Answer:
X= -4
X=-2
Step-by-step explanation:
for
|a|=b
assume
a=b and a=-b
so
3-2|0.5x+1.5|=-2
minus 3 both sides
-2|0.5x+1.5|=-1
divide both sides by -2
|0.5x+1.5|=0.5
set negative and postivive
0.5x+1.5=0.5 and 0.5x+1.5=-0.5
solve each
0.5x+1.5=0.5
minus 1.5 both sides
0.5x=-1
times - 2 both sides
x=-2
other
0.5x+1.5=-0.5
minus 1.5 from oth sides
0.5x=-2
times 2 both sides
x=-4
the solutions are x=-2 and x=-4
Answer:
x=-4
Step-by-step explanation:
the constant proportionality of y=5x
Answer:
k = 5
Step-by-step explanation:
The equation of proportionality is
y = kx ← k is the constant of proportionality
Given
y = 5x , then k = 5
please help with this question, I am quite confused
Answer:
Step-by-step explanation:
A-domain (-∞,∞)
B- Range(0,∞) the range is the set of values tat correspond with the domain
C- the y intercept (0,1) , y intercept is when x =0 (2/3)^0=1
D-the horizontal asymptote is x-axis y=0
E- the graph is always decreasing
F-it depend on the base
the figure is cut into 6 equal pieces shade 1/3 of the figure.
Answer:
Here,
The circle is cut into 6 equal parts.
It means all the piece of circle is divided forming 60°.
And according to the question we have shade its 1/3part.
means 1/3×360°
=120° so, we should shade 2 pieces of circle.
Hope it helps...
winthrop has $4.40 worth of nickles and dimes. If winthrop has 3.5 times as many nickles as he has dimes, how many dimes does he have?
Answer:
16
Step-by-step explanation:
If n is number of nickles and d is number of dimes:
5n + 10d = 440
n = 3.5d
Substitute:
5(3.5)d + 10d = 440
17.5d + 10d = 440
27.5d = 440
d = 16
What is the simplified form of the following expression?
[tex]2 (\sqrt[4]{16x}) - 2 (\sqrt[4]{2y} ) + 3 (\sqrt[4]{81x} ) - 4 (\sqrt[4]{32y} )[/tex]
We have
[tex]16=2^4\implies\sqrt[4]{16}=2[/tex]
[tex]81=3^4\implies\sqrt[4]{81}=3[/tex]
[tex]32=2^5\implies\sqrt[4]{32}=2\sqrt[4]{2}[/tex]
So
[tex]2\sqrt[4]{16x}-2\sqrt[4]{2y}+3\sqrt[4]{81x}-4\sqrt[4]{32y}[/tex]
is equivalent to
[tex]2^2\sqrt[4]{x}-2\sqrt[4]{2y}+3^2\sqrt[4]{x}-8\sqrt[4]{2y}[/tex]
which reduces to
[tex]13\sqrt[4]{x}-10\sqrt[4]{2y}[/tex]
Which of the following is an equation that best describes compound interest?
Answer:
Compound interest is best defined as:
Earning interest on interest.
Compound interest is earning interest on interest.
What is compound interest?Compound interest is an interest accumulated on the principal and interest together over a given time period. The interest accumulated on a principal over a period of time is also accounted under the principal. Further, the interest calculation for the next time period is on the accumulated principal value. Compound interest is the new method of calculation of interest used for all financial and business transactions across the world. The power of compounding can easily be understood, when we observe the compound interest values accumulated across successive time periods.
Compound Interest = Interest on Principal + Compounded Interest at Regular Intervals
The compound interest is calculated at regular intervals like annually(yearly), semi-annually, quarterly, monthly, etc; It is like, re-investing the interest income from an investment makes the money grow faster over time! It is exactly what the compound interest does to the money. Banks or any financial organization calculate the amount based on compound interest only.
as, we know that Compound interest is an interest accumulated on the principal and interest together over a given time period.
So, we can also write Earning interest on interest.
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Susan and Mark are standing at different places on a beach and watching a bird. The angles of elevation they make are 20º and 50º, respectively. If Susan and Mark are 7 kilometers apart and the bird is between them, the bird is at a height of kilometers from the ground.
Answer:
The bird is 2.44km high
Step-by-step explanation:
Hello,
To solve this question, we need to understand how they are and we can only get this with a correct pictorial diagram.
See attached document for better understanding.
From the first diagram, we understand that the bird is between them and also on top of them.
Assuming Susan, Mark and the bird all form a triangle at each other and the bird at the top, we can divide the the triangle into two equal parts.
But before then, we should know that sum of angles in a triangle is equal to 180°
Therefore,
20° + 50° + b° = 180
70° + b = 180
b = 180° - 70°
b = 110°
Dividing angle b into two equal parts = 55° on each side.
See the last attached document for better illustration.
Using SOHCAHTOA, we can find the adjacent of the triangle which corresponds to the height of the bird.
We have opposite = 3.4km and we're looking for adjacent. We can use tangent of the angle to find the adjacent.
Tanθ = opposite / adjacent
Tan 55° = 3.5 / adj
Adjacent = 3.5 / tan55
Adjacent = 3.5 / 1.43
Adjacent = 2.44km
The height of the bird is 2.44km
Answer:
A. 1.95
Step-by-step explanation:
PLATO
The roots of $7x^2 + x - 5 = 0$ are $a$ and $b.$ Compute $(a - 4)(b - 4).$[tex]The roots of $7x^2 + x - 5 = 0$ are $a$ and $b.$ Compute $(a - 4)(b - 4).$[/tex]
Using the factor theorem, we have
[tex]7x^2+x-5=7(x-a)(x-b)[/tex]
and expanding gives us
[tex]7x^2+x-5=7(x^2-(a+b)x+ab)\implies\begin{cases}ab=-5\\a+b=-1\end{cases}[/tex]
So we have
[tex](a-4)(b-4)=ab-4(a+b)+16=-5-4(-1)+16=\boxed{15}[/tex]
Please answer this now in two minutes
Answer:
m∠P: 52 degrees.
m∠Q: 128 degrees.
Step-by-step explanation:
In a rhombus, opposite angles are equal, and all angles add to be 360 degrees.
This means that m∠P = m∠P, and m∠Q = m∠S. Because that is the case, m∠P + m∠Q = 180 degrees.
(2w - 62) + (w + 71) = 180
2w + w - 62 + 71 = 180
3w + 9 = 180
3w = 171
w = 57
Now that we have the value of w, we can find the m∠P and m∠Q!
m∠P: (2 * 57) - 62 = 114 - 62 = 52 degrees
m∠Q: (57 + 71) = 128 degrees
To make sure we are right...
128 + 52 = 180
Hope this helps!
Which equation correctly uses the trigonometric ratio for sine to solve for y?
Answer:
b y = 9sin(36)
Step-by-step explanation:
sin A = opp/hyp
for the 36-deg angle, opp = y, and hyp = 9.
sin 36 = opp/hyp
sin 36 = y/9
y = 9 * sin 36
Answer: b y = 9sin(36)
Evaluate 3x2 - 4 when x = 2.
A. 12
B. 32
c. 2
D. 8
Answer:
8
Step-by-step explanation:
3x^2 - 4
Let x = 2
3 * 2^2 -4
Exponents first
3 *4 -4
Then multiply
12 -4
Now subtract
8
[tex]\text{Plug in and solve:}\\\\3(2)^2-4\\\\3(4)-4\\\\12-4\\\\8\\\\\boxed{\text{D). 8}}[/tex]
Find the perimeter of a square with a diagonal of 15√2.
Answer:
15
Step-by-step explanation:
Answer:
21.213
Step-by-step explanation:
which answer is equivalent to √16/√49
Answer:
sqroot 16/49 A
Step-by-step explanation:
The expression [tex]\frac{\sqrt{16}}{\sqrt{49}}[/tex] is equivalent to expression [tex]\sqrt{\frac{16}{49}}[/tex] because by property [tex]\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b} }[/tex].
The expression [tex]\frac{\sqrt{16}}{\sqrt{49}}[/tex] can be simplified by taking the square root of 16 and the square root of 49 separately.
√16 equals 4 because the square root of 16 is the number that, when multiplied by itself, gives 16.
Similarly, √49 equals 7 because the square root of 49 is the number that, when multiplied by itself, gives 49.
So, the expression [tex]\frac{\sqrt{16}}{\sqrt{49}}[/tex] simplifies to 4/7.
and we know that [tex]\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b} }[/tex]
[tex]\sqrt{\frac{16}{49}}[/tex] is equivalent to [tex]\frac{\sqrt{16}}{\sqrt{49}}[/tex] , which simplifies to 4/7.
Therefore, [tex]\sqrt{\frac{16}{49}}[/tex] is equivalent to [tex]\frac{\sqrt{16}}{\sqrt{49}}[/tex] .
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Find the inverse of the function 3+4x/1-5x
Answer:
the inverse of the function f^-1(x)=(x-3)/(4+5x)
Step-by-step explanation:
( 3+4x)/(1-5x)
y=4x+3/1-5x swap the variables
x=4y+3/1-5y solve for y
y=x-3/4+5x
The inverse of a function is :y=x-3/4+5x
What is inverse of a function?
The inverse function returns the original value for which a function gave the output.
If you consider functions, f and g are inverse, f(g(x)) = g(f(x)) = x. A function that consists of its inverse fetches the original value.
Steps are:
How do you solve inverse functions step by step?Finding the Inverse of a FunctionFirst, replace f(x) with y . Replace every x with a y and replace every y with an x .Solve the equation from Step 2 for y . Replace y with f−1(x) f − 1 ( x ) . Verify your work by checking that (f∘f−1)(x)=x ( f ∘ f − 1 ) ( x ) = x and (f−1∘f)(x)=x ( f − 1 ∘ f ) ( x ) = x are both true.for example:
Suppose, f(x) = 2x + 3 is a function.
Let f(x) = 2x+3 = y
y = 2x+3
x = (y-3)/2 = f-1(y)
This is the inverse of f(x).
Given function:
f(x)= ( 3+4x)/(1-5x)
now, swap the variables x and y.
y=4x+3/1-5x
Now solving for y
x=4y+3/1-5y
y=x-3/4+5x
Hence, the inverse of the function f^-1(x)=(x-3)/(4+5x).
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.....................
Answer:
B. √16 × √6
C. √96
Step-by-step explanation:
4√6
4 can be written as a square root.
4 = √16
√16 × √6
The square roots are multiplied, they can be written under one whole square root.
√(16 × 6)
√96
Rewrite the given function as an equivalent function containing only cosine terms raised to a power of 1.f(x)=7cos^2x
Answer:
Step-by-step explanation:
Using the double angle formulas,
cos(2x) = cos^2(x) - sin^2(x) ............(1)
1 = cos^2(x) + sin^2(x)............(2)
add (1) and (2)
1 + cos(2x) = 2 cos^2(x)
=> cos^2(x) = (1/2) (1+cos(2x)) ..............(3)
f(x) = 7 cos^2 (x)
substituting (3)
f(x) = (7/2) (1+cos(2x))
At the beginning of the school year, Jamie had $500 in her savings account. She wants to have at least $200 left in the account at the end of the school year. Each week, she withdraws $30 for spending money. To determine how many weeks she can spend $30, Jamie wrote and solved this inequality. 500 − 30x ≥ 200 −500 −500 −30x ≥ −300 x ≥ 10 Review Jamie's work. What was her error? Jamie should have used the less than or equal to sign when writing the inequality. Jamie should have reversed the inequality when using the division property of inequality. Jamie should have added 500 to both sides. Jamie should have started by dividing by –30.
Answer:
Jamie should have reversed the inequality when using the division property of inequality.
Step-by-step explanation:
Jamie wrote
500 − 30x ≥ 200
Subtract 500 from both sides
500-500-30x ≥ 200-500
-30x ≥ -300
Divide both sides by -30
x ≥ 10
Instead of reversing the inequality when using the division property of inequality
500 − 30x ≥ 200
Subtract 500 from both sides
500-500-30x ≥ 200-500
-30x ≥ -300
Divide both sides by -30
x <or= 10
the answer is B i hope this helps
^_^
Which equation represents a linear function that has a slope of Four-fifths and a y-intercept of –6? y = negative 6 x + four-fifths y = four-fifths x minus 6 y = four-fifths x + 6 y = 6 x + four-fifths
Answer:
The answer is
[tex]y = \frac{4}{5} x - 6[/tex]
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
From the question
m / slope = 4/5
c / y intercept = - 6
Substituting the values into the above formula
We have the final answer as
[tex]y = \frac{4}{5} x - 6[/tex]
Hope this helps you
Answer:
the correct answer is C.
Step-by-step explanation:
i got it right on edge 2020
Explain how you can determine the number of real number solutions of a system of equations in which one equation is linear and the other is quadratic–without graphing the system of equations.
Answer:
To determine the number of real number solutions of as system of equations in which one equation is linear and the other is quadratic
1) Given that there are two variables, x and y as an example, we make y the subject of the equation of the linear equation and substitute the the expression for y in x into the quadratic equation
We simplify and check the number of real roots with the quadratic formula, [tex]x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex] for quadratic equations the form 0 = a·x² - b·x + c
Where b² > 4·a·c there are two possible solutions and when b² = 4·a·c equation there is only one solution.
Step-by-step explanation:
Answer:
Isolate one variable in the system of equations. Use substitution to create a one-variable equation. Then, set the quadratic equation equal to zero and find the discriminant. If the discriminant is negative, then there are no real number solutions. If the discriminant is zero, then there is one real number solution. If the discriminant is positive, then there are two real number solutions.
Step-by-step explanation:
I just took the test on Edge 2020
Which three-dimensional figure is formed by the rotation given?
Answer: The bottom right
Step-by-step explanation: Take a peek at the pic :)
An insect is 3.5 millimeters long. Which expression finds the length of the insect in decimeters? Use the metric table to
help answer the question.
Metric Table
kilo-
1,000
hecto-
100
unit
deka-
10
centi-
deci-
0.1
1
milli-
0.001
0.01
A.) 3.5 x 100
B.) 3.5-100
C.) 3.5-10
D.) 3.5x 10
Answer:b
Step-by-step explanation:
C and D are wrong because both of them should be divided and by 100. A is wrong because you are supposed to divide because if you multiply 3.5 x 100 its 350 and it just doesn’t make any sense because milli is smaller than deci. So by process of elimination b is the right answer.
Answer:
b
Step-by-step explanation:
:D
.
What is y + 3 = 7(2 – 2) written in standard form?
Answer:
y = -3
Step-by-step explanation:
y + 3 = 7(2 - 2)
y + 3 = 0
Subtract 3 from both sides
y + 3 - 3 = 0 - 3
y = -3
Answer:
7x - y = 17
Step-by-step explanation:
Maybe you want the standard form of the point-slope equation ...
y +3 = 7(x -2)
__
y + 3 = 7x -14 . . . . . eliminate parentheses
17 = 7x -y . . . . . . . . add 14-y
7x - y = 17
Please answer this in two minutes
Answer:
x ≈ 5.7
Step-by-step explanation:
Using the Sine rule in Δ WXY
[tex]\frac{WY}{sinX}[/tex] = [tex]\frac{XY}{sinW}[/tex] , substitute values
[tex]\frac{x}{sin33}[/tex] = [tex]\frac{10}{sin107}[/tex] ( cross- multiply )
x sin107° = 10 sin33° ( divide both sides by sin107° )
x = [tex]\frac{10sin33}{sin107}[/tex] ≈ 5.7 ( to the nearest tenth )
The vertex of the parabola below is at the point (-3, -5). which of the equations below could be the one for this parabola?
A. x = -3(y + 5)^2
B. y = (x + 3)^2 -5
C. y = (x - 5)^2 + 3
D. y = (x + 3)^2 + 5
Answer:
Step-by-step explanation:
The coordinates of a vertex are (h, k). If our vertex is (-3, -5), then h = -3 and k = -5. The vertex form of a parabola is
[tex]y=(x-h)^2+k[/tex] so if we fill in our h and k values, the equation becomes
[tex]y=(x-(-3))^2+(-5)[/tex] and, simplified, is
[tex]y=(x+3)^2-5[/tex]
Choice B.
Carl ordered a refrigerator that weighs 192 pounds. It was shipped to him inside a box and surrounded by packaging material. The total weight of the refrigerator, box, and packaging material was 205 pounds. What is the weight of the box and packaging material?
Answer:
13 lbs
Step-by-step explanation:
You've decided you want a plant for your room. At the gardening store, there are 444 different kinds of plants (tulip, fern, cactus, and ficus) and 444 different kinds of pots to hold the plants (clay pot, plastic pot, metal pot, and wood pot). If you randomly pick the plant and the pot, what is the probability that you'll end up with a tulip in a plastic pot?
Answer:
1/197136
Step-by-step explanation:
If there would be one pot and one plant the possibility would be 1 to take it.
It there were 2 plants and 1 pot it would be 1/2*1 = 1/2
If there were 2 plants and 2 pots it would be 1/2*2 = 1/4
With 444 plants and 444 pots it is 1/444*444 = 1/197136
There are 4×4 = 16 different combinations of plant and pot. Of those, 7 are either clay pot or cactus. Thus the probability you won't get a clay pot or a cactuis is 9/16.
Haley works at a candy store. There are 10 types of bulk candy. Find the probability that one type of candy will be chosen more than once in 10 trials.
Answer:
Probability that one type of candy will be chosen more than once in 10 trials = 0.2639
Step-by-step explanation:
This is a binomial experiment because
- A binomial experiment is one in which the probability of success doesn't change with every run or number of trials.
- It usually consists of a number of runs/trials with only two possible outcomes, a success or a failure. (10 trials, with the outcome of each trial being that we get the required candy or not)
- The outcome of each trial/run of a binomial experiment is independent of one another.
Binomial distribution function is represented by
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = 10 trials
x = Number of successes required = number of times we want to pick a particular brand of candy = more than once, that is > 1
p = probability of success = probability of picking a particular brand of candy from a bulk with 10 different types of candies = (1/10) = 0.10
q = probability of failure = Probability of not picking our wanted candy = 1 - p = 1 - 0.1 = 0.90
P(X > 1) = 1 - P(X ≤ 1)
P(X ≤ 1) = P(X = 0) + P(X = 1)
P(X = 0) = ¹⁰C₀ (0.10)⁰ (0.90)¹⁰⁻⁰ = 0.3486784401
P(X = 1) = ¹⁰C₁ (0.10)¹ (0.90)¹⁰⁻¹ = 0.387420489
P(X ≤ 1) = 0.3486784401 + 0.387420489 = 0.7360989291
P(X > 1) = 1 - 0.7360989291 = 0.2639010709 = 0.2639
Hope this Helps!!!
Each square in the grid is a unit square with an area of 1 square unit.
What is the area of the figure?
square units
Answer:
6 square units
Step-by-step explanation:
Simply count the number of squares:
There are 4 squares aligned in a vertical column, and one to the right of that column (so up to this point you have 5 full squares). Then notice that you have two half squares in the shape of triangles. So two halves give us another full square. That totals 6 square units.
Eiko is wearing a magic ring that increases the power of her healing spell by 30\%30%30, percent. Without the ring, her healing spell restores HHH health points. Which of the following expressions could represent how many health points the spell restores when Eiko is wearing the magic ring?
Answer:
Options B: and C:
Step-by-step explanation:
Remember that 30% in fraction form is
The amount of health points (H) restored would depend on the amount of the current H so it means it would add 30% of the current which we can write as:
And since it would add that to the current total we can right the current total as:
So our equation would be:
For option B:
We can factor out the H and you will be left with:
Combine or add the fractions inside the parenthesis and you will have:
For option C:
We can simplify the fractions which will result in:
Then factor out the H and you will have:
Options B: and C:
Step-by-step explanation:
Remember that 30% in fraction form is
The amount of health points (H) restored would depend on the amount of the current H so it means it would add 30% of the current which we can write as:
And since it would add that to the current total we can right the current total as:
So our equation would be:
For option B:
We can factor out the H and you will be left with:
Combine or add the fractions inside the parenthesis and you will have:
For option C:
We can simplify the fractions which will result in:
Then factor out the H and you will have:
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
Please answer it now in two minutes
Answer:
c = 6√2
Step-by-step explanation:
The following data were obtained from the question:
Angle θ = 30°
Opposite = 3√2
Hypothenus = c
The value of 'c' can be obtained by using the sine ratio as shown below:
Sine θ = Opposite /Hypothenus
Sine 30° = 3√2/c
Cross multiply
c × sine 30° = 3√2
Divide both side by sine 30°
c = 3√2 / sine 30°
But: sine 30° = 1/2
c = 3√2 / sine 30°
c = 3√2 ÷ 1/2
c = 3√2 × 2
c = 6√2 yard
Therefore, the value of 'c' is 6√2 yard.