The value of a negative number such that the sum of that number and its square is 42 is -7.
What are negative numbers?A negative number is one that always has a value lower than zero and is denoted by the minus (-) symbol. On a number line, negative numbers are displayed to the left of zero. Negative numbers include -6 and -15 as examples.Let the negative number be -x.
According to the question, the sum of the negative number and its square is 42.
So, we form an equation
- x + (-x)² = 42
x² - x - 42 = 0
Solving the quadratic equation,
x² - 7x + 6x - 42 = 0
x(x - 7) + 6(x - 7) = 0
(x - 7)(x + 6) = 0
x = -6 and x = 7
We have taken the number -x to be negative.
So, -x = -6 and -x = 7
x = 6 and x = -7
Hence, the value of the negative number is -7.
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The correct question is: "Determine the value of a negative number such that the sum of that number and its square is 42."
The points J(-6, 0), K(3, 0), L(7, 8), and M(-2, 8) form parallelogram JKLM.
Plot the points then click the "Graph Quadrilateral" button. Then find the perimeter
of the parallelogram. Round your answer to the nearest tenth if necessary.
Answer:
72[tex]units^{2}[/tex]
Step-by-step explanation:
See pictures
help pls i think it’s 42 but i’m not sure
Answer:
42
Step-by-step explanation:
This triangle is right angled so we know it has a 90-degree angle at the corner with the box.
All angles add up to 180 in a triangle.
180 = 90 + 48 + x
180 - 90 = 48 + x
90 - 48 = x
x = 42
Hope that helps
The heights of three cylinders are 3cm, 9cm and 15cm. if the larger cylinder has a capacity of 725mililiters calculate calculate the capacities of the other cylinder
The capacity of 9 cm cylinder is 435 mililiters.
The capacity of 3 cm cylinder is 145 mililiters.
What is defined as the volume of cylindre?The volume of a cylinder is its density, which indicates how much material it can hold or how much of any material can be submerged in it. The volume of a cylinder is given by the formula πr²h, in which r is the radius of a circular base and h is the cylinder's height.For the given question;
The capacity of larger cylinder; 15 cm height is 725 millilitres.
Volume of 15 cm height cylinder = 725 cu. cm.
Thus,
πr²h = 725
Put h = 15 cm
πr²15 = 725
r² = 725/ 15π
r² = 145/3π
The volume of 9 cm cylinder = πr²9
Put the value of r² = 145/3π
V(h = 9 cm) = π×145×9/3π
V(h = 9 cm) = 435 cu. cm.
The volume of 3 cm cylinder = πr²3
Put the value of r² = 145/3π
V(h = 3 cm) = π×145×3/3π
V(h = 3 cm) = 145 cu. cm.
The capacity of 9 cm cylinder is 435 mililiters.
The capacity of 3 cm cylinder is 145 mililiters.
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Find the equation of a line that passes through the point (2,3) and has a gradient of 3.
Leave your answer in the form
ax+by=c
Where
a and b
and c are integers.
Answer:
-3x+y = -3
Step-by-step explanation:
First, I would write this in the point slop form of a line and the translate it into the standard form of a line.
[tex]y_{1}[/tex] - y = m([tex]x_{1}[/tex] -x) If the slope from of a line. Put in the x, y and the slope. You call the gradient, what I would call the slope.
y - 3 = 3(x -2) Distribute the 3
y - 3 = 3x -6 Subtract 3 from both sides
-3x + y - 3 = -6 Add 3 to both sides
-3x + y = -6
SOMEONE HELP PLEASE
a clothing business finds there is a linear relationship between the number of shirts, n, it can sell and the price, p, it can charge per shirt. In particular, historical data shows that 6000 shirts can be sold at a price of $81, while 10,000 shirts can be sold at a price of $45. Give a linear equation in the form p = mn + b that gives the price p they can change charge for n shirts.
Answer: p = ____
The linear equation in the form p = mn + b that gives the price p they can change charge for n- shirts is; p = (9/1000)n - 9.
What is defined as the linear equation?A linear equation is really an algebraic equation with only a constant and the first-order (linear) term of the form y=mx+b, in which m is the slope and b is indeed the y-intercept.The above is sometimes regarded to as a "linear equation of two variables," in which y and x are the variables.As per the given question;
number of shirts = n
The charge per shirt = p.
The equation describing the relation is;
p = mn + b
The price of 6000 shirts = $81.
Put the value is equation;
81 = 6,000m + b .....eq 1
The price of 10,000 shirts = $45.
45 = 10,000m + b .....eq 2
Solving eq 1 and eq 2 by elimination method.
m = 9/1000
Put the value of m in eq 2 and find b.
b = -9
Now, put the value of b and m in the equation.
p = (9/1000)n - 9
Thus, the equation in the form p = mn + b that gives the price p they can change charge for n shirts is; p = (9/1000)n - 9.
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? Work out the surface area of the
cuboid.
10m
5m
2m
The surface area of the cuboid with the, height of the cuboid being 5m, the width being 2m, and the length being 10m is 160[tex]m^{2}[/tex]
What is the surface area of the Cuboid ?Add the areas of each of the cuboid's six faces to determine its surface area. Additionally, we can label the prism's length (l), width (w), and height (h), and then calculate its surface area using the formula SA=2lw+2lh+2hw.
As we know:
Height =5m
Width= 2m
Length= 10m
T.S.A=2(LXW) + 2(LXH) + 2(WXH)
=2(10mx2m) + 2(10mx5m) + 2(2mx5m)
=(2x20m²) + (2x50m²) + (2x10m²)
=40m² + 100m² + 20m²
=160m²
Cuboid's surface area, which was determined using the formula 2lw+2lh+2hw, is 160 square meters.
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DOMAIN:
Inequality:
Interval:
O
JIDID
IO
Answer:
Yes the other person is correct
Step-by-step explanation:
oop their answer got deleted
my bad
Is the study experimental or observational?A political pollster reports that his candidate has a 10% lead in the polls with 10% undecided.(A) ExperimentalB) Observational
Answer:
B) Observational
Explanation:
Observational studies are studies where the researchers only observe the variables and don't make changes. When the political pollster reports the percentage, it only observes the decision of the people but they can't change what makes a person select one candidate or the other.
a local dog breeder wants to know if her great dane puppies weigh, on average, the same as the larger population of great dane puppies. her 16 puppies have an average weight of 6.7 pounds, with a standard deviation of 0.5 pound. the population of all great dane puppies has an average weight of 7 pounds, with a standard deviation of 0.45 pound. if she wanted to calculate the 95% confidence interval for her sample, which mean would she use in the formula?
For a confidence interval, she would use her sample mean, hence the mean of 6.7 pounds.
What is a t-distribution confidence interval?In the context of this problem, we use the t-distribution instead of the z-distribution, as we have the standard deviation for her sample.
The bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the parameters are defined as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.From the first bullet point, we get that she should use her sample mean for the calculation of the confidence interval, that is, the mean of 6.7 pounds should be used.
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Simplify the following expression completely.
(√10 - √9)²
An operation in mathematics is a function that converts 0–n parameters or operands into a definite output value. The complexity of the operation depends on how many operands there are. The expression is equal to -5.97.
What are mathematical operations?An operation in mathematics is a function that converts 0–n parameters or operands into a definite output value. The complexity of the operation depends on how many operands there are.
The operations that are most frequently studied are binary operations (i.e., operations of arity 2), which include addition and multiplication, and unary operations (i.e., operations of arity 1), which include additive inverse and multiplicative inverse. A zero-arity operation, also known as the nullary operation, is a constant. An illustration of a ternary operation, also known as an operation of arity 3, is the mixed product.
Usually, it is considered that the arity is constrained. Even so, infinitary operations are occasionally considered, in which case the "normal" finite dimensionality operations are referred to as finiteary operations.
A partial operation is described as being similar to an operation but using a partial function in place of a function.
[tex](a-b)^{2} = a^{2}+b^{2}-2ab[/tex]
[tex](\sqrt{10} - \sqrt{9})^{2}[/tex])= [tex](\sqrt{10}) ^{2} + (\sqrt{9) } ^{2} - 2* \sqrt{10} * \sqrt{9}[/tex]
= 10+ 9- 18.97
=-5.97
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The function f(x) = |x+3| is transformed by the following transformations to a new function g(x):
A translation 2 units down.
A translation 1 unit to the right.
Reflection across the x-axis.
What is the equation of the new function g(x)?
The equation of the new function g(x) is g(x) = 2 - |x+2|
Transformation of functionTransformation is. way of changing the position of an object on an xy-plane.
Given the parent function f(x) = |x+3|.
If the function is translated 2 units down and 1 unit right, then the resulting function will be |x+3 - 1| - 2 which is equivalent to |x+2| - 2
The reflection of the resulting function across the x-axis is given as:
g(x) = -(|x+2|-2)
g(x) = 2 - |x+2|
Hence the new function g(x) if the parent function undergo the transformation is g(x) = 2 - |x+2|
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In the number 2,222.222, what is the difference between the 2 in the tens place and the 2 in the column to its left? a. the 2 in the tens place represents of what the 2 to its left represents. b. the 2 in the tens place represents of what the 2 to its left represents. c. the 2 in the tens place represents 100 times what the 2 to its left represents. d. the 2 in the tens place represents 10 times what the 2 to its left represents.
This questions is testing the knowledge on place value and total value.
The two to the left of the 2 in the tens place is 100 times larger than the 2 in the 100ths place in the value.
The total value of the 2 in the tens position is 20.
The total value of the 2 in the tenth position is 0.2.
To obtain the difference, divide the 20 in the tens position to the 2 in the tenths position.
20/0.2 = 100
the 2 in the tens place represents 100 times what the 2 to its left represents.
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The weight of a shipment, y, is directly proportional to x, the reams of paper included. If a shipment of 3 reams of paper weighs 12 lbs, find the reams of paper in a shipment that weighs 96 lbs.
Step-by-step explanation:
y = kx
3 = k × 12
.: k = 12/3 = 4
Inputting that to when y = 96 Ibs.
We have:
96 = 4 × x
96 = 4x
.: x = 96/4
x = 24 realms.
Ali and mohammad are playing football. Ali's score is twice the difference of muhammad's score and 6. the sum of their scores is 420. write and solve to find each student's football score
Football scores of Ali and Mohammad are 213 and 207 respectively.
Given,
Sum of Ali and Mohammad's football score is 420.
Difference between Ali's football score and Mohammad's football score is 6.
Then,
A - B = 6 ⇒Equation1
Where A = Ali's football score, and B= Mohammad's football score
Let's assume,
Ali's football score =
Mohammad's football score =
Sum of Ali's football score and Mohammad's football score:
A + B = 420 ⇒Equation2
After subtracting Equation2 from Equation 1
(A+B) - (A-B) = 420 - 6
A + B - A + B = 414
Since first A is positive and second A is negative, they will cancel out each other.
2B = 414
B = 207
After putting value of B in Equation2,
A + 207 = 420
A = 420- 207
A = 213
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Janelys has a points card for a movie theater. She receives 20 rewards points just for signing up. She earns 12.5 points for each visit to the movie theater. She needs at least 165 points for a free movie ticket.
The inequality shows that the number of visits that Janelys needs at least 165 points for a free movie ticket is 12.
How to calculate the number of visits?From the information, Janelys has a points card for a movie theater and she receives 20 rewards points just for signing up and earns 12.5 points for each visit to the movie theater.
The number of visits that are needed to earn at least 165 points will be illustrated as x. This will be:
20 + 12.5x >= 165
Collect like terms
12.5x >= 165 - 20
12.5x >= 145
Divide
x >= 145 / 12.5
x >= 11.6
Therefore, she needs at least 12 visits.
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Janelys has a points card for a movie theater. She receives 20 rewards points just for signing up. She earns 12.5 points for each visit to the movie theater. She needs at least 165 points for a free movie ticket. How may visits are needed?
O
Lines a and b are parallel Line c is perpendicular to both line a and line b. Which
statement about lines a, b, and c is NOT always true?
☐
The sum of the slopes of line b and line c is 0.
The product of the slopes of line a and line c is -1.
Ja
9
E
G
Line a and line b have the same slope.
The product of the slopes of line c and line b is -1.
The statement "The sum of the slopes of line b and c is 0" is not always true.
Given:
Lines a and b are parallel.
Line c is perpendicular to both line a and line b.
The statements "The product of the slopes of line a and line c is -1" and "The product of the slopes of line c and line b is -1" are both True.The reason is that a perpendicular line has a slope of -1 /m when one line has a slope of m. Alternatively put, the slopes are negative reciprocals of one another.
The statement "Line a and line b have the same slope" is true.This is because two lines that are parallel have the same slope.
The statement "The sum of the slopes of line b and c is 0" is false.This is because even if the two lines are perpendicular on adding their slopes together the outcome would not be 0. For instance, if b has a slope of 2, then c will have a slope of -1/2, and their sum will be 3/2.
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Please help! I need to get this done ASAP.
The trigonometric expression sin(30°) + cos(60°) is equal to 1.
What is trigonometry?
Trigonometry is the study of relationships between angles and side lengths of triangles. The use of geometry in astronomical studies gave rise to the field in the Hellenistic era in the third century BC. Greek mathematicians focused on chord calculation, whereas Indian mathematicians created the earliest tables of values for trigonometric ratios (also known as trigonometric functions), such as sine.
There are two trigonometric ratios in the given expression,
sin(30°) and cos(60°).
Here, sin(30°) is equal to the value 1/2
i.e. sin(30°) = 1/2
And, cos(60°) is equal to the value 1/2
i.e. cos(60°) = 1/2
Adding these equations, we get
sin(30°) + cos(60°) = 1/2 + 1/2 = 2/2 = 1
therefore, on solving the given trigonometric expression we get answer value 1.
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Can someone help with this???
Answer:
a.25
b.26
c. Eva as her unit rate is faster than Sarah
ask me if u want me to explain
Rope A is 25 times as long as Rope B and Rope
B is 18 times as long as Rope C. If Rope A is
3,600 cm long, how long is Rope C?
Answer:
Step-by-step explanation:
A=25xB
B=18xC
A=3600cm
B=A/25
B=3600/25
B=144
C=B/18
C=144/18
C=8
Solve the following equation for x = 5.
Answer: 5= 4x + 8
-8 -8
-3= 4x
the answer is x = 0.75
i don't know if I'm right if I am not I am sorry
Which of the following fractions could you add together easily?
280= -8 (-14+×)
What's the solution??
Answer:
x = -21
Step-by-step explanation:
The first you have to do is distribut the -8 to the -14 and x. Once you do that, you get 280 = 112 - 8x. Next, you need to subtract 112 from each side, so you get 168 = -8x. Now, you divide -8 from each side and you get -21 = x. Hope this helps!
Compare the two groups of data. which statement is true?
The true statement is the range of Mrs Plum's class is 14 greater than the range of Mr Scarlet's class.
What is the range?A box plot is a graph that is used to describe a dataset. A box plot is made up of two lines and a box. The two lines are known as whiskers.
The end of the first whisker represents the minimum number and the end of the second whisker represents the maximum number. The difference between the whiskers is the range.
Range is used to measure the variation of a dataset. It is the difference between the maximum number and the minimum number.
Range = maximum number - minimum number
Range of Miss Scarlet's class = 98 - 65 = 33
Range of Miss Plum's class = 98 - 51 = 47
Difference in range = 47 - 33 = 14
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Solve the equation for y. Then find the value of y for each value of x. 3x - 5y = 19; x = -1, 0, 1
please help me
Answer: y = -4.4
y = -3.8
y = -3.2
Step-by-step explanation:
can some one help picture below
Answer:
3 1/2
Step-by-step explanation:
each dozen needs 1/2 cup of chocolate chips so 1/2 times 7 = 3 1/2
what do you add to 4 1/7 to make 6
Answer:
Step-by-step explanation:
4 1/7 = 29/7
6 = 42/7
What you need to add to 4 1/7 is:
6 - 4 1/7
42/7 - 29/7
13/7.
In mixed fractions, it's 1 6/7.
If Mrs. Davis and her sisters also get haircuts,
about how much will they pay in all?
Using mathematical operations, yes Mrs. Davis and her two sisters can get hair coloured under $100 including $10, and their actual cost will be $96.85.
What exactly are mathematical operations?A mathematical function known as an operation converts zero or more input values into a precisely defined output value.The quantity of operands affects the operation's arity.The four mathematical operations are functions that change one number into another by taking input values, or numbers, as inputs.They are addition, subtraction, multiplication, and division.So, the total cost of hair coloring:
Can, all 3 get the hair colored for less than $100 with a $10 tip?When the cost of hair coloring is $28.95.Now, calculate as follows:
$28.95 × 3 = $86.85$86.85 + $10(Tip) = $96.85Therefore, using mathematical operations, yes Mrs. Davis and her two sisters can get hair coloured under $100 including $10, and their actual cost will be $96.85.
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The complete question is given below:
Could Mrs.Davis and her two sisters get their hair colored for less than $100 if they include a $10 tip explain also the cost is $28.95 for the hair coloring.
calculate a 95% confidence interval for a sample mean of 20 with a sample standard deviation of 10 and a sample size of 9. the answer should be accurate to the nearest decimal. given t
With a 95% confidence interval, the average is between 13.4667 and 26.5333.
Confidence interval is the measure of the degree of uncertainty or certainty in a sampling method. It is equal to the sample mean, plus or minus the margin of error (z value multiplied by standard deviation divide by the square root of the sample size).
CI = x ± z(σ/√n)
where CI = confidence interval
x = mean
σ = standard deviation
n = sample mean
z = z value at the confidence interval
The corresponding z value at 95% confidence interval is 1.96.
Substitute the given into the formula and solve for CI.
CI = x ± z(σ/√n)
CI = 20 ± (1.96)(10/√9)
CI = 20 ± (1.96)(10/3)
CI = 20 ± 6.5333
CI = (13.4667, 26.5333)
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someone help me please
Answer:
(x + 2)² - 11, so a = 2 and b = 11
Which is NOT a solution for 5-2x ≥-3?
A 0
B 2
C 4
D 5
Answer:
D 5
Step-by-step explanation:
Solve the inequality
5-2x ≥-3
Subtract 5 from each side
5-2x-5 ≥-3-5
-2x ≥-8
Divide by -2, remembering to flip the inequality
-2x/-2 ≤-8/-2
x ≤4
The only number not less than or equal to 4 in the choices is 5.
5 is not a solution
Answer:
Answer D is correct
Step-by-step explanation:
First, let us solve for x.
[tex]5 - 2x \geqslant - 3[/tex]
First, subtract 5 by both sides.
[tex] - 2x \geqslant - 3 - 5 \\ - 2x \geqslant - 8[/tex]
Divide both sides by -2.
[tex]x \leqslant 4[/tex]
Remember that, when you divide or multiply both sides by a negative number it change the direction of the inequality sign.Now, let us identify the equality sign and write the solutions of it.
[tex] \sf \leqslant \: \: \rightarrow \: \: x \: is \: less \: than \: or \: equals \: to \: 4[/tex]
Solutions
x = { 4, 3, 2, 1, 0...}
Accordingly, as 5 is greater than 4, 5 is not a solution for this given inequality.