Step-by-step explanation:
Let the required number be x.
Therefore, according to the given condition:
[tex] {x}^{2} - 10 = 3x \\ \therefore \: {x}^{2} - 3x - 10 = 0 \\ \therefore \: {x}^{2} - 5x + 2x - 10 = 0 \\ \therefore \: x(x - 5) + 2(x - 5) = 0 \\ \therefore \: (x - 5)(x + 2) = 0 \\ \therefore \: x - 5 = 0 \: \: or \: \: x + 2 = 0 \\ \therefore \: x = 5 \: \: or \: \: x = - 2 \\ [/tex]
Therefore, x = - 2 is the negative solution.
Good morning ☕️
Answer:
the negative solution is -2Step-by-step explanation:
First ,we need to model the situation by expressing it as an equation
so, let x represent the uncknown negative number :
We get
x² - 10 = 3x
then
x² - 3x - 10 = 0
now using the quadratic formula:
Let Δ be the discriminant
Δ = b² - 4ac = (-3)² - 4(1)(-10) = 9 + 40 = 49 → √∆ = 7
Therefore
[tex]x = \frac{3+7}{2}=5 \\or\\x= \frac{3-7}{2}=-2[/tex]
_______________________________________
:)
Use the Pythagorean Theorem to find the missing length and then round the result to the nearest tenth.
a = 4, b = 4, c =
Answer:
Answer is 5
Step-by-step explanation:
if you have any doubts see the image
The Pythagorean Theorem was used on a right triangle with sides of length 4 to find that the hypotenuse has a length approximately equal to 5.7.
Explanation:Here, your task is to apply the Pythagorean Theorem which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, both a and b are given as 4. We can therefore calculate c as follows:
First, square the lengths of both a and b: 4^2 + 4^2 = 16 + 16Combine like terms: 16 + 16 = 32Find the square root of the sum to find c: sqrt(32) is approximately 5.7 (to the nearest tenth).Learn more about Pythagorean Theorem here:https://brainly.com/question/19649203
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WILL GIVE BRAINLIEST!!!
Jack wants to determine the best-selling CD in his town. He surveys 30 shoppers as they leave the mall. What type of sampling is this?
Need answer for this please
Answer:
Learning about functions vs. new language
Step-by-step explanation:
They both follow strict laws (typically stricter for functions).Practice makes perfect: both can be learned to points of practical perfection.The brain must first attribute meaning or value to elements of either in order to build a learning pattern.There are 8 male teachers and 5 female teachers who teach English in the school. What is the ratio of the number of male teachers to the number of female teachers?
Answer:
8:5
Step-by-step explanation:
Given there are 8 male teachers and 5 female teachers,The ratio of number of male teachers to female teachers
= no. Of male teachers/no. Of female teachers
That’s
8/5
8:5
8:5 = 160%
theres not really an explanation to this hope it helps :)
What is the measure of ABC?
Answer:
120
Step-by-step explanation:
The projected value (in millions of dollars) of a large manufacturing company is modeled by the function V(t) = 230(1.12)t, where V(t) is the value of the company t years after 2018. What does 230 represent in the function?
A) The growth factor of the company.
B) The value of the company in 2018.
C) The projected value of the company.
D) The value of the company after t years.
230 is the value of the company in 2018.
Option (B) is correct.
To find 230 represent in the function.
What is arithmetic?science that deals with the addition, subtraction, multiplication, and division of numbers.
It is given that:
The equation of a exponential growth function is equal to
[tex]V(t)=a(1+r)^{t}[/tex]
where,
V(t) is the value of the company
t is the number of years after 2018
a is the initial value or y-intercept
r is the rate of change
Put the value,
a=230
1+r=1.12
r=1.12-1=0.12
r=12%
so 230 is the value of the company when the value of t is equal to zero.
Remember that t is the number of years since 2018
Therefore ,230 is the value of the company in 2018.
Learn more about arithmetic here:
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An article reports that blue eyed people earn less than brown eyed people, with these numbers: average blue-eyed salary $35,000, average brown-eyed salary $37,000, p-value 0.45. Based on that reported p-value, and using the common definition of "statistical significance," which is the case?
a. The results are nowhere near to being statistically significant.
b. The results are almost but not quite statistically significant.
c.The results are just barely statistically significant.
d.The results are strongly statistically significant.
A group of 10 people is choosing a chairperson and vice-chairperson. They put all 10 people's names into a hat. The first name drawn becomes chair. The second name drawn becomes vice-chair. How many possible combinations of chair and vice-chair are there?
a.19
b.90
c.100
d.10! (10 factorial)
Answer:
a.
Step-by-step explanation:
A p-value less than 0.05 (typically ≤ 0.05) is statistically significant. It indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null is correct (and the results are random). Therefore, we reject the null hypothesis, and accept the alternative hypothesis.
------------------------
First question:
The first question involves the test of an hypothesis.
Tests have significance levels, which normally are either 0.01, 0.05 or 0.1. If the p-value is less than the significance level, the results are significant, while if they are more, the results are not significant.
In this question, the p-value is 0.45, which is considerably more than any significance level, meaning that the results are nowhere near to being statistically significant, and the correct option is:
a. The results are nowhere near to being statistically significant.
A similar problem can be found at https://brainly.com/question/22968227
------------------------
Second question:
The order in which the people are chosen is important, as the first and second person chosen have different roles, and thus, the permutations formula is used.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, there are 2 people from a set of 10, so:
[tex]P_{10,2} = \frac{10!}{8!} = 10\times9 = 90[/tex]
90 possible combinations, option b.
A similar problem can be found at https://brainly.com/question/24245547
Find the value of x.
Answer:
x = 8
Step-by-step explanation:
Two secants drawn from an external point to the circle.
The (outside ) × (whole) of one secant is equal to the (outside) × (whole) of the other secant, that is
(x + 2)(x + 2 + 2x - 8) = (x + 1)(x + 1 + 2x - 5)
(x + 2)(3x - 6) = (x + 1)(3x - 4) ← expand both sides using FOIL
3x² - 12 = 3x² - x - 4 ( subtract 3x² - x - 4 from both sides )
x - 8 = 0 ( add 8 to both sides )
x = 8
Sarah has 2 apples bob eats 1 how much does sarah have after bob ate one
Answer:
sarah has 1 apple left
Rene’s parents have put a half hour daily limit on how long the tv is watched in their house. What is the maximum number of hours that can be watched over 7 days if they stick to the limit?
Answer:
3.5
Step-by-step explanation:
30 · 7 = 210
210 ÷ 60 = 3.5
The sum of two numbers is 14. The larger number minus three times the lesser number is -2. What is the lesser number?
A) 10
B) 12
C) 4
D) 3
Answer:
c) 4
Step-by-step explanation:
The sum of two numbers is 14. The larger number minus three times the lesser number is -2
To solve this question, we need to write the statement mathematically;
Let the two numbers be x and y
"The sum of two numbers is 14" can be mathematically written as x+y = 14
and
"The larger number minus three times the lesser number is -2" can be mathematically written as x - 3y = -2
x + y = 14 ------------------(1)
x - 3y= -2 -------------------(2)
Subtract equation (2) from equation (1)
[x - x = 0 y - (-3y)=4y 14-(-2)=16]
4y = 16
To get the value of y divide both-side of the equation by 4
4y/4 = 16/4
y = 4
Substitute y=4 into equation (1)
x + y =14
x +4 =14
Subtract 4 from both-side of the equation
x + 4 -4 = 10]-4
x = 10
x=10 and y =4
Therefore the lesser number is 4
1. Point is on the line . Find the measure of angle .
Answer:
180°
Step-by-step explanation:
Answer:180
Step-by-step explanation:
9. Lula bought new furniture on her credit card for $993. If she pays it off in 6 months there will be no interest on her purchase. How much will her payments be if evenly distributed over 6 months?
Answer:
$165.50 dollars
Step-by-step explanation:
$993 / 6 = $165.50
Lula will need to pay $165.50 each month for 6 months to pay off her $993 furniture purchase without interest.
Lula purchased furniture on her credit card and plans to make payments over a period of 6 months with no interest charged. To calculate the monthly payment amount, you would divide the total cost of the furniture by the number of months over which she plans to pay.
The formula to find out the monthly payment is:
Monthly Payment = Total Cost / Number of Months
So for Lula, it looks like this:
Monthly Payment = $993 / 6
Monthly Payment = $165.50
Therefore, if Lula pays $165.50 each month, she will have the furniture paid off in 6 months without incurring any interest.
For the geometric sequence: 112.5, 225, 450, 900,..., find the 21st term.
Answer:
Step-by-step explanation:
The 21st term of the given geometric sequence can be found by using the formula for the n-th term of a geometric sequence: a_n = a_1 * r^(n-1). In this case, it is 112.5 * 2^(21-1).
Explanation:In a geometric sequence, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. In this case, 225 divided by 112.5 gives us the common ratio of 2. Therefore, to find the 21st term of the given geometric sequence, we use the formula: a_n = a_1 * r^(n-1). Here, a_n is the n-th term, a_1 is the first term, r is the common ratio and n is the term which we want to find.
So, substituting the given values into the formula, a_21 = 112.5 * 2^(21-1). Calculate this and you'll have the 21st term of the geometric sequence.
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Which lines are perpendicular to the line y – 1 = One-third(x+2)? Check all that apply.
Answer:
Lines that have a slope of -3
Step-by-step explanation:
Take the negative reciprocal of 1/3 and all lines that have that as the slope are perpendicular
Answer:
1. y + 2 = –3(x – 4)
3. y = -3x – 5/3
5. 3x + y = 7
Step-by-step explanation:
because yes
Which of the following expressions is equivalent to that expression?
A.(n+4)^5
B.(n+4)^1/5
C.(n+4)^5/3
D.(n+4)^3/5
Option D:
[tex](n+4)^{\frac{3}{5}}[/tex] is the equivalent expression for [tex]\sqrt[5]{(n+4)^{3}}[/tex].
Solution:
Given expression:
[tex]\sqrt[5]{(n+4)^{3}}[/tex]
To find the equivalent expression for the given expression.
[tex]\sqrt[5]{(n+4)^{3}}[/tex]
Using radical rule: [tex]$\sqrt[m]{a}=a^{\frac{1}{m}}[/tex]
[tex]$=\left((n+4)^{3}\right)^{\frac{1}{5}}[/tex]
Using exponent rule: [tex]$\left(a^{b}\right)^{c}=a^{b c}[/tex]
[tex]$=(n+4)^{3 \cdot \frac{1}{5}}[/tex]
[tex]$=(n+4)^{\frac{3}{5}}[/tex]
[tex]\sqrt[5]{(n+4)^{3}}=(n+4)^{\frac{3}{5}}[/tex]
Hence [tex](n+4)^{\frac{3}{5}}[/tex] is the equivalent expression for [tex]\sqrt[5]{(n+4)^{3}}[/tex].
Option D is the correct answer.
24x-12-43x-6
Simplify.
Please help!! ASAP!!
Answer:
-30
Step-by-step explanation:
Hope this helps! Brainliest is appriciated.
Answer:
[tex]24x - 12 - 43x - 6 \\ 24x - 43x - 12 - 6 \\ - 19x - 18[/tex]
5x-6=10-3x solve for x
Answer:
x = 2
Step-by-step explanation:
Start by combining like terms.
Collecting x terms onto the left side results in 8x;
collecting constants onto the right side results in 16.
Therefore, 8x = 16, and x = 2
Emily and her children went into a grocery store and she bought $20.80 worth of bananas and peaches. Each banana costs $0.80 and each peach costs $2.
Answer:
The number of bananas that Emily bought was 6 and the number of peaches that Emily bought was 8
Step-by-step explanation:
The complete question is
Emily and her children went into a grocery store and she bought $20.80 worth of bananas and peaches. Each banana costs $0.80 and each peach costs $2. She bought a total of 14 peaches and bananas altogether. Determine the number of peaches and the number of bananas that Emily bought
Let
x ----> the number of bananas that Emily bought
y ----> the number of peaches that Emily bought
we know that
She bought a total of 14 bananas and peaches altogether
so
[tex]x+y=14[/tex] -----> equation A
She bought $20.80 worth of bananas and peaches
so
[tex]0.80x+2y=20.80[/tex] -----> equation B
Solve the system by graphing
Remember that the solution is the intersection point both graphs
using a graphing tool
The solution is the point (6,8)
see the attached figure
therefore
The number of bananas that Emily bought was 6 and the number of peaches that Emily bought was 8
Triangle ADE is similar to triangle ABC. Which statement is TRUE concerning the slope of the line formed by the hypotenuse of each triangle? A) EA DE = CB AC B) DE EA = CB AC C) DE EA = AC CB D) EA DE = AC CB
Answer:
[tex]B) \frac{DE }{EA} =\frac{CB}{AC}[/tex]
Step-by-step explanation:
If ant two given triangles are SIMILAR, then they have equal corresponding angles and their corresponding sides are PROPORTIONAL.
For example: if Δ ABC ≈ Δ PQR, then
∠A = ∠P , ∠B = ∠Q and ∠C = ∠R
and [tex]\frac{AB}{PQ} = \frac{BC}{QR} = \frac{AC}{PR}[/tex]
Now, here given: Δ ADE ≈ Δ ABC
Then by the SIMILAR postulate their corresponding angles are equal and their corresponding sides are Proportional.
[tex]\implies \frac{AD}{AB} = \frac{DE}{BC} = \frac{AE}{AC}[/tex] ............. (1)
Consider from above:
[tex]\frac{DE}{BC} = \frac{AE}{AC}\\\implies \frac{DE}{AE} = \frac{BC}{AC}[/tex] ............. (2)
Here, the given options are:
[tex]A) \frac{EA }{DE} =\frac{CB}{AC}[/tex] FALSE
[tex]B) \frac{DE }{EA} =\frac{CB}{AC}[/tex] TRUE (from 2)
[tex]C) \frac{DE }{EA} =\frac{AC}{CB}[/tex] FALSE
[tex]C) \frac{EA}{DE} =\frac{AC}{CB}[/tex] FALSE
Answer:
b
Step-by-step explanation:
took test
quadrilateral PQRS is a kite. M
a number w divided by 5 equals 6
Answer:
w = 30
Step-by-step explanation:
w ÷ 5 = 6
Multiply both sides of the equation by 5
w = 30
Hope this helps :)
Answer:30
Step-by-step explanation:
5 divided by 30 is 6
4.5(32 divided by 8) +12
Marcy would not reveal her equation, but she said that she could multiply the left side by 4 and the right side by 8 and still maintain its balance. mr. kim verified she was correct . What is Marcys equation
Answer:
4x=8y
Step-by-step explanation:
Ok so a number multiplied by 4 equal a number multiplied by 8.
Both numbers can't have the same variable because if they had the same varable that means they are the same number which in that case means Marcy is wrong but we know she is right because Mr.Kim said so.
let's plug in numbers. If they had the same variable it would be:-4x=8x
let x=2, 4(2)=8(2)
8=16 not true
if the variables were not the same:-4x=8y
let x=4
let y=2 4(4)=8(2)
16=16 true
6. The population of a town is 680 000 correct to the nearest 10 000. Write down
(a) The least possible population of the town.
(b) The greatest possible population of the town.
Answer:
a) 675 000
b) 685 000
Step-by-step explanation:
The population of a town is 680 000 correct to the nearest 10 000.
a) To find it lower bound, we level of accuracy by 2 and then subtract from 680 000
The lower bound is:
680 000-5000=675,000
Therefore the least possible population of the town is 675 000
b) We repeat the same process to find the upper bound
680 000+5000=685,000
Round 721295.198715 to the nearest ten.
To round 721295.198715 to the nearest ten, we increase the tens place from 9 to 0 due to the ones place being 5, resulting in 721300.
Explanation:To round the number 721295.198715 to the nearest ten, we should look at the digit in the ones place, which is 5. Since the ones digit is 5 or greater, we need to round up the tens place.
Therefore, the tens digit increases by one from 9 to 0, and all digits to the right of the tens place become zero.
Thus, 721295 rounds up to 721300 when rounded to the nearest ten.
Note that we ignore the decimal and its subsequent numbers because they do not influence the rounding of a number to the nearest ten.
An item that costs $50.00 is marked 20% off. Sales tax for the item is 8%. What is the final price, including tax? Show your work.
a. solve the problem with the discount applied before the sales tax.
b. solve the problem with the discount applied after the sales tax.
c. compare your answers in parts (a) and (b). Explain
Answer:
$40 ; $43.20
Step-by-step explanation:
a) 50 * (1 - .20) = 50 * .8 = 40
b) 50 * (1 - .20) * (1 + .08) = 43.20
c) The sales tax increases the price from a by 8%
Answer:
a) 40 dollars
b) 43.20 dollars
c) In Part A the instructions tell you to find the 20% in the 50 dollars But in part B it tells you to solve the problem with the discount applied after the sales tax.
Step-by-step explanation:
Find the area of the triangle. Round your answer to the nearest thousandths.
A=1/2 bh
Answer:
Step-by-step explanation:
height of triangle=√(11²-8.6²)=√(11+8.6)(11-8.6)=√(19.6×2.4)
=√(4×4.9×4×0.6)=4√(4.9×0.6)=4√2.94
area of triangle=1/2 bh=1/2×2×8.6×4√2.94
=34.4×√2.94
≈58.984
Write the ratios for sin M, and tan M
sin M =
Answer:
see explanation
Step-by-step explanation:
sin M = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{KL}{ML}[/tex] = [tex]\frac{2\sqrt{11} }{12}[/tex] = [tex]\frac{\sqrt{11} }{6}[/tex]
tan M = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{KL}{KM}[/tex] = [tex]\frac{2\sqrt{11} }{10}[/tex] = [tex]\frac{\sqrt{11} }{5}[/tex]
Which statement is true of triangles P and Q?
Answer:
The answer is CAnswer:
The answer is C
Step-by-step explanation:
All of the side lengths on the pre-image multiplied by 3 equal out to the side lengths proportional, and the angles are all the same, making them congruent. Please consider giving brainliest.