Answer:
x = - 2 ± [tex]\sqrt{70}[/tex]
Step-by-step explanation:
(x + 2)² - 46 = 24 ( add 46 to both sides )
(x + 2)² = 70 ( take square root of both sides )
x + 2 = ± [tex]\sqrt{70}[/tex] ( subtract 2 from both sides )
x = - 2 ± [tex]\sqrt{70}[/tex]
then solutions are
x = - 2 - [tex]\sqrt{70}[/tex] , x = - 2 + [tex]\sqrt{70}[/tex]
You want your daily sodium intake to be less than 2300 milligrams. For breakfast, you eat a cereal bar with the nutrition label shown. What are the possible amounts of sodium you can eat during the rest of the day? Nutrition Facts Serving Size Servings Per Container Amount Per Serving Calories 120 Total Fat 3g 1 Bar (37g) Calories from Fat 30 % Daily Value* 5% 3% Saturated Fat 0.5g Trans Fat Og Cholesterol Omg Sodium 125mg 0% 5% The possible amounts of sodium you can eat during the rest of the day should be less than mg
Subtracting the maximum sodium intake from the intake of the cereal bar, you can eat amounts of sodium less than 2,175 mg of sodium the rest of the day.
How to find the amount of sodium you can eat during the rest of the day?From the text, the intake has to be less than 2300 mg. From the table, each cereal bar has 125 mg of sodium.
You eat one cereal bar, hence the remaining amount you can eat is found as follows:
2300 - 125 = 2,175.
You can eat amounts of sodium less than 2,175 mg of sodium the rest of the day.
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Please help I need to get this one question right so I can pass my lesson
Answer:
I think the answer is
Statement A
Step-by-step explanation:
A lecture hall has 50 seats.
43 seats are occupied and 7 seats are empty.
Use this information to answer the questions below.
Answer:14% of the seats are empty
Step-by-step explanation:
7/50 = ?/100
50×2=100
so 7×2=?
?=14
14/100=14%
What is the equation of the line that is perpendicular to
the given line and has an x-intercept of 6?
O y = -x + 8
O y = -x + 6
Oy=x-8
Oy=x-6
The equation of the line that is perpendicular to the given line y = x + 6 and has an x-intercept of 6 is B. y = -x + 6.
A line is plotted on the cartesian plane and is straight, thus named a straight line. A straight line is a two-dimensional geometrical figure.
Given the line:
y = x + 6
Compare the equation with
y = mx + c,
m = 1 and c= 6.
As it is given that the new line is perpendicular to the old one, then
the slope of the new line, m' [tex]= -\frac{1}{m} = -\frac{1}{1} = -1[/tex].
As the x-intercept is 6, c' = 6.
So, the equation of the new line is
y = m'x + c'
y = -x + 6
Therefore, the new line is y = -x + 6.
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The complete question is as follows:
What is the equation of the line that is perpendicular to
the given line and has an x-intercept of 6?
y = x + 6
A. y = -x + 8
B. y = -x + 6
C. y = x - 8
D. y = x - 6.
5. Given the points A(-3, -4) and B(2, 0), find the coordinates of the point P on
directed line segment AB that partitions AB in the ratio 1 to 4.
The correct answer is (x,y)=(-1,-2.4)
The coordinates are a pair of numbers that, using the horizontal and vertical lines, precisely pinpoint a point's location on a cartesian plane. typically represented by (x, y), the point's x and y values on a graph. Every point or an ordered pair comprises two coordinates.
The x coordinate, also known as the abscissa, is the first, and the y coordinate, also known as the ordinate. Any real number, whether positive or negative, can represent the coordinates of a point.
We have given the point
A(-3,-4) and B(2,0)
(x1,y1)=(-3,-4)
(x2,y2)=(2,0)
As P divided line segment AB in the ratio 2 to 3
m/n=2/3
x=(mx2+nx1)/m+n
x=(2)(2)+(3)(-3)/2+3
x=4-9/5
x=-5/5
x=-1
y=(my2+ny1)/m+n
y=(2)(0)+(3)(-4)/2+3
y=0-12/5
y=-12/5
y=-2.4
(x,y)=(-1,-2.4)
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Determine the x- and y-coordinates of a point through which the resultant of the parallel forces passes.
The resultant of the parallel force passes, x=2.8888 in and y=-5.4444 in
Taking moment about 'y'
∈Mx=RXx
x=260/90
x=2.8888 in
Taking moment about 'x'
∈My=RXy
y= -490/90
y= -5.4444 in
What is the example of parallel forces?When two forces of equal strength act in the same direction within the same plane, with the counterforce in the centre, this is known as a parallel force system.
A see-saw is an illustration of this. The fulcrum in the middle provides the counterforce to keep the seesaw in a neutral position while the children apply the two forces at the ends. The significant vertical forces on an aeroplane while it is in flight is another illustration (see image at right).
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Help please thank you
From the given integer numbers, the states that have temperatures within 10ºC of Delaware are: California, Hawaii and Idaho.
Which states have temperatures within 10ºC of Delaware?The temperature in Delaware is of 5 ºC, hence for our range, we have that:
The lower temperature is of 5 - 10 = -5ºC.The higher temperature is of 5 + 10 = 15ºC.Alaska(< -5), Tennessee(>15) and WV(<-5) do not have temperatures in this range, hence the states that have temperatures within 10ºC of Delaware are: California, Hawaii and Idaho.
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HURRYY!! BEST ANSWER GETS BRAINLIEST!!
15. The dimensions of a cylindrical can are shown below.
1
10 in.
3 in.
What is the volume of the can, in terms of ?
A. 60 π cubic inches
TL
B. 90 cubic inches
C. 30 π cubic inches
D. 18 π cubic inches
Answer:
volume of cylinder is πr²h so whatever your radius is then square it multiply by height. don't multiply by pi as it gives it to you in the answer
What is a rounded to the nearest hundredth
Consider the line that passes through the point P(-1,-1) and is parallel to the line x-y=7. Write the point slope equation of the line. Use exact values.
Answer: y=x
Step-by-step explanation:
[tex]x-y=7\\x-y+y=7+y\\x=7+y\\x-7=7+y-7\\x-7=y[/tex]
The line that parallel to the line x-y=7 is:
[tex]y=x+b[/tex]
The line that passes through the point P(-1,-1), hence:
[tex]-1=-1+b\\-1+1=-1+b+1\\0=b\\Thus,\\y=x+0\\y=x[/tex]
PLEASE HELP ASAP!! WILL MARK BEAINLIEST
Answer:
1. x = 2/3y + 8/3
2. x=−y+1
Step-by-step explanation:
Solve for x
3x−2y=8
Add 2y to both sides.
3x−2y+2y = 8+2y
3x=2y+8
Divide both sides by 3.
3x/3 = 2y+8/3
x = 2/3y + 8/3
Answer:
x = 2/3y + 8/3
#2
solve for x.
x+y=1
Add -y to both sides.
x+y+−y=1+−y
x=−y+1
Answer:
x=−y+1
solve for y.
x+y=1
Add -x to both sides.
x+y+−x=1+−x
y=−x+1
Answer:
y=−x+1
Sorry if this is too much
charlotte denning earns both $13/hour and $26 for every sale she completes. during the most recent week, she worked 47 hours and made a total of 71 sales.
Answer: nice for her
Step-by-step explanation:
cly cloudy
Watch help video
Solve for x, rounding to the nearest hundredth.
110 • 10^4x = 55
[tex]110\cdot 10^{4x}=55\implies 10^{4x}=\cfrac{55}{110}\implies 10^{4x}=\cfrac{1}{2}\implies 10^{4x}=2^{-1} \\\\\\ \log\left( 10^{4x} \right)=\log\left( 2^{-1} \right)\implies 4x\log_{10}\left( 10 \right)=-1\log_{10}(2)\implies 4x(1)=-\log(2) \\\\\\ 4x=-\log(2)\implies x=-\cfrac{\log(2)}{4}\implies {\LARGE \begin{array}{llll} x\approx -0.08 \end{array}}[/tex]
What is the range?
0-5 -6 -4 -3
Answer: 2 I think
Step-by-step explanation:
what does the remainder theorem conclude given that f(x)x 5 has a remainder of 17?enter your answer by filling in the boxes.
The remainder theorem conclude given that F(-5)=17
When, x= -5
x+5=0
So, F(-5) = 17
What is Remainder Theorem explain?According to the remainder theorem, the result of dividing p(x) by (x - a) is p. (a). According to the factor theorem, (x - a) can only be a factor of p(x) if f(a) = 0. It is used to locate the rest. A linear polynomial's status as a factor of the input polynomial is determined using this method.
The remainder theorem is used to calculate the remainder when a polynomial is split by a linear polynomial. We are aware that long division of polynomials can be used to find the remainder after dividing one polynomial by another. The remainder can instead be discovered using the remainder theorem.
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two cruise ships leave port at the same time. ship a sails north at a speed of 60 mph while ship b sails east at a speed of 50 mph.
Answer: y= 60x, y=50x
Step-by-step explanation:
Please Provide the whole question
Show full work please
The temperature in degrees celcius in which bacteria cannot survive is greater than 3.66
Subject of formulaThis is a way of representing a variable with another
Given the inequality below;
q/5 C + 32 ≥ 120
Substitute C = 120oF
q/5(120) + 32 ≥ 120
24q + 32 ≥ 120
24q ≥ 120 - 32
24q ≥ 88
q ≥ 88/24
q ≥ 3.66
Hence the temperature in degrees celcius in which bacteria cannot survive is greater than 3.66
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13. Find the coordinate for the point that is 1/6 the
distance from A to B.
A
-5
B
37
8 1/3 × 3
porfa qué alguien me ayude :(
Answer:
es 25
Step-by-step explanation:
3. You have $2.75. You want to buy trading cards that cost $0.25 each.
How many can you buy?
Question:
You have $2.75. You want to buy trading cards that cost $0.25 each.
How many can you buy?
Answer:
11 trading cards
Step-by-step explanation:
If you do 2.75 ÷ 0.25 you would get 11 and to check the answer you could simply multiply you would do 0.25 x 11 to get the answer 2.75.
I hope it helps you!
~XxBells is a cute girlxX~
#Learn with Brainly
scores on the act college entrance exam follow a bell-shaped distribution with mean 21 and standard deviation 5. wayne’s standardized score on the act was −0.6. what was wayne’s actual act score?
Wayne's actual act score is 18
A z-score tells you where the score lies on a normal distribution curve.
A standard deviation is a measure of how dispersed the data is in relation to the mean.
Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Given,
The mean = 21
Standard deviation =5
z-score = -0.6
We know z-score = (x-mean)/ Standard deviation
Substitute the values
-0.6 = [tex]\frac{x-21}{5}[/tex]
x-21 = -0.6 ×5
x-21 = -3
x=-3+21
x=18
Hence, the Wayne's actual act score is 18
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For every left handed person, rhere are about 4 right handed people. If there are 30 students in a class, predoct the number of students who are right handed
Answer:
4 right handlers for everytime 5 people
solution:
4/5. = x/30
x = (4)(30)/5
x= 24
there are 24 right handed people
Step-by-step explanation:
I am left handed so I know this is true :)
Write an algebraic expression that models the situation.
Jenny had $105, but she is spending $13 per week.
The algebraic expression that models the situation when Jenny had $105, but she is spending $13 per week is 105 - 13w.
How to calculate the value?Let the number of weeks be represented by x
Therefore, since Jenny had $105, but she is spending $13 per week, the appropriate expression will be:
= 105 - (13 × w)
= 105 - 13w
The expression is 105 - 13w.
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What is the value of −3 + |−17|?
20
14
−14
−20
Answer:
b) 14
Step-by-step explanation:
Given problem,
→ -3 + |-17|
Let's solve the problem,
→ -3 + |-17|
→ -3 + 17
→ 14
Hence, the answer is 14.
a newspaper company is selecting four houses to receive a free newspaper on your block. there are 10 houses on your block that are numbered 1-10. what is the probability that the four houses selected for a free newspaper will all be even numbered houses?
The probability that the four houses selected for a free newspaper will all be even numbered houses is: 1/42.
What is probability?Probability refers to the possibility of the occurrence of an event.
P(E) = probability of occurrence of an event E = Number of favorable outcomes, divided by total number of outcomes
Now, according to question,
There are 10 houses numbered 1-10. Thus the number of even numbered houses = 5 (2, 4, 6, 8, 10)
The probability that the first selected house for free newspapers is even numbered = 5/10 = 1/2
The probability that the second selected house for free newspapers is even numbered = 4/9
The probability that the third selected house for free newspapers is even numbered = 3/8
The probability that the fourth selected house for free newspapers is even numbered = 2/7
The final probability that the four houses selected for a free newspaper will all be even numbered houses is = 1/2(4/9)(3/8)(2/7) = 1/42
Hence, The probability that the four houses selected for a free newspaper will all be even numbered houses is: 1/42.
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What are the zeros of the polynomial function?
Select all correct zeros of each function.
The zeroes of the polynomial functions are listed below:
Roots: 2, 3, - 1. Roots: 3, - 2 (multiplicity 2), 1 Roots: 0 (multiplicity 3), 2, - 3.How to determine the zeros of a polynomial
Polynomials are algebraic constructions whose form is summarized by the following sum:
p(x) = ∑ cₙ · xⁿ, for n ∈ {0, 1, ..., m}
An alternative form to describe polynomials is using products of binomials of the form (x - r), where r is a root (zero) of the polynomial. The root of the polynomial is a value such that the result of the expression is equal to zero.
Then, we proceed to find the zeros of each polynomial function:
1) f(x) = 2 · x · (3 - x) · (x + 1). Roots: 2, 3, - 1.
2) f(x) = 2 · (x - 3) · (x + 2)² · (x - 1). Roots: 3, - 2 (multiplicity 2), 1
3) f(x) = x³ · (x - 2) · (x + 3). Roots: 0 (multiplicity 3), 2, - 3.
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When sampling from the population of interest, it is a good idea to have a representative sample. True or false?.
Answer: True, common sense dictates this.
Answer: true
Step-by-step explanation:
A straight line segment is drawn from A to C as shown at the right.
If AB=2x-4, BC= 4x + 12, and AC = 32, find .x.
Answer:
Step-by-step explanation:
just need points dont mind me
If a number is a natural number then it is also a whole number inverse Converse contrapositive and biconditional truth value
For the conditional statement, we have that:
The inverse is: If a number is not a natural number, then the number is also not a whole number, which has a false truth value.The converse is: If a number is a whole number, then it is also a natural number, which has a false truth value.The contra-positive is: If a number is not a whole number, then it is also not a natural number, which has a true truth value.The bi-conditional is: A number is a natural number if, and only if, it is also a whole number, which has a true truth value.What is the conditional statement?
The conditional statement has the following format:
p -> q.
For this problem, we have that the events are given as follows:
p: natural number.q: whole number.Hence p -> q is a true statement, as the set of whole numbers are the naturals plus the 0.
What is the inverse of the statement?The inverse is given by:
~p -> ~q.
In which ~ represents the negation symbol.
Hence:
If a number is not a natural number, then the number is also not a whole number.
This statement has a false truth value, as the number 0 is whole but not natural.
What is the converse of the statement?The converse is given by:
q -> p.
Hence:
If a number is a whole number, then it is also a natural number.
This statement has a false truth value, as the number 0 is whole but not natural.
What is the contra-positive of the statement?The contra-positive is given by:
~q -> ~p.
Hence:
If a number is not a whole number, then it is also not a natural number.
This statement has a true truth value, as all natural numbers are whole numbers.
What is the bi-conditional of the statement?The bi-conditional is given by:
p <-> q
In which <-> represents the term if, and only if.
Hence:
A number is a natural number if, and only if, it is also a whole number.
This statement has a true truth value, as all natural numbers are whole numbers.
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What is the break-even quantity for the following situation? fc = $1,400 per week vc = $2 per unit rev = $6 per unit group of answer choices 100 600 1,400 350 250
According to the question, to calculate break-even quantity with the given data. And the data is in dollars which is as follows:
Fixed cost (f(c)) = [tex]$1400[/tex] per week;
Variable cost (v(c)) = [tex]$2[/tex] per unit
Revenue = [tex]$6[/tex] per unit
Let us consider the break-even quantity to be ‘a’.
As per break-even point formula: Total costs = Total Revenue
And Total costs = Fixed cost + variable cost ;
Total Revenue = (price per unit)(quantity sold)
Using above formulas, the above expression can be re-written as:
Fixed cost + variable cost = (price per unit)(quantity sold)
[tex]($1400)+($2a) = ($6a)[/tex]
[tex]4a = 1400[/tex]
[tex]a = 350[/tex]
Therefore, the break-even quantity is [tex]350[/tex] units.
What is the break-even quantity?
Break-even quantity in the firm is the incremental value which is used to sell in order to cover the cost of the marketing program or other companies investments. And in this, the total cost is equal to the total revenue.
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