Use the function below to find f(-2)
f(x)=5^x
Answers
Answer:
1/25
Step-by-step explanation:
f(x)=5^x
Let x = -2
f(-2)=5^-2
We know that a^-b = 1/a^b
= 1/5^2
= 1/25
Related Questions
10-² =
Exponential form
Answers
Copy the base to the right side of the equality
10-^2=10
Rewrite the exponent -2 as the product of (-1) and 2
10-^2=10^(-1)x2
First, use the Power of a Power Property
10-^2=(10^(-1) ) ^2
Any number raised to the power of can be written as its reciprocal
10^-2=(1/10)^2
Next, use the Power of a Quotient Property
10^-2=1^2/10^2
1 raised to any power equals 1
10^-2=1/10^2
so the answer is 10^-2=1/10^2
Answer:
Step-by-step explanation:
the answer is 0.01
The base of the exponential form is 10 and the power is -2 therefore the answer is 0.01 if the power was 2 the answer would have been 100
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The cost of one t-shirt is 128. How much will be the cost of 20
Answers
The cost of 20 T-Shirt will be 2560 when cost of one t-shirt is 128.
When a selling price and profit are provided, cost price equals selling price plus profit. When the selling price and loss are disclosed, cost price equals selling price plus loss.
Profit is calculated as S.P. - C.P. If the selling price is less than the cost price, the difference between the two is the loss incurred. Loss is also equal to C.P. - S.P.
We must divide the gross profit by the entire revenue for the year, multiply by 100, and then find the gross profit margin. We must divide net income (or net profit) by the entire annual revenue before multiplying the result by 100 to get the net profit margin.
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helppp please I have limited time
Answers
Answer:
p = T - a - b
Step-by-step explanation:
Hope that helps, not sure if it is correct though.
-8/9 + (-2)/57
find the absolute value of the following rational number
Answers
The absolute value of the Rational number -474/513 is 474/513.
To find the sum of the rational numbers -8/9 and -2/57, you need to have a common denominator. The least common multiple (LCM) of 9 and 57 is 513. So, you can rewrite the fractions with a common denominator:
-8/9 = (-8/9) * (57/57) = -456/513
-2/57 = (-2/57) * (9/9) = -18/513
Now, you can add the fractions:
-456/513 + (-18/513) = (-456 - 18)/513 = -474/513
To find the absolute value of the rational number -474/513, you simply ignore the negative sign and take the value as positive:
| -474/513 | = 474/513
Therefore, the absolute value of the rational number -474/513 is 474/513.
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not sure at all how to solve this pls help
Answers
Applying the law of sines
we have that
\(A=\frac{1}{2}\cdot AB\cdot BC\cdot\sin (B)\)substitute given values
we have
AB=7.6
BC=7.01
B=31.09 degrees
\(A=\frac{1}{2}\cdot7.6\cdot7.01\cdot\sin (31.09)\)A=13.76 unit2Consider the parabola given by the equation:
f
(
x
)
=
−
2
x
2
−
8
x
+
14
Find the following for this parabola:
A) The value of
f
(
−
5
)
:
B) The vertex = (
,
)
C) The
y
intercept is the point (0,
)
D) Find the two values of
x
that make
f
(
x
)
=
0
. Round your answers to two decimal places. Write the values as a list, separated by commas:
x
=
Answers
Answer:
Sure, here are the answers to your questions:
**A) The value of $f(-5)$ is $-2$.**
To find the value of $f(-5)$, we can simply substitute $x=-5$ into the equation $f(x)=-2x^2-8x+14$. This gives us:
$$f(-5)=-2(-5)^2-8(-5)+14=-2(25)+40+14=-50+54=4$$
**B) The vertex of the parabola is $(2,6)$.**
To find the vertex of the parabola, we can complete the square. This involves adding and subtracting $\left(\dfrac{{b}}{2}\right)^2$ to both sides of the equation, where $b$ is the coefficient of the $x$ term. In this case, $b=-8$, so we have:
$$\begin{aligned}f(x)&=-2x^2-8x+14\\\\ f(x)+20&=-2x^2-8x+14+20\\\\ f(x)+20&=-2(x^2+4x)\\\\ f(x)+20&=-2(x^2+4x+4)\\\\ f(x)+20&=-2(x+2)^2\end{aligned}$$
Now, if we subtract 20 from both sides, we get the equation of the parabola in vertex form:
$$f(x)=-2(x+2)^2-20$$
The vertex of a parabola in vertex form is always the point $(h,k)$, where $h$ is the coefficient of the $x$ term and $k$ is the constant term. In this case, $h=-2$ and $k=-20$, so the vertex of the parabola is $(-2,-20)$. We can also see this by graphing the parabola.
[Image of a parabola with vertex at (-2, -20)]
**C) The $y$-intercept is the point $(0,14)$.**
The $y$-intercept of a parabola is the point where the parabola crosses the $y$-axis. This happens when $x=0$, so we can simply substitute $x=0$ into the equation $f(x)=-2x^2-8x+14$ to find the $y$-intercept:
$$f(0)=-2(0)^2-8(0)+14=14$$
Therefore, the $y$-intercept is the point $(0,14)$.
**D) The two values of $x$ that make $f(x)=0$ are $2.5$ and $-3.5$.**
To find the values of $x$ that make $f(x)=0$, we can set the equation $f(x)=-2x^2-8x+14$ equal to zero and solve for $x$. This gives us:
$$-2x^2-8x+14=0$$
We can factor the left-hand side of the equation as follows:
$$-2(x-2)(x-3)=0$$
This means that either $x-2=0$ or $x-3=0$. Solving for $x$ in each case gives us the following values:
$$x=2\text{ or }x=3$$
However, we need to round our answers to two decimal places. To do this, we can use the calculator. Rounding $x=2$ and $x=3$ to two decimal places gives us the following values:
$$x=2.5\text{ and }x=-3.5$$
Therefore, the two values of $x$ that make $f(x)=0$ are $2.5$ and $-3.5$.
Which category in the table shows the least portion?
please hurry if you can! 12 points
Answers
The value given for "8th grade Participate in Sports" is 0.22, which is the least value among all the categories in the table.
Define the term percentage?A number can be expressed as a fraction of 100 using a percentage. "%" is used to represent it. Frequently, proportions, rates, and changes throughout time are expressed using percentages.
Based on the table provided, it appears that the category with the least portion is "8th grade Sports participators" with a value of 0.22.
For "6th grade Sports participators", the value is 3/20, which is equivalent to 0.15, and for "7th grade Sports participators", the value is 18%, which is equivalent to 0.18.
For "Other school activities" category, the least value is 0.45 for "7th grade Other school activities" and the highest value is 33% for "6th grade Other school activities". Therefore, "8th grade Sports participators" has the least portion among all the categories in the given table.
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Rumus suatu fungsi di nyatakan dengan f (x) = 2x + 5. Jika f(a) = 7, nilai a adalah
Answers
Step-by-step explanation:
As my previous answer got deleted for being wrong (in which it was right), I will answer again.
The answer is 1. Why? Just plug it into the equation. F(1) = 2(1) + 5 = 7.
This is proof that it is right, and that there are some corrupt admins on brainly.
How to get to this solution?
Well notice how we are given what f(a) is. It is 2a + 5. So plug this in for f(a).
If we do so, we get 2a + 5 = 7.
Solving this equation, we get a = 1.
2. The diagram above shows a wooden structure in the form of a cone mounted on hemispherical base. The vertical height of the cone is 24cm and the base 7cm. Calculate correct to 3 significant figures the surface area of the structure. (Take π= 22/7)
Answers
The surface area of the wooden structure is approximately 1012 cm².
To calculate the surface area of the wooden structure, we need to find the surface area of the cone and the surface area of the hemispherical base, and then add them together.
Surface Area of the Cone:
The surface area of a cone is given by the formula:
A_{cone = \(\pi \times r_{cone} \times (r_{cone} + s_{cone})\), \(r_{cone\) is the radius of the base of the cone and \(s_{cone\) is the slant height of the cone.
The vertical height of the cone is 24 cm, and the base radius is 7 cm, we can calculate the slant height using the Pythagorean theorem:
\(s_{cone\) = \(\sqrt{(r_{cone}^2 + h_{cone}^2).\)
Using the given measurements:
\(s_{cone\) = √(7² + 24²) cm
\(s_{cone\) ≈ √(49 + 576) cm
\(s_{cone\) ≈ √625 cm
\(s_{cone\) ≈ 25 cm
Now, we can calculate the surface area of the cone:
\(A_{cone\) = π × 7 cm × (7 cm + 25 cm)
\(A_{cone\) = (22/7) × 7 cm × 32 cm
\(A_{cone\) = 704 cm²
Surface Area of the Hemispherical Base:
The surface area of a hemisphere is given by the formula:
\(A_{hemisphere\) = \(2 \times \pi \times r_{base}^2\), \(r_{base\) is the radius of the base of the hemisphere.
Given that the base radius is 7 cm, we can calculate the surface area of the hemispherical base:
\(A_{hemisphere\) = 2 × (22/7) × (7 cm)²
\(A_{hemisphere\) = (22/7) × 2 × 49 cm²
\(A_{hemisphere\) = 308 cm²
Total Surface Area:
To calculate the total surface area, we add the surface area of the cone and the surface area of the hemispherical base:
Total Surface Area = \(A_{cone} + A_{hemisphere}\)
Total Surface Area = 704 cm² + 308 cm²
Total Surface Area = 1012 cm²
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How to do because I dont know need help ASAP 20 points
Answers
Some arithmetic sequences could be easier to write as functions. As long as I know what value "n" has, I can find out any term in a particular Sequence whenever I need to. You might choose the implicit term over the prior term of a Sequence if it is known.
What is meant by Arithmetic Sequences?The arithmetic mean can be calculated as one approach. Divide the total by the total number of values after adding up all the values.
A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.
Some arithmetic sequences could be easier to write as functions. You are aware of the prior term.
Consider that we only have the numbers (...,4,...) from an arithmetic sequence with a common difference of 5.
The complete question is:
You are given the first four terms of an arithmetic sequence. Under what conditions might a recursive formula be preferred over the explicit formula? Under what conditions might an explicit formula be preferred over the recursive formula?
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Natalie is selling fruit at the Saturday market. She has a
otal of 48 pears that she wants to sell. She makes bags of
pears and sells them for $5 per bag. In which equation
oes b represent the number of bags of pears?
Answers
If Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.
To represent the number of bags of pears, b, that Natalie sells at the Saturday market, we can use the following equation:
b = total_number_of_pears / pears_per_bag
In this equation, "total_number_of_pears" represents the total quantity of pears Natalie has, and "pears_per_bag" represents the number of pears she puts in each bag.
Given that Natalie has a total of 48 pears, we can substitute the value into the equation:
b = 48 / pears_per_bag
Now, we need to determine the number of pears she puts in each bag. The information provided states that Natalie sells bags of pears, and each bag is sold for $5. However, the specific number of pears per bag is not given. To proceed, we need this information.
Let's assume that Natalie puts 4 pears in each bag. We can substitute this value into the equation:
b = 48 / 4
Simplifying the equation gives:
b = 12
So, if Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.
It's important to note that the specific value of "pears_per_bag" will affect the final result. If Natalie puts a different number of pears in each bag, the equation will yield a different number of bags sold.
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A quadratic function has a vertex at (3, -10) and passes through the point (0, 8). Which of the following equations best represents the function? O y = 2(x+3)² +8 O y = 2(x+3)² – 10 Oy=(x-3)²-10 O y = 2(x-3)² – 10
Answers
\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\)
\(\begin{cases} h=3\\ k=-10\\ \end{cases}\implies y=a(~~x-3~~)^2 + (-10)\hspace{4em}\textit{we also know that} \begin{cases} x=0\\ y=8 \end{cases} \\\\\\ 8=a(~~0-3~~)^2 + (-10)\implies 8=9a-10\implies 18=9a\implies \cfrac{18}{9}=a \\\\\\ 2=a\hspace{7em}y=2(~~x-3~~)^2 + (-10)\implies \boxed{y=2(x-3)^2-10}\)
A washer and a dryer cost $993 combined. The washer costs $43 more than the dryer. What is the cost of the dryer?
Answers
Answer:425
Step-by-step explanation:
993-43=950
950/2=425
Answer:
$475
Step-by-step explanation:
Let's call the cost of the dryer x. That means the cost of the washer is x + $43. The combined cost of the two is $993, so we can write the equation:
x + (x + $43) = $993
Expanding the right side:
2x + $43 = $993
Subtracting $43 from both sides:
2x = $950
Dividing both sides by 2:
x = $475
So the cost of the dryer is $475.
How many fluid ounces are there in 6 quarts?
Answers
Answer:
The answer is 192. Hope this helps!
Pre-Quiz
Practice
Post-Quiz
Finish
Finish
Welcome,
Math
Guided
Learning
Using Proportions to Solve Problems - Item 34688
A pet store has 150 goldfish and betta fish altogether.
The ratio of goldfish to betta fish is 2:3.
How many goldfish does the pet store have?
CLEAR
What fraction of the fish are goldfish?
How many goldfish does the pet store have?
goldfish
Answers
Answer:
2/5 and there is 60 goldfish
Step-by-step explanation:
Solve |x+4|=9. ..............
Answers
Can I get Brainly?
all i need is for question 15 to be answered please help
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given equations
\(\begin{gathered} x(t)=3t^2-1 \\ y(t)=2t \end{gathered}\)STEP 2: Plot the given parametric function
The functions give:
A hyperbola is an open curve with two branches, the intersection of a plane with both halves of a double cone. The plane does not have to be parallel to the axis of the cone; the hyperbola will be symmetrical in any case.
Therefore, the conic section for the given functions is Hyperbola.
Use triangle XYZ to answer questions 3-5.
1) Use special right triangles to help find the length of segment XY. What is the exact height of triangle XYZ?
Click the keyboard button to enter your answer.
2)What is the exact area of triangle XYZ? Leave your answer in radical terms.
Click the keyboard button to enter your answer. Show your work.
3)What is the area of triangle XYZ to the nearest tenth of a square in?
Answers
Answer:
Step-by-step explanation:
What is the solution to g-8= -24?
Answers
Answer:
g=16
Step-by-step explanation:
Answer:
g=-16
Step-by-step explanation:
ugriuhgi5ughoiruhr PLEASE HELP 10 POINTS!
Answers
Answer:
A = 6
B = 6
C = 7
D = 4
Step-by-step explanation:
A-B equals, if A =5x^2-4x-11 and B=-x^2+3x-5
Answers
Answer:
A-B = 6x^2-7x-6
Step-by-step explanation:
A = 5x^2-4x-11
B = x^2+3x-5
A-B = (5x^2-4x-11) - (-x^2+3x-5) = 5x^2-4x-11+x^2-3x+5 = 6x^2-7x-6
) Quantifier negation.
Form the negation of the following statements. Then apply De Morgan’s law and/or conditional law, when
applicable. Negation should appear only within predicates, i.e., no negation should be outside a quantifier
or an expression involving logical connectives. Show all steps.
a) ∀x (P(x) ∧ R(x))
b) ∀y∃z(¬P(y) → Q(z))
c) ∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))
Answers
The negations of the given statements with the application of De Morgan's law and/or conditional law.
a) ∃x (¬P(x) ∨ ¬R(x))
De Morgan's law:
∃y ∀z(¬P(y) ∧ ¬Q(z))
b) ∃y ∀z(¬P(y) ∧ ¬Q(z))
The double negation:
∃y ¬∃z(P(y) ∨ Q(z))
c) ¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))
The conditional law:
¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))
Let's form the negation of the given statements and apply De Morgan's law and/or conditional law, when applicable:
a) ∀x (P(x) ∧ R(x))
The negation of this statement is:
∃x ¬(P(x) ∧ R(x))
Now let's apply De Morgan's law:
∃x (¬P(x) ∨ ¬R(x))
b) ∀y∃z(¬P(y) → Q(z))
The negation of this statement is:
∃y ¬∃z(¬P(y) → Q(z))
Using the conditional law, we can rewrite the negation as:
∃y ¬∃z(¬¬P(y) ∨ Q(z))
c) ∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))
The negation of this statement is:
¬∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))
Using the conditional law, we can rewrite the negation as:
¬∃x (P(x) ∨ (∀z (R(z) ∨ ¬Q(z))))
Applying De Morgan's law:
¬∃x (P(x) ∨ (∀z ¬(¬R(z) ∧ Q(z))))
Simplifying the double negation:
¬∃x (P(x) ∨ (∀z ¬(R(z) ∧ Q(z))))
Using De Morgan's law again:
¬∃x (P(x) ∨ (∀z (¬R(z) ∨ ¬Q(z))))
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1. What are parallel lines?
2. Write the converse of Theorem 3.8. Is the converse true?
3. Can you prove that lines p and q are parallel? If so, describe how.
Answers
Answer:
lines that never touch and are next to each other are parallel
Step-by-step explanation:
A tank contains 180 liters of fluid in which 50 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 6 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t.
Answers
Answer:
\(\mathbf{A(t) = 180 - 130e ^{-\dfrac{t}{30}}}\)
Step-by-step explanation:
Given that:
A tank contains 180 liters of fluid in which 50 grams dissolved inside.
Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 6 L/min
The salt pumped out\(= \dfrac{6 L}{180 L} = \dfrac{1}{30}\) of initial amount added salt
At (t = 0) = 50
To determine the number A (t)
\(\dfrac{dA}{dt}=Rate_{in} - Rate _{out}\)
\(A' = 6 - \dfrac{1}{30}A\)
\(A' + \dfrac{1}{30}A = 6\)
Integrating factor \(y = e^{\int\limits pdt\)
\(y = e^{\int\limits \dfrac{1}{30}dt}\)
\(y = e^{\dfrac{t}{30}}\)
\((e^{ \frac{t}{30}}A)' =4 e ^{\dfrac{t}{30}}+c\)
Taking integral on the both sides;
\(Ae ^{\dfrac{t}{30}}= 6 * 30 e^{\dfrac{t}{30}} + c\)
\(A = 180+ ce^ {-\dfrac{t}{30}}\)
At A(t = 0) = 50
50 = 180 + C (assuming C = \(ce ^{-\dfrac{t}{30}}\))
C = 50 - 180
C = 130
\(\mathbf{A(t) = 180 - 130e ^{-\dfrac{t}{30}}}\)
What is BD?
PLEASE HELP!!!
Answers
Answer:
bd – boundary. (Also written as fr or ∂.) Bi – Airy function of the second kind. BIDMAS – Brackets, Indices, Divide, Multiply, Add, Subtract.
Step-by-step explanation:
What day comes three days after the day which comes two days after the day which comes immediately after the day which comes two days after Monday?
Answers
Answer:
Step-by-step explanation:
Tuesday
Answer: Tuesday
Step-by-step explanation:
Second after Monday is Wednesday and then immediately is Thursday and second after Thursday is Saturday after which three days is Tuesday.
6/5 + ? = 27/10? Help me pls
Answers
\(\cfrac{6}{5}~~ + ~~\boxed{?}~~ = ~~\cfrac{27}{10}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{10}}{10\left( \cfrac{6}{5}~~ + ~~\boxed{?} \right)~~ = ~~10\left( \cfrac{27}{10} \right)}\implies 12+10\boxed{?}=27 \\\\\\ 10\boxed{?}=15\implies \boxed{?}=\cfrac{15}{10}\implies \boxed{?}=\cfrac{3}{2}\)
Please help me with this math problem
1. Josiah is making a candle by pouring melted wax into a mold in the shape of a square pyramid. Each side of the base of the pyramid is 12 in and the height of the pyramid is 14in. To get the wax for the candle, Josiah melts cubes of wax that are each 6 in by 6 in by 6 in. How many of the wax cubes will Josiah need in order to make the candle? Show your work.
Answers
Answer:
10 wax cubes
Step-by-step explanation:
the volume of the square pyramid can be found by using the following formula:
\(V = \frac{1}{3} * B * h\)
where b is the base of the pyramid and h is the height of the pyramid
The area of the base of the pyramid is given as 12 in * 12 in = 144 in^2
So, the volume of the pyramid is:
V = (1/3) * 144 in^2 * 14 in = 2,016 in^3
Each wax cube has a volume of 6 in * 6 in * 6 in = 216 in^3.
To find the number of wax cubes needed, we can divide the volume of the pyramid by the volume of each wax cube:
Number of wax cubes = Volume of pyramid / Volume of each wax cube
Number of wax cubes = 2,016 in^3 / 216 in^3
Number of wax cubes = 9.33 (rounded to two decimal places)
Since we can't have a fraction of a wax cube, Josiah will need to use 10 wax cubes to make the candle.
t is no more than 2 units from 9
Answers
Answer:
11 or 7
Step-by-step explanation:
9 + 2 = 11
9 - 2 = 7
are the following ratios equal. write yes or no. use the theroem that the product of the extremes equals the product means.
Answers
The ratios will be equal if the theorem that the product of the extremes equals the product means follows.
Let us understand the equality of ratios through example. The example ratio will be -
7:10 = 21:30
In this ratio, 7 and 30 are first and last numbers and hence they are extremes. The number 10 and 21 are in middle and hence considered mean. Now, we will perform multiplication to if the ratios are equal or not.
Product of extremes = 7 × 30
Extremes product = 210
Product of means = 21 × 10
Means product = 210
Since the products are equal, the ratios are also equal.
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The complete question is -
Are the following ratios equal? write yes or no. use the theroem that the product of the extremes equals the product means.
Ratio = 7:10 and 21:30.