Answer:
$59.4
Step-by-step explanation:
The original price of the shoes was £60 before the 10% discount was applied, resulting in a final price of £54.
1. First, let's denote the original price of the shoes as [tex]\( x \)[/tex] pounds.
2. Since Nathalie bought the shoes during the sale, she received a 10% discount.
3. Therefore, she paid 90% of the original price after the discount. This can be represented as [tex]\( 0.90x \)[/tex].
4. According to the given information, Nathalie paid £54 for the shoes. So, we can set up the equation:
[tex]\[ 0.90x = 54 \][/tex]
5. To find the original price [tex](\( x \))[/tex], we need to isolate it by dividing both sides of the equation by 0.90:
[tex]\[ x = \frac{54}{0.90} \][/tex]
6. Solving the equation gives us:
[tex]\[ x = 60 \][/tex]
7. Hence, the original price of the shoes was £60 before the 10% discount was applied.
The complete question is here:
In a sale, normal prices are reduced by 10% Nathalie bought a pair of shoes in the sale for £54. What was the original price of the shoes?
Which expressions are equivalent to 6^16 ? Check all that apply
For this case we will indicate expressions equivalent to 6 ^ {16}:
We can write the following:
[tex]6 ^ {16} = 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6\\6 ^ {16} = (6 ^ 8) ^ 2\\6 ^ {16} = 6 ^ {\frac {32} {2}}[/tex]
Answer:
The equivalent expressions are shown in the previous part.
Answer:
3,4,6Step-by-step explanation:
What function is the square root parent function, F(x) = [tex]\sqrt{x}[/tex] the inverse of?
A. [tex]F(x) = x^2[/tex], where [tex]x[/tex] ≥ [tex]0[/tex]
B. [tex]F(x) = |x|[/tex]
C. [tex]F(x)=\frac{1}{\sqrt{x} }[/tex]
D. [tex]F(x) = x^2[/tex]
You can think of an inverse function as a function that “unwraps” x from whatever operations are attached to it. In the case of F(x) = √x, we can ”unwrap” x by squaring it. This narrows our options down to either A or D. Keep in mind that since there are no real number solutions to the square root of a negative number, we need to limit our domain to non-negative values. In other words, x ≥ 0. With that restriction, our answer is A.
The answer is:
The inverse of the given function is:
A. [tex]f(x)^{-1}=x^{2}[/tex]
Where,
[tex]x\geq 0[/tex]
Why?Inversing a function involves inversing the function variables. If we want to inverse a function, we need to rewrite the variable "x" with "y" and rewrite the variable "y" with "x", and then, isolate the variable "y".
Also, the domain of the original function will be the range of its inverse function, and the range of the original function, will be the domain of the its inverse function.
We are given the function:
[tex]f(x)=\sqrt{x}[/tex]
[tex]f(x)=y=\sqrt{x}[/tex]
So, inversing we have:
[tex]y=\sqrt{x}[/tex]
[tex]x=\sqrt{y}[/tex]
[tex](x)^{2}=(\sqrt{y})^{2}\\\\x^{2}=(y^{\frac{1}{2}})^{2}\\\\x^{2}=y^{\frac{2}{2} }\\\\x^{2}=y[/tex]
So, we have that the given function is only "part" of its inverse function, since negative square roots does not exist, it means that the domain of the given function starts from the number 0 taking only positive numbers.
Hence, we have that the answer is:
A. [tex]F(x)=x^{2}[/tex]
Where,
[tex]x\geq 0[/tex]
Have a nice day!
The vertices of the feasible region represented by a system are (0, 100), (0, 80), (80, 60), (80, 0), and (120, 0). What are the minimum and maximum values of the objective function F = 8x + 5y? M
Answer:
[tex]\boxed{\text{Min = 400; Max = 960}}[/tex]
Step-by-step explanation:
F = 8x + 5y
At (0, 100): F = 8×0 + 5×100 = 0 + 500 = 500
At (0, 80): F = 8×0 + 5×80 = 0 + 400 = 400 — MINIMUM
At (80, 60): F = 8×80 + 5×60 = 640 + 300 = 940
At (80, 0): F = 8×80 + 5×0 = 640 + 0 = 640
At (120, 0): F = 8×120 + 5×0 = 960 + 0 = 960 — MAXIMUM
The minimum value is [tex]\boxed{ 400}[/tex]and the maximum value is [tex]\boxed{ \text{ 960}}[/tex].
Answer:
Minimum; 400
Maximum; 960
☆
EDGE2022; Good Luck :D
What is the value of X if 5^x^+^2=5^9?
X=-11
X=-7
X=7
X=11
Answer:
[tex]\large\boxed{x=7}[/tex]
Step-by-step explanation:
[tex]5^{x+2}=5^9\iff x+2=9\qquad\text{subtract 2 from both sides}\\\\x+2-2=9-2\\\\x=7[/tex]
The value of x if 5ˣ⁺²=5⁹ is 7. Therefore, the correct answer is option C.
The given equation is 5ˣ⁺²=5⁹.
Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
We know that, when the bases are equal their exponents are equal.
x+2=9
x=9-2
x=7
Therefore, the correct answer is option C.
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Hyperbolas
label the foci, the vertices, and the asymptotes.
(y−3)^2/1 - (x+2)^2/4 = 1
let's notice something on this hyperbola, the fraction that is positive, is the fraction with the "y" variable, that simply means that the hyperbola is opening vertically, namely runs over the y-axis or it has a vertical traverse axis, which means, that, the foci will be a certain "c" distance from the center over the y-axis, well, with that mouthful, let's proceed.
[tex]\bf \textit{hyperbolas, vertical traverse axis } \\\\ \cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2}\\ asymptotes\quad y= k\pm \cfrac{a}{b}(x- h) \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\cfrac{(y-3)^2}{1}-\cfrac{(x+2)^2}{4}=1\implies \cfrac{[y-3]^2}{1^2}-\cfrac{[x-(-2)]^2}{2^2}=1~~ \begin{cases} h=-2\\ k=3\\ a=1\\ b=2 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ c=\sqrt{a^2+b^2}\implies c=\sqrt{1+4}\implies c=\sqrt{5} \\\\\\ \stackrel{\textit{so then the foci are at}}{(-2~~,~~3\pm \sqrt{5})}\qquad \qquad \qquad \stackrel{\textit{and its vertices are at }}{(-2~~,~~3\pm 1)}\implies \begin{cases} (-2,4)\\ (-2,2) \end{cases}[/tex]
now let's check for the asymptotes.
[tex]\bf y=3\pm \cfrac{1}{2}[x-(-2)]\implies y=3\pm \cfrac{1}{2}(x+2) \\\\[-0.35em] ~\dotfill\\\\ y=3+ \cfrac{1}{2}(x+2)\implies y=3+\cfrac{x+2}{2}\implies y=\cfrac{6+x+2}{2} \\\\\\ y=\cfrac{x+8}{2}\implies y=\cfrac{1}{2}x+4 \\\\[-0.35em] ~\dotfill\\\\ y=3- \cfrac{1}{2}(x+2)\implies y=3-\cfrac{(x+2)}{2}\implies y=\cfrac{6-(x+2)}{2} \\\\\\ y=\cfrac{6-x-2}{2}\implies y=\cfrac{-x+4}{2}\implies y=-\cfrac{1}{2}x+2[/tex]
. A man is 25 years old. His mother is exactly three times his age. How old will the man's mother be when he is 35 years old?
Answer:
Step-by-step explanation:
105 years old. Since if he 35 the mother is 105>>------->(35 x 3= 105)
85 years old. 25•3=75 the difference between 75 and 25 is 50, which means she is 50 years older than him. 35+50=85.
A car has a 12-volt battery. The engine has a resistance of 0.22 ohms. How many amps will be drawn from the battery when the key is turned?
Answer:
54.5 amps to the nearest tenth.
Step-by-step explanation:
V = IR where V = volts, I = current and R = resistance.
12 = I * 0.22
I = 12/0.22
I = 54.5 Amps.
When the key is turned and the engine starts, the battery will supply approximately 54.55 amps to the engine.
The question regarding how many amps will be drawn from the 12-volt battery when a car engine with a resistance of 0.22 ohms is started can be solved using Ohm's Law. Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. The formula is given by I = V / R.
Therefore, the current drawn from the battery can be calculated as follows:
Voltage (V) = 12 voltsResistance (R) = 0.22 ohmsCurrent (I) = V / R = 12 / 0.22 = 54.55 ampsSo, when the key is turned and the engine starts, the battery will supply approximately 54.55 amps to the engine.
Help
Plz and thank you
Answer: try question cove but brainly is good so keep using it
]
A square patio was enlarged by adding 9 feet to the length and width of the original square patio. If the area of the enlarged patio is 441 ft.2, what was the side length of the original patio?
Answer:
The side length of the original patio was [tex]12\ ft[/tex]
Step-by-step explanation:
Let
x----> the side length of the original square patio
we know that
[tex]441=(x+9)^{2}\\ \\x^{2} +18x+81=441\\ \\ x^{2} +18x- 360=0[/tex]
Solve the quadratic equation by graphing
The solution is [tex]x=12\ ft[/tex]
see the attached figure
Answer:
for study island it is 11 feet
Step-by-step explanation:
Find the first four iterates of the function f(x) = 3x - 7 with an initial value of x0 = 4.
a.
-5, -8, -17, -44
c.
5, 8, 17, 44
b.
-7, -11, -15, -49
d.
7, 11, 15, 49
Answer:
c. 5, 8, 17, 44
Step-by-step explanation:
Put the given number into the formula and do the arithmetic:
3·4 -7 = 5 . . . . . matches answer choice C only
___
You know the correct answer at this point. You can check the other numbers if you wish:
3·5 -7 = 8
3·8 -7 = 17
3·17 -7 = 44
A study estimates the cost of tuition at the university will increase by %2.8 each year. The cost of tuition at the university in 2015 was $33,741
The compounding tuition fee function's complete expression is,b(x)=33741(1.028)ˣ.
How do you calculate compound interest?If n is the number of times the interest is compounded each year and r is the yearly rate of compound interest, the final amount after 't' years is:
[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]
The function b(x) is expressed as follows:
[tex]\rm b(x) = 33741(1+\frac{0.028}{1} )^x\\\\[/tex]
Where ;
Rate(r)=2.8 percent
Total after x years(b)
Initial amount ( P)= 33741
x represents the number of years since 2015.
Hence, the compounding tuition fee function's complete expression is,b(x)=33741(1.028)ˣ.
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Which best explains why this triangle is or is not a right triangle?
Answer:
It is a right triangle.
Step-by-step explanation:
By the Inverse Pythagoras Theorem if 39^2 = 36^2 + 15^2 then it is a right triangle.
39^2 = 1521
36^2 + 15^2 = 1296 + 225 = 1521.
So it is a right triangle.
Based on the converse of the Pythagorean Theorem, the triangle with the following side lengths is a right triangle.
What is the Converse of the Pythagorean Theorem?
The converse of the Pythagorean Theorem states that a triangle is a right triangle if the sum of the squares of two of its legs are equal to the square of the length of the longest side (hypotenuse).
The longest side in the triangle is 39 in. Therefore:
39² = 36² + 15²
1,521 = 1,521
Based on this, we can conclude that the triangle given is a right triangle.
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The right rectangular prism is packed with unit cubes of the appropriate unit fraction edge lengths. Find the volume of the right rectangular prism in centimeters. (Figure not to scale)
Answer:
The volume is equal to [tex]112\frac{1}{2}\ cm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the rectangular prism is equal to
[tex]V=LWH[/tex]
we have
[tex]L=4\frac{1}{2}\ cm=\frac{4*2+1}{2}=\frac{9}{2}\ cm[/tex]
[tex]W=5\ cm[/tex]
[tex]H=5\ cm[/tex]
substitute the values
[tex]V=(\frac{9}{2})(5)(5)[/tex]
[tex]V=112.5\ cm^{3}[/tex]
Convert to mixed number
[tex]112.5\ cm^{3}=112\frac{1}{2}\ cm^{3}[/tex]
Answer:
D
Step-by-step explanation:
The graphs of two sine functions are shown below.
The function whose graph is B was obtained from the function whose graph is A by one of the following changes. That change was:
a phase shift
a period change
a change in amplitude
the addition of a negative constant
Answer:
"a period change"
Step-by-step explanation:
Simple ways of understanding transformations are:
Phase shift: 2 graphs would be shifted version of each other, all other things constant.
Period change: the 2 graphs would have different cycles, one would be compressed/stretched version of the other, all other things constant
Amplitude Change: The height/crest of the graphs would vary, that is the amplitude. All other things constant.
Addition of Negative constant: this would shift the 1 graph downwards with respect to the other graph, it is a vertical shift. All other things constant.
Now carefully looking at the 2 graphs given, we can see that the cycles are different. One is a more "relaxed", or "stretched" version of the other. This means, the period is changed.
2nd answer choice is right.
Help! Anyone can you explain?
A goblet contains 3 red balls, 2 green balls, and 6 blue balls.
If we choose a ball, then another ball without putting the first one back in the goblet, what is the probability that the first ball will be red and the second will be blue?
Answer:
[tex]\texttt{Probability that the first ball will be red and the second will be blue = }\frac{9}{55}[/tex]
Step-by-step explanation:
Total number of balls = 3 + 2 + 6 = 11
Probability is the ratio of number of favorable outcome to total number of outcomes.
[tex]\texttt{Probability that the first ball will be red = }\frac{\texttt{Total number of red balls}}{\texttt{Total number of balls}}\\\\\texttt{Probability that the first ball will be red = }\frac{3}{11}[/tex]
Now we have 10 balls in which 6 are blue.
[tex]\texttt{Probability that the second ball will be blue = }\frac{\texttt{Total number of blue balls}}{\texttt{Total number of balls}}\\\\\texttt{Probability that the first ball will be red = }\frac{6}{10}=\frac{3}{5}[/tex]
[tex]\texttt{Probability that the first ball will be red and the second will be blue = }\frac{3}{11}\times \frac{3}{5}\\\\\texttt{Probability that the first ball will be red and the second will be blue = }\frac{9}{55}[/tex]
If the coefficient of determination for a data set is 0.25 and the SEA for the data set is 12, what is the SST for the data set
A. 16
B. 20
C. 8
D. 12
Answer:
A
Step-by-step explanation:
We can use a simple formula to solve for SST. The formula is:
[tex]SST=\frac{SSE}{1-R^2}[/tex]
Where
the coefficient of determination is [tex]R^2[/tex]
Now, we are given [tex]R^2[/tex] is 0.25 and SSE is 12 (not SEA, it's SSE). we simply put it into the formula and solve for SST:
[tex]\\SST=\frac{12}{1-0.25}\\SST =16[/tex]
correct answer choice is A
Different sized containers are filled with oil. Later, vinegar is added to make a salad dressing. The ratio used is 1 tablespoon of vinegar (y) to 0.5 tablespoons of oil (x). Which of the following statements is true?
The function is y = 2x because the recipe calls for a ratio of 2 parts oil to 1 part vinegar.
The function is y = 2x because the recipe calls for a ratio of 2 parts vinegar to 1 part oil.
The function is y = 1/2x because the recipe calls for a ratio of 2 parts oil to 1 part vinegar.
The function is y = 1/2x because the recipe calls for a ratio of 2 parts vinegar to 1 part oil.
the answer is the second one
Answer:
The answer is b!!
help please will give brainliest thank you
Independent, means the first event won't affect the second event.
The independent events would be :
A, B, E, F
Match the input values on the left (X) with the output values on the right (Y).
y = 2x + 7
1 11
2 13
3 9
4 15
Answer:
1 9
2 11
3 13
4 15.
Step-by-step explanation:
When x = 1 y = 2(1) + 7 = 9.
x = 2, y = 2(2)+7 = 11
x = 3, y = 2(3) + 7 = 13
x = 4, y = 2(4) + 7 = 15.
The location of point V is (-3,3). The location of point X is (9,13). Determine the location of point W which is 3/4 of the way from V to X
ANSWER
[tex]W(\frac{9}{7},\frac{51}{7} )[/tex]
EXPLANATION
We want to find the coordinates of the point W(x,y) which divides V(-3,3) and X(9,13) in the ratio m:n=3:4.
The x-coordinate of this point is given by:
[tex]x= \frac{mx_2+nx_1}{m + n} [/tex]
[tex]x= \frac{3(9)+4( - 3)}{4 + 3} [/tex]
[tex]x= \frac{21 - 12}{4 + 3} [/tex]
[tex]x= \frac{9}{7} [/tex]
The y-coordinates is given by;
[tex]y= \frac{my_2+ny_1}{m + n} [/tex]
[tex]y= \frac{3(13)+4( 3)}{4 + 3}[/tex]
[tex]y= \frac{39+12}{4 + 3}[/tex]
[tex]y= \frac{51}{7}[/tex]
Hence
[tex]W(\frac{9}{7},\frac{51}{7} )[/tex]
Can someone please help me out with this question? I need an answer ASAP. Thank you!!!
Evaluate the expression:
v ⋅ w
Given the vectors:
r = <8, 8, -6>; v = <3, -8, -3>; w = <-4, -2, -6>
Multiply corresponding components, then add the products:
[tex]v\cdot w=3(-4)+(-8)(-2)+(-3)(-6)=22[/tex]
The resultant of the dot product of two vectors is:
[tex]v\cdot w=22[/tex]
Step-by-step explanation:We are asked to find the dot product of the two vectors v and w.
The vectors are given by:
r = <8, 8, -6>; v = <3, -8, -3>; w = <-4, -2, -6>
This means that in the vector form they could be written as follows:
[tex]r=8\hat i+8\hat j -6\hat k\\\\v=3\hat i-8\hat j -3\hat k\\\\w=-4\hat i-2\hat j -6\hat k[/tex]
Hence, the dot product of two vectors is the sum of the product of the entries corresponding to each direction component.
i.e. the x-component get multiplied to each other, y-component get multiplied to each other and so happens with z.
Hence, the dot product of v and w is calculated as:
[tex]v\cdot w=3\times (-4)-8\times (-2)-3\times (-6)\\\\i.e.\\\\v\cdot w=-12+16+18\\\\i.e.\\\\v\cdot w=22[/tex]
After the program was completed, the coach monitored each of the 30 athletes for five athletic events. At the end of this process, he reported that the average number of muscular injuries for athletes enrolled in the strength training program is equal to the average number of muscular injuries for athletes not enrolled in the strength training program. What can be concluded from the coach's report?
Answer:
B
Step-by-step explanation:
Todd's cube has an edge that measures5 inches. Kara's cube has an edge of3 inches. If Kara's cube was stackedon top of Todd's cube, what wouldbe the total volume of the combinedsolid? ?
Answer:
152 in³
Step-by-step explanation:
Each cube's volume is the cube of its edge length, so the total volume is ...
(5 in)³ + (3 in)³ = 125 in³ +27 in³ = 152 in³
How many females with college degrees work at his two stores?
Answer:
30
Step-by-step explanation:
At the northside store there are 12 females with college degrees
At the southside store there are 18 females with college degrees
The total number of females at the two stores with college degrees is
12+18 = 30
pleaseeeeee help thanks!
I think it's C. Trout increased its predicted average population.
Answer:
b
Step-by-step explanation:
because it increases the most
Find the measure of x for this shape.
A. 36
b.28
c.32
d.22
let's recall that in an isosceles triangle, the twin sides make twin angles at the bottom/base, so on the triangle on the left-side, if the "vertex" atop has an angle of 116°, then the twin sides below are simply 180° - 116 = 64, split that in half and that's 32° each.
The same is true for the isosceles triangle on the right side. Also recall that a flat-line is always 180°, 32 + 72 + 76 = 180.
Check the picture below.
HELP!! THIS TEST WORTH 36 POINTS!!! WILL MARK BRAINLEIST!!!!
Natalie applied for a new credit card.
Which information about Natalie could appear on her credit report?
Choose all answers that are correct.
A. her savings account number
B. amount of available credit on her credit cards
C. amount she owes on her mortgage
D. her gender
Answer:
A, B, C
Step-by-step explanation:
If Jamaal will be paid $5.00 an hour for delivering pizzas, and he works for 4 hours, how much will he be paid?
Answer:
$20
Step-by-step explanation:
4×5=$20
this is random do not look
Help me please!!!!!!!!
Answer:
82
Step-by-step explanation:
The sum resolves to ...
13 + 18 + 23 + 28 = 82
_____
for n=2, the term is 5·2 +3 = 10+3 = 13
The coefficient of n is 5, so you know the next term will be 5 more than this:
for n=3, the term is 5·3 +3 = 15+3 = 18
Additional terms are each 5 more than the one before. Since there are so few terms, you can add them up directly as quickly as you can use any other formula. For a longer series, you might find the average term (here, 41/2), then multiply by the number of terms (here, 4). The result is the sum of the series:
4·(41/2) = 82
What is the value of tan A.
Answer:
15/8.
Step-by-step explanation:
Tan A = opposite / adjacent side
= 15/8.
The value of tan A is 15/8.
What is Trigonometry?It is a mathematical functions which deals with the angles and sides of the right angle triangle.Trigonometric functions include, sine, cosine, tangent, cotangent, secant and cosecant.
Given: Right angled triangle
AB = 8
AC = 17
BC = 15
We have to find tan A.
We know,
tan A = Opposite side / Adjacent side
In the given right angle triangle:
Opposite side = BC
Adjacent side = AB
⇒ tan A = BC/AB
⇒ tan A = 15/8
Therefore, the value of tan A is 15/8.
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