For this case we must solve the following inequality:
[tex]8x-5 \geq27[/tex]
We add 5 to both sides of the inequality:
[tex]8x\geq27 + 5\\8x\geq32[/tex]
DIviding between 8 on both sides of the equation:
[tex]x \geq \frac {32} {8}\\x \geq4[/tex]
Thus, the solution is given by all the numbers greater than or equal to 4
Answer:
[tex]x \geq4[/tex]
Answer: [tex]x\geq4[/tex]
Step-by-step explanation:
Given the inequality [tex]8x-5\geq27[/tex], you need to solve for the variable "x".
You must follow these steps to solve for the variable "x":
- First, you need to add 5 to both sides of the inequality. Then:
[tex]8x-5+(5)\geq27+(5)\\\\8x\geq32[/tex]
- And finally, you need to divide both sides of the inequality by 8.
Therefore, you get:
[tex]\frac{8x}{8}\geq\frac{32}{8}\\\\x\geq4[/tex]
Can someone help me please
A: 8,250
B: 22
Step-by-step explanation:
A: 15 * 250 = 3,750 + 4,500 = 8,250
B: 10,000 - 4,500 = 5,500/250 = 22. 22 * 250 + 4,500 = 10,000
estimate a 15% tip on a dinner bill of $61.72 by first roundong the bill amount to the nearest ten dollars.
Answer:
$71
Step-by-step explanation:
First
61.72 times .15= 9.258
Second
61.72+9.258= 70.978
10 points for correct answer
Answer:
[tex]y=\frac{1}{52}x^2[/tex]
Step-by-step explanation:
The focus of the parabola is (0,13)
and the directrix is y=-13.
The equation of this parabola is given by:
[tex]x^2=4py[/tex]
The vertex of this parabola is at the origin.
The value of p is the distance from the vertex to the focus.
p=13-0=13
The equation of the parabola is
[tex]x^2=4(13)y[/tex]
[tex]x^2=52y[/tex]
Or
[tex]y=\frac{1}{52}x^2[/tex]
Polly spent 77/100 of a dollar to buy some mints how can you express 77/100 as a money amount
$ 0.77 or 77 cents
because 77 out 100 is written in decimal form as .77
Hello there!
Answer:
Your answer would be $0.77
Step-by-step explanation:
The reason why $0.77 would be the correct answer is because that represents something that is lower than a dollar, more so you would know it as "cents."
When you look at the question, it says, "77/100 of a dollar." What that means is that there is 77 of a dollar, and a dollar is equivalent to one whole.
The denominator "100" represents a whole, so that means that there is 77 out of a whole.
When you know currencies, cents are lower than a whole, therefore would be represented as a decimal.
77/100 is equivalent to 0.77.
As a money amount, it would be $0.77.
$0.77 should be the CORRECT answer.
?÷4=-3
answer please
Answer: -12
x/4=-3
(x/4)(4)=-3(4)
x=-12
Which is the least common multiple of 8 and 10
i’m pretty sure the answer is 40
Answer:
The answer is 40.
Step-by-step explanation:
Because the multiples of 8: 8, 16, 24, 32, 40, 48...etc
and 10: 10, 20, 30, 40, 50....etc and both of them have 40 so that's your LCM.
Hope i helped you! :)
Find the center and radius of the circle whose diameter has an endpoint at (-3, -4) and the origin.
The center of the circle is (-1.5, -2) and the radius is 3.205.
Explanation:To find the center and radius of the circle, we can use the formula for the distance between two points in a coordinate plane. The two points given are (-3, -4) and the origin (0, 0), which represents the diameter of the circle. The center of the circle is the midpoint of the diameter, which can be found by taking the average of the x-coordinates and the y-coordinates. So, the center is ( (-3+0)/2 , (-4+0)/2 ) = (-1.5, -2). The radius of the circle is half the length of the diameter, which can be found using the distance formula as the distance between the center and one of the endpoints of the diameter. So, the radius is the distance between (-1.5, -2) and (-3, -4), which is √((-3-(-1.5))² + (-4-(-2))²) = √(2.5² + 2²) = √(6.25 + 4) = √10.25 = 3.205.
Two more than the quotient of a number 9 is 8
Answer:
Equation: x/9 + 2 = 8
Solution: x = 54
Step-by-step explanation:
I'd imagine the question is asking "two more than the quotient of a number and 9 is 8." Let's break this down:
- two more than means we're going to be adding two to the following quantity in the sentence.
- the quotient of a number and 9 we can interpret as a division expression. We don't know what "a number is," so we can give it a label (I'll pick n), and we can now write it is x/9. Taken with that last bullet point, our expression becomes x/9 + 2.
- Finally, we're told that the result of this expression is 8, so we can write the compete equation as x/9 + 2 = 8.
Now, if we want to solve this:
We can start by subtracting 2 from either side, giving us
x/9 = 6
And multiplying either side by 9 gives us the solution
x = 54.
Solve this quadratic equation using the quadratic formula. 2x 2 - 10x + 7 = 0
Answer:X=11/10
Step-by-step explanation:
2x2-10x+7=0
4-10x+7=0
11-10x=0
-10x= -11
Divide both side by -10
-10x/-10. -11/-10
Answer= 11/10
Answer:
x₁ = 5 + √11
2
x₂ = 5 - √11
2
Step-by-step explanation:
quadratic formula is given by
x = -b ±√b² - 4ac
2a
a = 2, b = -10, c = 7
x = -(-10) ± √-10² - 4*2*7
2*2
x = 10 ± √100 - 56
4
x = 10 ± √44 = 2(5 ± √11) = 5 ± √11
4 4 2
x₁ = 5 + √11
2
x₂ = 5 - √11
2
Write the comparison below as a ratio in simplest form using a fraction a colon and the word to 11 ounces to 5 ounces
Answer:
Fraction Colon To
[tex]\frac{11}{5}[/tex] 11 : 5 11 to 5
Answer with explanation:
We have to write the comparison below as in fractions , in colon and in words to 11 ounces to 5 ounces.
In Fractions
[tex]\frac{11}{5}[/tex]
In Colon
11 :5
In Words
→1 Ounce=29 grams (Approx)
The ratio of Ash gourd bought by me and my mother was 11 ounce to 5 ounce.
5a - 5b is it monomial binomial trinomial
Binomial
A monomial is just one term. A binomial is two monomials added or subtracted together. A trinomial is three monomials added or subtracted together.
Answer:
It is a binomial because it has two terms
The ordered pairs show (height in inches, men’s shoe size). (70, 9.5) (67, 8) (69, 9) (72, 11.5) (68, 7.5) (60, 6) (71, 11) Use the regression calculator to generate the regression equation used to make predictions. What is the approximate height of a man who wears a size 7 shoe? Round to the nearest whole number. inches
Answer:
64
Step-by-step explanation:
Just completed this for edge.
Regression equation : Y = 0.44352X - 21.29443
Approximate height of man who wears size 7 shoe = 64 inches
What is regression?
Regression can be defined as a measurement that is used to quantify how the change in one variable will affect another variable. Regression is used to find the cause and effect between two variables.
Given, ordered pairs
(height in inches, men’s shoe size).
(70, 9.5)
(67, 8)
(69, 9)
(72, 11.5)
(68, 7.5)
(60, 6)
(71, 11)
Using regression calculator
Regression equation
Y = 0.44352X - 21.29443
Approximate height of a man who wears a size 7 shoe
7 = 0.44352X - 21.29443
0.44352X = 28.29443
X = 28.29443/0.44352
X = 63.7951614 ≈ 64
Approximate height = 64 inches
Hence, Y = 0.44352X - 21.29443 is the regression equation,
64 inches is the approximate height of the man wearing size 7 shoe
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Sandy wants to cover a wooden cylinder with a diameter of 1 ft and a height of 4 ft with carpet to build a scratching post for her cats. What are the steps she needs to take to complete this task?
Final answer:
To cover the wooden cylinder with carpet, Sandy needs to find the surface area of the cylinder and then cut out a piece of carpet that matches that area.
Explanation:
To cover the wooden cylinder with carpet, Sandy needs to find the surface area of the cylinder and then cut out a piece of carpet that matches that area. The surface area of a cylinder can be found using the formula: SA = 2πr(r+h), where r is the radius of the base and h is the height of the cylinder. In this case, the diameter of the cylinder is 1 ft, so the radius is 1/2 ft. The height of the cylinder is 4 ft. Plugging these values into the formula, we get: SA = 2π(1/2)(1/2 + 4) = 2π(1/2)(9/2) = 9π square ft.
Find the surface area and volume of each figure. Round each answer to the nearest hundredth.
Answer: Surface area is equal to 200[tex]cm^{2}[/tex]
Volume is equal to 333.33[tex]cm^{3}[/tex]
Step-by-step explanation:
First, let's do surface area.
The surface area of a pyramid is equal to 1/2(perimeter of base)(lateral height) + area of the base
The perimeter of the base is 10(4) = 40; as the base is a square with a side length of 10.
The lateral height is given as 5 cm.
The area of the base is 10(10) = 100.
We can plug those numbers into the equation to get 1/2(40)(5) + 100, which comes out to be 200[tex]cm^{2}[/tex].
Now for volume.
The volume of a pyramid is equal to 1/3(area of the base)(height).
We already have the area of the base, which is 100.
The height is given as 10 cm.
Plugging those numbers into the equation, we get 1/3(100)(10), which is 1000/3 or about 333.33[tex]cm^{3}[/tex].
Hope this helps!
PLEASE HELP PRECALCULUS
SEE ATTACHMENT
Answer:
1+6i
Step-by-step explanation:
Given:
f(x)=x^4 - 2x^3 + 38x^2 - 2 + 37
zero of f(x) = 1-6i
another zero of function = ?
Conjugate Zero theorem:
As per conjugate zero theorem, if a function f(x) has real coefficients and one of zero is a complex number then the conjugate of that complex number will also be a zero of that function i.e. complex zeroes will occur in complex conjugate pairs.
conjugate of 1-6i is 1+6i
hence another zero of f(x) will be 1+6i !
Find the measure of one exterior angle of the following polygon:
Nonagon
Answer:
40°
Step-by-step explanation:
1. Shape of a nonagon: 9 (root non-)
2. Total exterior angle: 360° (constant for all polygons)
3. Given that this polygon is regular, the one exterior angle of an nonagon is 360°/9 = 40°.
Answer:
40°Step-by-step explanation:
An exterior angle and an interior angle are supplementary angles.
Two Angles are Supplementary when they add up to 180°.
Therefore the measure of exterior angle is equal to different between 180° and an interior angle.
Method 1:
You can use the formula of the measure of interior angle of the regular polygon with n-sides:
[tex]\alpha=\dfrac{180^o(n-2)}{n}[/tex]
We have a nonagon. Therefore n = 9. Substitute:
[tex]\alpha=\dfrac{180^o(9-2)}{9}=(20^o)(7)=140^o[/tex]
[tex]180^o-140^o=40^o[/tex]
Method 2:
Look at the picture.
[tex]\alpha=\dfrac{360^o}{9}=40^o[/tex]
[tex]2\beta[/tex] - it's an interior angle
We know: The sum of measures of these three angles of any triangle is equal to 180°.
Therefore:
[tex]\alpha+2\beta=180^o\to2\beta=180^o-\alpha[/tex]
Substitute:
[tex]2\beta=180^o-40^o=140^o[/tex]
[tex]\theta[/tex] - it's a exterior angle
[tex]2\beta+\theta=180^o\to\theta=180^o-2\beta[/tex]
substitute:
[tex]\theta=180^o-140^o=40^o[/tex]
What best describes the expression 5 over y?
5 times some number
5 minus some number
5 divided by some number
5 more than some number
Answer: 5/y
Step-by-step explanation:
plz help i'm having troubled understanding how to do this
Answer:
1/2 - 2/6 = 1/6
Step-by-step explanation:
to answer two that are different simply take the lesser up or higher down example: 1/2-2/4 this would be zero because 2 x 1/2 = 2/4
1/2-2/6= 0.16
hope this helps
In 18 years time Halley will be five times as old as she was two years ago. Write this information in the form of an equation involving Halley's present age, a years How old is Halley now?
To solve any questions relating to ages, I find it easier to make a table, like in the picture below.
See picture for answer and clear diagram.
-----------------------------------------------------------------
Notes/Explanations + answer in written form
Let's say that Halley's age now is: x
That means that her age in 18 years is: x + 18
It also means that her age 2 years ago is: x - 2
In the question, we are told that when Halley is 18 years older than her current age, she will be 5 times the age she was when she was 2 years younger than her current age
That means:
Halley's current age + 18 years = 5 times (Halley's current age - 2 years)
So we get this equation (which we solve to get the answer) :
x + 18 = 5 * (x -2) ( expand the brackets)
x + 18 = 5x - 10 (subtract x from both sides)
18 = 4x - 10 (add 10 to both sides)
28 = 4x (now divide both sides by 4)
7 = x
Therefore, Halley's current age is 7 years
-------------------------------------------------
Note: equation is: x + 18 = 5 * (x -2)
What is the value of -5^6?
Answer:
-15625 i think
For this case we must find the value of the following expression:[tex]-5 ^ 6 = -1 * 5 ^ 6[/tex]
This means that we must multiply the 5 six times, and then multiply by -1, that is:
[tex]5 ^ 6 = 5 * 5 * 5 * 5 * 5 * 5 = 15,625[/tex]
Then multiply by -1:
[tex]-15,625[/tex]
Answer:
[tex]-5 ^ 6 = -15,625[/tex]
Solve each equation by completing the square 6x2+12x-27=-9
Answer:
the answer to this question is x=3\4
Answer:
1 and 2
Step-by-step explanation:
look this solution :
Match the equations representing parabolas with their directrixes. y + 8 = 3(x + 2)2 y − 14 = -(x − 3)2 y + 7.5 = 2(x + 2.5)2 y − 17 = -(x − 3)2 y + 7 = (x − 4)2 y − 6 = -(x − 1)2 Directrix Equation of Parabola y = -7.25 arrowRight y = 6.25 arrowRight y = 17.25 arrowRight y = 14.25 arrowRight
Answer:
Part 1) [tex]y+8=3(x+2)^{2}[/tex] -----> [tex]y=-8.08[/tex]
Part 2) [tex]y-14=-(x-3)^{2}[/tex] ----> [tex]y=14.25[/tex]
Part 3) [tex]y+7.5=2(x+2.5)^{2}[/tex] ----> [tex]y=-7.625[/tex]
Part 4) [tex]y-17=-(x-3)^{2}[/tex] -----> [tex]y=17.25[/tex]
Part 5) [tex]y+7=(x-4)^{2}[/tex] ----> [tex]y=-7.25[/tex]
Part 6) [tex]y-6=-(x-1)^{2}[/tex] ----> [tex]y=6.25[/tex]
Step-by-step explanation:
we know that
The equation of a vertical parabola in vertex form is equal to
[tex]y-k=\frac{1}{4p}(x-h)^{2}[/tex]
where
(h,k) is the vertex
The directrix is
[tex]y=k-p[/tex]
case 1) we have
[tex]y+8=3(x+2)^{2}[/tex]
the vertex is the point (-2,-8)
[tex]\frac{1}{4p}=3[/tex]
[tex]p=\frac{1}{12}[/tex]
The directrix is equal to
[tex]y=-8-\frac{1}{12}=-8.08[/tex]
case 2) we have
[tex]y-14=-(x-3)^{2}[/tex]
the vertex is the point (3,14)
[tex]\frac{1}{4p}=-1[/tex]
[tex]p=-\frac{1}{4}[/tex]
The directrix is equal to
[tex]y=14+\frac{1}{4}=14.25[/tex]
case 3) we have
[tex]y+7.5=2(x+2.5)^{2}[/tex]
the vertex is the point (-2.5,-7.5)
[tex]\frac{1}{4p}=2[/tex]
[tex]p=\frac{1}{8}[/tex]
The directrix is equal to
[tex]y=-7.5-\frac{1}{8}=-7.625[/tex]
case 4) we have
[tex]y-17=-(x-3)^{2}[/tex]
the vertex is the point (3,17)
[tex]\frac{1}{4p}=-1[/tex]
[tex]p=-\frac{1}{4}[/tex]
The directrix is equal to
[tex]y=17+\frac{1}{4}=17.25[/tex]
case 5) we have
[tex]y+7=(x-4)^{2}[/tex]
the vertex is the point (4,-7)
[tex]\frac{1}{4p}=1[/tex]
[tex]p=\frac{1}{4}[/tex]
The directrix is equal to
[tex]y=-7-\frac{1}{4}=-7.25[/tex]
case 6) we have
[tex]y-6=-(x-1)^{2}[/tex]
the vertex is the point (1,6)
[tex]\frac{1}{4p}=-1[/tex]
[tex]p=-\frac{1}{4}[/tex]
The directrix is equal to
[tex]y=6+\frac{1}{4}=6.25[/tex]
The correct matches are: Directrix y = -7.25 → Equation of Parabola: y + 7 = (x - 4)², Directrix y = 6.25 → Equation of Parabola: y - 6 = -(x - 1)², Directrix y = 17.25 → Equation of Parabola: y - 17 = -(x - 3)², Directrix y = 14.25 → Equation of Parabola: y - 14 = -(x - 3)².
To match the equations representing parabolas with their directrixes, it's essential to understand the standard form of a parabola's equation related to its axis of symmetry.
For a vertical parabola, the standard form is y = a(x - h)² + k, where the vertex is at (h, k) and the directrix is y = k - 1/(4a) for a parabola that opens upwards, or y = k + 1/(4a) for a parabola that opens downwards.
For a horizontal parabola, the standard form is x = a(y - k)² + h. In our case, all given equations are in the vertical form where x is squared.
Let's take each equation and find its directrix:
y + 8 = 3(x + 2)² opens upwards; its directrix is y = -8 - 1/(4*3) = -8.25 or y = -8 - 1/12.y - 14 = -(x - 3)²opens downwards; its directrix is y = 14 + 1/4 = 14.25.y + 7.5 = 2(x + 2.5)²opens upwards; its directrix is y = -7.5 - 1/(4*2) = -7.75 or y = -7.5 - 1/8.y - 17 = -(x - 3)² opens downwards; its directrix is y = 17 + 1/4 = 17.25.y + 7 = (x - 4)² opens upwards; its directrix is y = -7 - 1/4 = -7.25.y - 6 = -(x - 1)² opens downwards; its directrix is y = 6 + 1/4 = 6.25.With the directrix found for each equation, the correct matches are:
Directrix y = -7.25 → Equation of Parabola: y + 7 = (x - 4)²Directrix y = 6.25 → Equation of Parabola: y - 6 = -(x - 1)²Directrix y = 17.25 → Equation of Parabola: y - 17 = -(x - 3)²Directrix y = 14.25 → Equation of Parabola: y - 14 = -(x - 3)²What can you say about the relationship between M and P? Which letter is the correct answer?
Answer:
Choice C is correct
Step-by-step explanation:
The first step is to re-write the equations in exponential form.
The first equation can be written as;
[tex]\frac{M}{N}=10^{4}[/tex] since the base is 10 and 4 the exponent.
The second equation can be written as;
[tex]\frac{P}{N}=10^{5}[/tex]
The second step is to make N the subject of the formula in both equations.
Solving for N from this equation [tex]\frac{M}{N}=10^{4}[/tex], yields;
[tex]N=\frac{M}{10^{4}}[/tex]
Solving for N from the second equation [tex]\frac{P}{N}=10^{5}[/tex], yields;
[tex]N=\frac{P}{10^{5}}[/tex]
Therefore;
[tex]\frac{M}{10^{4}}=\frac{P}{10^{5} }\\\\P=10M[/tex]
Find the f(-1) of f(x)=5x+12
Answer:
f(- 1) = 7
Step-by-step explanation:
To evaluate f(- 1) substitute x = - 1 into f(x)
f(- 1) = 5(- 1) + 12 = - 5 + 12 = 7
For this case we have a function of the form[tex]y = f (x)[/tex], where:
[tex]f (x) = 5x + 12[/tex]
We must find the value of the function when x = -1.
That is, [tex]f (-1)[/tex]:
[tex]f (-1) = 5 (-1) +12\\f (-1) = - 5 + 12[/tex]
Different signs are subtracted and the sign of the major is placed:
[tex]f (-1) = 7[/tex]
Answer:
[tex]f (-1) = 7[/tex]
The force pulling a truck downhill is 2,000N, the mass of the truck is 40,000 kg. What is the acceleration?
For this case we have that Newton's second law is given by:
[tex]F = m * a[/tex]
Where:
m: It's the mass
a: Acceleration
F: It's the force
According to the data we have:
[tex]2,000 = 40,000 * a[/tex]
Dividing between 40,000 on both sides of the equation:
[tex]a = \frac {2,000} {40,000}\\a = 0.05[/tex]
Thus, the acceleration is [tex]0.05 \frac {m} {s ^ 2}[/tex]
Answer:
[tex]0.05 \frac {m} {s ^ 2}[/tex]
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Answer:
Angle B: 135 degrees
Angle A: 60 degrees
Angle C: 75 degrees
Step-by-step explanation:
Angle B is 135 degrees
We have the complement of angle B, which is the lowest left corner of the triangle and it says 45 degrees.
So, B = 180 - 45 = 135 degrees
Angle A.
The lines crossing form 2 pair of identical angles from their tip... The exterior angle is 60 degrees, so the interior angle A is also 60 degrees.
Angle C.
Just like for angle B, we get angle C by subtracting its complement:
C = 180 - 105 = 75 degrees.
We can also validate by calculating the sum of the interior angles of the triangle: 45 + 60 + 75 = 180, which is perfect.
Which of the following relations is a function?
A. (2,4), (-5, 6), (2, 3), (-6, 2)
B. (8, 1), (-5, 4), (2, 1), (8, 2)
C. (2,4), (-5, 2), (8, 1), (-6, 2)
D.
(2,0).(-5, 3), (8, 1), (-5,5)
Answer: OPTION C
Step-by-step explanation:
A relation is a function when each input value has one and only output value.
For option A:
(2,4), (-5, 6), (2, 3), (-6, 2)
You can observe that the input value "2" has two output values. Then it is not a function.
For option B:
(8, 1), (-5, 4), (2, 1), (8, 2)
You can observe that the input value "8" has two output values. Then it is not a function.
For option C:
(2,4), (-5, 2), (8, 1), (-6, 2)
You can observe that each input value has only one output values. Then it is a function.
For option D:
(2,0).(-5, 3), (8, 1), (-5,5)
You can observe that the input value -5 has two output values. Then it is not a function.
For a set of data to be a function each x value has to have different y values.
A. (2,4), (-5, 6), (2, 3), (-6, 2)
B. (8, 1), (-5, 4), (2, 1), (8, 2)
D. (2,0).(-5, 3), (8, 1), (-5,5)
The bolded coordinates are the ones of each data set that makes it not a function. As you can see the x values all have different y values.
This leaves C. as the answer!
Hope this helped!
What is the equation?
Answer:
y = 2/5x.
Step-by-step explanation:
This is the correct answer to this question.
Hope this helps!!!
Kyle.
Y=2/5x is the answer to this graph as the equation
Simply 7+3 • (8 ÷ 4)
7+3= 10
8/4=2
VEry easy okay
Answer: 13
Step-by-step explanation:
Given the expression [tex]7+3(8[/tex]÷[tex]4)[/tex], you can rewrite it as:
[tex]=7+3(\frac{8}{4})[/tex]
First, you need to solve the operation that is inside the parentheses. Then, you must divide 8 by 4:
[tex]=7+3(2)[/tex]
Now you need to eliminate the parentheses. To do this, you must multipy 3 by 2, then:
[tex]=7+6[/tex]
And finally, you must make the addition. Therefore, you get:
[tex]=13[/tex]
Describe the end behavior of the following function:
F(x)=x^5-x^3+x^2
Answer:
Step-by-step explanation:
Keep in mind that this is a polynomial and all odd-powered polynomials start low (read that as "in Quadrant III") and end high ("Quadrant I"). So yes, the fourth answer choice, D, is the correct one.
(D) The graph of the function starts with low and high ends.
Function:A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.Initially, functions represented the idealized relationship between two changing quantities. A planet's position, for instance, depends on time. In the past, the idea was developed with the infinitesimal calculus at the end of the 17th century, and the functions that were taken into consideration until the 19th century were differentiable (that is, they had a high degree of regularity).Solution -Remember that this is a polynomial and that all odd-powered polynomials have a low starting point (read it as "in Quadrant III") and a high ending point ("Quadrant I").
Therefore, the correct answer is (D) the graph of the function starts with low and high ends.
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