attached below.
More about the number system link is given below.
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Find the probability that a randomly selected point within the circle falls in the white area. Please, and thank you.
Answer:
About 68.2%.
Step-by-step explanation:
We want to find the probability that a randomly selected point lands in the white area.
To do so, we can find the probability that the point does not land in the white area (i.e. the red area) and then subtract it from 100%.
The circle has a radius of 4 cm. Note that the base of the triangle is the diamater, so the base measures 8 cm. The height of the triangle is the radius, so it measures 4 cm. Thus, the area of the triangle is:
[tex]\displaystyle \begin{aligned} A &= \frac{1}{2}bh \\ &= \frac{1}{2}(8)(4) \\ &= 16\text{ cm}^2\end{aligned}[/tex]
Likewise, the area of the entire circle will be:
[tex]\displaystyle \begin{aligned} A &= \pi r^2 \\ &= \pi(4)^2 \\ &=16\pi \text{ cm}^2\end{aligned}[/tex]
Then the probability that a randomly seleted point lands in the red area is:
[tex]\displaystyle P\left(\text{Red}\right) = \frac{\text{Red}}{\text{Total}} =\frac{16}{16\pi} = \frac{1}{\pi}[/tex]
The probability that the point lands in the red area or the non-red area (i.e. white area) must total 100%. In other words:
[tex]\displaystyle P\left(\text{Red}\right) + P\left(\text{White}\right) = 1[/tex]
Thus:
[tex]\displaystyle P\left(\text{White}\right) = 1 - P\left(\text{Red}\right)[/tex]
Substitute:
[tex]\displaystyle P\left(\text{White}\right) = 1 - \left(\frac{1}{\pi}\right)[/tex]
Use a calculator. Hence:
[tex]\displaystyle P\left(\text{White}\right) \approx 0.6817 = 68.2\%[/tex]
The probability that a randomly selected point lands in the white area is about 68.2%.
Just need help
the equations are above
Answer:
6×4p=24p
15a÷3=5a
3t×8y=24ty
24ef÷12e=2f
-4fx-5px-3 =-x(4f+5p)-3
-9abc÷3a=-3bc
5-5√3/2-√11 rationalize
Step-by-step explanation:
[tex] \frac{5 - 5 \sqrt{3} }{2 - \sqrt{11} } [/tex]
To rationalize the surd multiply both the numerator and the denominator by
2 + √11
That's
[tex] \frac{5 - 5 \sqrt{3} }{2 - \sqrt{11} } \times \frac{2 + \sqrt{11} }{2 + \sqrt{11} } [/tex]
Multiply the numerators and the denominator separately
That's
[tex] \frac{(5 - 5 \sqrt{3} )(2 + \sqrt{11} )}{(2 - \sqrt{11})(2 + \sqrt{11} ) } [/tex]
Simplify
[tex] \frac{10 + 5 \sqrt{11} - 10 \sqrt{3} - 5\sqrt{33} }{?} [/tex]
[tex] \frac{10 + 5 \sqrt{11} - 10 \sqrt{3} - 5 \sqrt{33} }{4 - 2 \sqrt{11} + 2 \sqrt{11} - 11} [/tex]
[tex] \frac{10 + 5 \sqrt{11} - 10 \sqrt{3} - 5 \sqrt{33}}{4 - 11} [/tex]
[tex] \frac{10 + 5 \sqrt{11} - 10 \sqrt{3} - 5 \sqrt{33}}{ - 7} [/tex]
We have the final answer as
[tex] - \frac{10 + 5 \sqrt{11} - 10 \sqrt{3} - 5 \sqrt{33}}{7} [/tex]
Hope this helps you
Sum and Product of zeroes of the quadratic polynomial 16s² - 16s + 4 respectively is:Sum and Product of zeroes of the quadratic polynomial 16s² - 16s + 4 respectively is:
Answer:
The sum and product of zeroes are 1 and 1/4, respectively.
Step-by-step explanation:
To determine the zeroes of the quadratic polynomial, let equalize the polynomial to zero and solve in consequence:
[tex]16\cdot s^{2}-16\cdot s + 4 = 0[/tex]
By the General Quadratic Formula:
[tex]s_{1,2} = \frac{16\pm \sqrt{(-16)^{2}-4\cdot (16)\cdot (4)}}{2\cdot (16)}[/tex]
[tex]s_{1,2} = \frac{1}{2}[/tex]
Which means that zeroes are [tex]s_{1}=s_{2}=\frac{1}{2}[/tex].
The sum and product of zeroes are, respectively:
[tex]s_{1}+s_{2} =\frac{1}{2}+\frac{1}{2}[/tex]
[tex]s_{1}+s_{2} = 1[/tex]
[tex]s_{1}\cdot s_{2} = \left(\frac{1}{2} \right)^{2}[/tex]
[tex]s_{1}\cdot s_{2} = \frac{1}{4}[/tex]
The sum and product of zeroes are 1 and 1/4, respectively.
Which expression has the same value as 4x – 3y?
O 3y - 4x
0 -3y - 40
Submit Answer
4x + 3y)
0-4x + (-3y)
POP Teleco
o
Answer:
4x+(-3y)
Step-by-step explanation:
[tex]\\ \rm\longmapsto 4x+(-3y)[/tex]
(-)(-)=(+)(+)(-)=(-)(-)(+)=(-)(+)(+)=(+)[tex]\\ \rm\longmapsto 4x-3y[/tex]
If the lateral surface area of a cube is 100 square inches, what is the length of an edge?
Answer:
Length of an edge=4.0825 inches
Approximately 4.1 inches
Step-by-step explanation:
Lateral surface area of a cube=100 square inches
There are 6 square surfaces on a cube.
6a^2=surface area of a cube
6a^2=100
Divide both sides by 6
a^2=100/6
a^2=16.6667
Find the square root of both sides
√a^2=√16.6667
a=√16.6667
x=4.0825 inches
Length of an edge=4.0825 inches
Answer:
2√5
Step-by-step explanation:
I got it correct on founders edtell
find the volume of each figure. Round to the nearest tenth if necessary.
Answer:
3166.7
Step-by-step explanation:
Volume=pi*r^2*h
=pi*12^2*7=3166.7
Answer:
3166.7
Step-by-step explanation:
Volume of a cylinder= pi × radius² × height
3.14 × 12² ×7 = 3166.7
Help please! <3 Simplify the expression to find the correct answer. Show your work and explain how you got that answer. [tex]\frac{1}{3}\sqrt{21}-\frac{2}{3}\sqrt{3} x \sqrt{7}[/tex] A. [tex]-\frac{1}{3}\sqrt{21}[/tex] B. [tex]\frac{2}{3}\sqrt{21}[/tex] C. [tex]\frac{2}{3}\sqrt{18×7}[/tex] D. [tex]-\frac{1}{3}\sqrt{63}x\sqrt{7}[/tex]
Answer:
-1/3 sqrt(21)
Step-by-step explanation:
1/3 sqrt(21) - 2/3 sqrt(3) * sqrt(7)
We know sqrt(a) * sqrt(b) = sqrt(ab)
1/3 sqrt(21) - 2/3 sqrt(21)
Factor out sqrt(21)
sqrt(21) (1/3-2/3)
sqrt(21) (-1/3)
-1/3 sqrt(21)
Answer: Choice A) [tex]-\frac{1}{3}\sqrt{21}[/tex]
=====================================================
Work Shown:
I'm guessing that the x you wrote is to signify multiplication. If so, then one way to do the steps is shown in the attached image below.
In step 2, I used the rule that sqrt(x)*sqrt(y) = sqrt(x*y).
LENGTH OF ARCS. URGENT.
Since the angle of the arc is 90°, we'll plug that in for theta. We're finding the length of the arc, so we'll use the circumference formula.
please help!!! will give brainliest!!!
Answer:
the image or text isnt there?
Step-by-step explanation:
The cosst of 4 1 /4 kg of sugar is £68 .find the coast o 1 kg
Step-by-step explanation:
Hi, there!!
Here according to the question we must find the cost of 1 kg sugar.
Given that:
17/4 kg of sugar cost £68.
then 1 kg sugar costs,
=[tex] \frac{68}{ \frac{17}{4} } [/tex]
after reciprocal we get,
= £68×4/17
=£16
The answer would come £16.
Therefore, The cost of 1 kg sugar is £. 16.
Hope it helps....
Answer:
£ 16
Step-by-step explanation:
Cost of 4 1/4 kg sugar = £ 68
4 1/4 = 17/4
Cost of 17/4 kg of sugar = 68
Cost of 1 kg of sugar =68 ÷ (17/4)
[tex]= 68* \frac{4}{17}\\\\=4*4\\[/tex]
= £ 16
A can do a piece of work in 3 days and B in 6 days. In how many days will they do it together?
Answer: 2 days
Step-by-step explanation:
We will add there work together
= 1/3 + 1/6
= 2/6 + 1/6 (LCM 6)
= 3/6
= 1/2
Therefore 1/2 = 2 days
Therefore it will take them 2 days
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