Answer:
$64
Step-by-step explanation:
Equation: 50 + 15x = 1010
x = (1010 - 50) ÷ 15 = 64
Since x is the total amount of money deposited in the bank per week, the answer is $64.
How do you find the maximum or minimum value of a quadratic polynomial?
need help with number 9 pls
Answer:
i) a = 2, b = - 3, c =-6
Step-by-step explanation:
4x² - 12x + 3
4x² - 6x - 6x + 9 - 6
(2x - 3)(2x - 3) - 6
(2x - 3)² - 6
(2x + (- 3) )² - 6
In form of (ax + b)² - 6
a = 2, b = - 3, c =-6
Select the correct answer.
Which function does this graph represent?
A downward open parabola rises from (negative 2 point 4, negative 4) to (negative 1, 2) and declines through (0 point 4, negative 4) on the x y coordinate plane.
A.
f(x) = 3(x + 1)2 + 2
B.
f(x) = -3(x + 1)2 + 2
C.
f(x) = -3(x + 1)2 − 2
D.
f(x) = 3(x − 1)2 + 2
The parabola represented by this graph has the following equation:
y = -16.67(x + 1)² + 2
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
A downward open parabola rises from (-2.4, 4) to (-1,2), and declines through (0.4, -4) on the coordinate plane, hence the vertex is given by:
(-1,2), hence the coefficients are h = -1 and k = 2, and the equation is:
y = a(x - h)² + k
y = a(x + 1)² + 2
We have that when x = -0.4, y = -4, hence the leading coefficient is found as follows:
y = a(x + 1)² + 2
-4 = a(-0.4 + 1)² + 2
a = -6/0.6²
a = -16.67
Hence the equation is:
y = -16.67(x + 1)² + 2
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what is a constant
for example
[tex]y=x^{3} -3x^{2} +Kx+8[/tex] where K is the constant
what does that mean
Answer:
see explanation
Step-by-step explanation:
K is a constant means that K is a fixed numerical value
A right triangle has side lengths 4 units, 5 units, and x units. It is unknown if the missing length is the longest or shortest side.
Rounded to the nearest tenth, what is the difference between the possible values of x?
3.0 units
3.4 units
6.4 units
8.0 units
Answer: B
Step-by-step explanation:
Answer:
3.4 units
Step-by-step explanation:
Nelly works part-time in a shop to
cover her university expenses.
The table below shows how many
hours she worked each day last week.
Hours worked
Day
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
3½
5
2½
4
25
Nelly's weekly pay is worked out
as follows: Monday to Friday
• £8 per hour for the first 15 hours
• £10 per hour for any extra hours
Saturday
.
• double the normal rate of £8 per hour
Work out Nelly's total pay for last week?
You must show all your working.
Using proportions, Nelly's total pay for last week was of £220.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
From Monday to Friday, she worked 17 hours, hence:
For 15 hours, she was paid £8 per hour.For the last 2 hours, she was paid £10 per hour.On Saturday, she worked 5 hours, and was paid £16 per hour.
Hence her total payment is found as follows:
15 x 8 + 2 x 10 + 5 x 16 = £220.
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how many ounces of water must be added 100 oz. of 60% iodine to produce a 55% solution ? round your answer to the nearest hundreth.
Answer:
10 ounces
Step-by-step explanation:
Answer:
9.09 ounces
Step-by-step explanation:
The added water can be calculated by writing an equation for the amount of iodine in the diluted solution.
SetupLet x represent the number of ounces of water added to the 60% solution. The total amount of iodine in the mixture is ...
0.60(100) +0(x) = 0.55(100+x) . . . . . ounces of iodine in the mix
SolutionSimplify the equation:
60 = 55 +0.55x
5 = 0.55x . . . . . . . subtract 55
x = 5/0.55 ≈ 9.09
9.09 ounces of pure water must be added to produce a 55% solution.
8. The cost of renting a scooter is $40 plus $4.50 per hours. Abby wants to spend less than $75
on the scooter rental. Write and solve an inequality to find the number of hours she can rent
the scooter.
Answer:
Step-by-step explanation:
4.5x + 40 < 75
4.5x < 35
x<7.7
If you were to take a cross section of a right circular cone parallel to its base, what shape would you get?
The cross section of a right circular cone parallel to its base is a circle.
What is a three dimensional shape?A three dimensional shape is a shape that has length, width and height. Examples of three dimensional shapes are cone, cylinder, prism and pyramid.
A two dimensional shape is a shape that have both length and width. Examples of two dimensional shape are circle, rectangle, square.
A cone is a three-dimensional solid geometric shape having a circular base and a pointed edge at the top
The cross section of a right circular cone parallel to its base is a circle.
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A plane intersects one cone of a double-napped cone such that the plane is neither parallel to the generating line nor perpendicular to the axis. what conic section is formed?
The conic section will form an Ellipse.
What is Circle?The collection of all points in the plane that make up a circle are all equally spaced from a certain point known as the "centre," making the form a closed two-dimensional shape. The reflection symmetry line is created by all lines that traverse the circle. Additionally, it is symmetrical in rotation around the center at all angles.
What is conic section?A conic section is a curve formed when the surface of a cone and a plane connect. The hyperbola, parabola, and ellipse are the three forms of conic sections; the circle is a special case of the ellipse, though historically it was occasionally referred to as a fourth type.
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What is the solution for x in the equation?
10x − 4.5 + 3x = 12x − 1.1
x =
Answer: x= 3.4
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Answer:
x = 3.4
Step-by-step explanation:
[tex]10x - 4.5 + 3x = 12x -1.1 \\ 13x - 4.5 = 12x - 1.1 \\ 13x - 12x - 4.5 = 12x - 12x - 1.1 \\ x - 4.5 = - 1.1 \\ x - 4.5 + 4.5 = - 1.1 + 4.5 \\ x = 3.4[/tex]
A coin is flipped twice. What is the probability of getting heads on the first flip and tails on the second flip?
Answer: 0.25 or 25%
Step-by-step explanation:
Answer:
25%
Step-by-step explanation:
question no.3 ♀️
is 1,2 correct ?
Answer:
YES THEY ARE CORRECT ✅Good luck ✅In an analysis of variance study, we consider 3 treatments. We have 4 observations for the first treatment, 5 observations for the second treatment, and 6 observations for the third treatment. What are the degrees of freedom associated with SSE
In the analysis of variance study, if we consider 3 treatments, in which we have 4 observations for the first treatment, 5 observations for the second treatment, and 6 observations for the third treatment. Then, the degrees of freedom associated with SSE in each case is 2, 3, and 4, respectively.
Degrees of Freedom Associated with SSE
The number of degrees of freedom in statistics refers to the quantity of values that can fluctuate in a statistic's final calculation. Various amounts of data or information can be used to estimate statistical parameters.
In order to find the degrees of freedom associated with SSE in an Analysis of Variance (ANOVA) study, we subtract 2 from the number of observations. In n is the number of observations, then (n-2) gives the degrees of freedom associated with SSE.
Thus, for the first treatment, n = 4
⇒ Degrees of freedom = 4-2
= 2
For the second treatment, n = 5
⇒ Degrees of freedom = 5-2
= 3
For the third treatment, n = 6
⇒ Degrees of freedom = 6-2
= 4
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f(x)= x³ lf x=-2₁ y =?
If x=-1, y =?
If x= 0, y =?
Answer:
Step-by-step explanation:
if x= -2, f(x)= -8
x= -1, y= -1
x=0, y=0
The grocery store where Ms. Maple works pays her $6.50 per hour. Any time she works more than 40 hours per week, she is paid time and a half for the additional hours. Her weekly pay, w, is found using the following equation, where h is the total number of hours worked.
Answer:
$279.25
Step-by-step explanation:
Multiply 6.50x43
[tex]w = 279.50 + (0.5 \times 6.50) \times (43 - 40)[/tex]
Multiply 0.5x6.50
[tex]w = 279.50 + 3.250 \times (43 - 40)[/tex]
Add 43-40
[tex]w = 279.50 + 3.250 \times 3[/tex]
Multiply 3.250x3
[tex]w = 279.50+ 9.750[/tex]
Solution
Consider two forces of 17 and 42 pounds both acting in the horizontal direction on a single object. find the resultant force acting on the object. magnitude = direction angle =
The forces have a magnitude of 59 pounds, and their direction angles are zero.
What is the magnitude of force?The total amount of forces exerted on an object is referred to as the magnitude of force. The strength of the force increases when all the forces are pulling in the same direction. The force's strength reduces when forces are exerted on an item from different angles.When two forces operating on a body in opposite directions along the same line of action are equal in magnitude, they cancel one another out. When two forces operating on a body in opposite directions along the same line of action are equal in magnitude, they cancel one another out.According to this formula, the amount of net force acting on an item is equal to the mass times the acceleration of the object.Magnitude is a term that refers to size or importance. The depth of the Grand Canyon serves as an illustration of magnitude. The scope of the hunger crisis in the world serves as an illustration of magnitude. A measurement of the energy released by an earthquake, as shown on the Richter scale (geology).Two forces of 17 and 42 pounds act horizontally on an object.
i.e
F1 = 17 pounds
F2 = 42 pounds
As the magnitude of the force represents the sum of all the forces
The direction is the same
Magnitude : 17 + 42 = 59 pounds
The Direction angles : 0
As they have the same direction so angle will be 0.
The forces have a magnitude of 59 pounds, and their direction angles are zero.
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Answer:59 and 0
Step-by-step explanation:
EDGE
radians and degrees
180° irc =
[tex]\Large\texttt{Answer}[/tex]
[tex]180^\circ=\pi\:radians}[/tex]
[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]
[tex]\Large\texttt{Process}[/tex]
⇨ For converting from degrees to radians, use this conversion factor:
[tex]\bf{\cfrac{\pi}{180}}[/tex]
⇨ Convert
[tex]\bf{\cfrac{180}{1}\times\cfrac{\pi}{180}}[/tex]
⇨ The 180s cancel out, and we have:
[tex]\pi[/tex]
Hence
[tex]\bf{180^\circ=\pi\:radians}[/tex]
Hope that helped
Billy graphed the system of linear equations to find an approximate solution.
y = A system of equations. y equals negative StartFraction 7 over 4 EndFraction x plus StartFraction 5 over 2 EndFraction. y equals StartFraction 3 over 4 EndFraction x minus 3.x +
y = x – 3
A coordinate grid with 2 lines. The first line is labeled y equals negative StartFraction 7 over 4 EndFraction x plus StartFraction 5 over 2 EndFraction and passes through the (0, 2.5) and (2.2, negative 1.4). The second line is labeled y equals StartFraction 3 over 4 EndFraction x minus 3 and passes through (0, negative 3, 0.14) and (2.2, negative 1.4)
Which points are possible approximations for this system? Select two options.
The points that are possible approximations for this system are; (2.2, -1.4) and (2.2, -1.35)
How to find the solution of a linear graph?
We are given the equations of the linear graphs as;
y = ⁷/₄x + ⁵/₂
y = ³/₄x - 3
Notice that the lines intersect each other and by definition, if the lines of the system of equations intersect, then the system has one solution. This means that the point of intersection of the lines is the solution of the system. It can be written as:
(x, y)
x is the x-coordinate .
y is the y-coordinate.
In this case, we can identify that:
- the x-coordinate of the point of intersection is between; x = 2 and x = 3
- The y-coordinate of the point of intersection is between y = -1 and y = -2
Based on the above, we can conclude that the points that are possible approximations for this system are; (2.2, -1.4) and (2.2, -1.35)
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Answer: B and C) 2.2, -1.4 and 2.2, -1.35
Step-by-step explanation:
Hope this helps!
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Pls and Ty!
A shop is having a 10% off sale. Find the sale price of a cap which normally costs $12?
Answer: $10.8
Step-by-step explanation: To do this, we need to find 90% of $12 because the cap is 10% off. We can do this by multiplying 12 by 0.9. 12 x0.9 = 10.8.
An industrial machine produces widgets, but it has a 0.12 defective rate. what is the probability that the machine produces fewer than 3 defective widgets in a production run of 75 items?
The probability that the machine produces fewer than 3 defective widgets in a production run of 75 items is 0.041.
What is the probability?A probability refers to the ratio of favorable events to the n number of total events.
Also, it means the chance that a particular event (s) will occur expressed on a linear scale from 0 to 1 which can also be expressed as a percentage between 0 and 100%.
Given data
An industrial machine produces 3 widgets.
It has a 0.12 defective rate.
Defective rate fewer than 3
Total Probability = P of 2 defective + P for 1 defective
Total Probability = 2/74 + 1/73
Total Probability ≈ 0.04072565716
Total Probability ≈ 0.041
Therefore, the required probability for fewer than 3 defective rate is 0.041
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(06.01) evaluate the expression 34 ÷ (14 − 5) × 2. numerical answers expected! answer for blank 1:
Answer:
1.89
Step-by-step explanation:
34 ÷ (14 − 5) × 2
34 ÷ (9) × 2
34 ÷ 18
1.89
Numerical expression:
numerical expression is a phrase involving numbers.
In mathematics, a numerical expression is a set of numbers that have been written together by utilizing arithmetic operators addition, subtraction, multiplication, and division.
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By evaluating the expression 34 ÷ (14 − 5) × 2 we get = 1.89
What is BODMAS ?Children can use the acronym BODMAS to help them remember the proper sequence to carry out mathematical operations when solving problems. The abbreviation BODMAS stands for B-Brackets, O-Orders (powers/indices or roots), D-Division, M-Multiplication, A-Addition, and S-Subtraction.
What is numerical expression?A numerical expression is a sentence that uses numbers. A numerical expression in mathematics is a group of integers that have been combined using the addition, subtraction, multiplication, and division arithmetic operators.
According to the given Information :Appling the BODMAS
= 34 ÷ (14 − 5) × 2
= 34 ÷ (9) × 2
= 34 ÷ 18
= 1.89
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A ladder is leaning against a building and makes a 28 degree angle with the ground. the top of the ladder reaches up the building. what is the length of the latter
The length of the ladder is 75ft.
What is hypotenuse?The longest side, or hypotenuse, of a right-angled triangle is the side that faces away from the right angle. The Pythagorean theorem asserts that the hypotenuse's square length equals the sum of the squares of the lengths of the other two sides, and this can be used to determine the hypotenuse's length.
According to the information:The ladder makes an angle of 28° with the ground and the top of the ladder reaches 35ft
Therefore, we have:
Sineα = opposite/hypotenuse
Where:
Opposite = 35
Hypotenuse = Length
α = 28°
substitute values and solve for the length, as following:
Sine(28) = 35/Length
Length = 35/Sine(28)
Length = 75ft
Therefore,
The length of the ladder is 75 ft.
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a.) 6(x+2) = 5(x-y)
b.) 5(a-2x) = 9(x+1)
make x the subject
a) 6x + 12 = 5x - 5y
6x-5x = -5y-12
x = -5y-12
b) 5a-10x = 9x+9
-10x-9x = 9-5a
-19x = 9-5a
x = 9-5a/-19
Distribute to create an equivalent
expression with the fewest symbols
possible.
2(3 – 8y)
=
Answer:
6 - 16y
Step-by-step explanation:
2(3 – 8y) = 2 × 3 - 2 × 8y = 6 - 16y
Find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it. lim x→[infinity] ln(x) x
The limit of [tex]\lim_{x \to \infty} \frac{lnx}{x}[/tex] using L'Hospital rule is 0.
According to the given question.
We have to find the limit of ln(x)/x when x approaches to infinity.
If we let x = ∞, we get an indeterminate form [tex]\frac{\infty}{\infty}[/tex] ie. [tex]\frac{ln(x)}{x} = \frac{\infty}{\infty}[/tex].
And, we know that whenever we get indeterminate form ∞/∞ we apply L'Hospital rule.
Therefore, defferentiating numerator ln(x) and x with respect to x.
[tex]\implies \frac{d(ln(x))}{dx} = \frac{1}{x}[/tex] and [tex]\frac{d(x)}{dx} =1[/tex]
So,
[tex]\lim_{x\to \infty}\frac{\frac{1}{x} }{1}[/tex]
[tex]= \lim_{x \to \infty} \frac{1}{x}[/tex]
As, x tends to ∞, 1/x tends to 0. Because ∞ is very large number and 1 divided by a very large number always approaches to 0 and it is very close to zero.
Therefore,
[tex]\lim_{x \to \infty} \frac{1}{x} = 0[/tex]
Hence, the limit of [tex]\lim_{x \to \infty} \frac{lnx}{x}[/tex] is 0.
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36) The ratio of Slade's stickers to Corbett's stickers is 5: 2. If Corbett
has 27 fewer stickers than Slade, how many stickers do they have
in all?
Answer: 63 Stickers
Step-by-step explanation:
Given information:
Ratio = Slade : Corbett = 5 : 2
Corbett has 27 fewer stickers
Set variables:
Let x be the number of stickers Corbett has
Let x + 27 be the number of stickers Slade has
Set proportional equation:
[tex]\frac{2}{5}~ =~\frac{x}{x~+~27}[/tex]
Cross multiply the system
[tex]2~(x~+~27)~=~5~*~x[/tex]
Simplify by distributive property
[tex]2~*~x~+~2~*~27~=~5x[/tex]
[tex]2x~+~54~=~5x[/tex]
Subtract 2x on both sides
[tex]2x~+~54~-~2x~=~5x~-~2x[/tex]
[tex]54~=~3x[/tex]
Divide 3 on both sides
[tex]54~/~3~=~3x~/~3[/tex]
[tex]{x=18}[/tex]
Add Corbett's and Slade's amounts together
Corbett = x = 18 stickers
Slade = x + 27 = 18 + 27 = 45 stickers
Total = 18 + 45 = [tex]\Large\boxed{63~Stickers}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
63 stickers
Step-by-step explanation:
Define the variables:
Let x be the number of stickers Slade had.If Corbett has 27 fewer stickers than Slade:Given ratio:
Slade : Corbett = 5 : 2
Substitute the defined variables:
[tex]\implies \sf x : x - 27 = 5 : 2[/tex]
[tex]\implies \sf \dfrac{x}{x-27}=\dfrac{5}{2}[/tex]
Cross multiply:
[tex]\implies \sf 2x=5(x-27)[/tex]
Expand:
[tex]\implies \sf 2x=5x-135[/tex]
Subtract 5x from both sides:
[tex]\implies \sf -3x=-135[/tex]
Multiply both sides by -1:
[tex]\implies \sf 3x=135[/tex]
Divide both sides by 3:
[tex]\implies \sf x=45[/tex]
Therefore, Slade had 45 stickers.
Substitute the found value of x into the expression for the number of stickers Corbett had:
[tex]\implies \sf 45-27=18[/tex]
Therefore, Corbett had 18 stickers.
Total number of stickers = 45 + 18 = 63
find the slope in the line 3-4
Answer:
-0.5, either ⅙ or ⅓
Step-by-step explanation:
slope = rise / run
3) slope = (6 - 7) / (3 - 1)
slope = -1 / 2
slope = -0.5
ur mouse is blocking 4 (I'll do 2 scenarios):
4) slope = (-4 - -5) / (2 - -4)
slope = 1 / 6
I will leave it in fractional form
4) slope = (-4 - -6) / (2 - -4)
slope = 2 / 6
slope = 1/3
slope = 0.33
Someone help i cant answer this
Answer:
100%, 20%, 60%
Step-by-step explanation:
250/250 = 100/100 = 100%
50/250 = 1/5 = 20/100 = 20%
150/250 = 3/5 = 60/100 = 60%
Please gimme a hand I appreciate it in advance!!!
Answer:
30 degrees
Step-by-step explanation:
They are corresponding angles.
Answer: 30 degrees
Step-by-step explanation:
mangle8 and mangle 4 are corresponding angles meaning the angles are both the same.