there is a mound of g pounds of gravel in a quarry. throughout the day, 300 pounds of gravel are added to the mound. two orders of 900 pounds are sold and the gravel is removed from the mound. at the end of the day, the mound has 1,300 pounds of gravel. write the equation that describes the situation. then solve for g.
The required equation is g+300-900-900=1300.
The value of g is 2800 pounds.
What is the solution to the equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
Initially, there is a mound of g pounds of gravel, then 300 pounds are added, and then two orders of 900 pounds are sold. At the end of the day, the mound has 1,300 pounds of gravel.
The equation for the given information is formed as follows:
g+300-900-900=1300
Solve the equation to find the value of g,
g+300-1800=1300
g-1500=1300
g=1300+1500
g=2800
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please help me find the solution
Step-by-step explanation:
ATTACHED IS THE SOLUTION!!
MATH HELP!!! 100PTS!!!
Let p(x)=2x−4 and r(x)=6x−1/9x+1.
Solve p(x)=r(x) for x exactly. If there is more than one answer, enter your exact solution(s) in a comma separated list.
Answer:
[tex]x =\dfrac{20 +\sqrt{454}}{18}, \quad \dfrac{20 -\sqrt{454}}{18}[/tex]
Step-by-step explanation:
Given functions:
[tex]p(x)=2x-4[/tex]
[tex]r(x)=\dfrac{6x-1}{9x+1}[/tex]
Solve for p(x) = r(x):
[tex]\begin{aligned}p(x) & = r(x)\\\implies 2x-4 & = \dfrac{6x-1}{9x+1}\\(2x-4)(9x+1)&=6x-1\\18x^2+2x-36x-4&=6x-1\\18x^2-40x-3&=0\end{aligned}[/tex]
As the found quadratic equation cannot be factored, use the Quadratic Formula to solve for x:
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore:
[tex]a=18, \quad b=-40, \quad c=-3[/tex]
Substitute the values of a, b and c into the quadratic formula and solve for x:
[tex]\begin{aligned}\implies x & =\dfrac{-(-40) \pm \sqrt{(-40)^2-4(18)(-3)} }{2(18)}\\\\& =\dfrac{40 \pm \sqrt{1816}}{36}\\\\& =\dfrac{40 \pm \sqrt{4 \cdot 454}}{36}\\\\& =\dfrac{40 \pm \sqrt{4}\sqrt{454}}{36}\\\\& =\dfrac{40 \pm2\sqrt{454}}{36}\\\\& =\dfrac{20 \pm\sqrt{454}}{18}\end{aligned}[/tex]
Therefore, the solutions are:
[tex]x =\dfrac{20 +\sqrt{454}}{18}, \quad \dfrac{20 -\sqrt{454}}{18}[/tex]
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A company has two large computers. The slower computer can send all the company's email in minutes. The faster computer can complete the same job in minutes. If both computers are working together, how long will it take them to do the job
Both the computers will take 18 minutes to do the job together.
The slower computer sends all the company's email in 45 minutes.
The faster computer completes the same job in 30 minutes.
Let's take minutes t to complete the task together.
As they complete one job, we get the following equation:
[tex]\frac{t}{45}[/tex]+[tex]\frac{t}{30}[/tex]=1
LCM of 45 and 30 is:
45 = 3 x 3 x 5
30 = 2 x 3 x 5
LCM = 2 x 3 x 3 x 5 = 90
Now, solving for t;
⇒[tex]\frac{2t+3t}{90} = 1\\\frac{5t}{90} =1\\5t=90\\[/tex]
Dividing both sides by 5;
[tex]\frac{5t}{5}=\frac{90}{5}[/tex]
We get t = 18
Hence, it will take both the computers 18 minutes to do the job together.
A company has two large computers. The slower computer can send all the company's emails in 45 minutes. The faster computer can complete the same job in 30 minutes. If both computers are working together, how long will it take them to do the job?
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Simplify. Rewrite the expression in the form 3^n3 n 3, start superscript, n, end superscript. 3^4\cdot 3^2=3 4 ⋅3 2 =3, start superscript, 4, end superscript, dot, 3, squared, equals
The expression 3⁴ × 3² when rewritten in the form 3ⁿ is; (3²)³
How to use law of exponents?
We want to find the expression;
3⁴ × 3²
Now, according to law of exponents, we know that;
y² × y³ = y⁽² ⁺ ³⁾
Thus, applying that exponent form to our question gives us;
3⁴ × 3² = 3⁽⁴ ⁺ ²⁾ = 3⁶
Now, we want to find the answer in the form 3ⁿ. Thus;
3⁶ = (3²)³
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Answer: 3^6 on khan academy
Step-by-step explanation: add the exponents 4 and 2 and you get the exponent 6
Determine the vertex of the quadratic relation y=2(x+2)(x-6)
Answer:
(2, -32)
Step-by-step explanation:
1) Expand them.
y = 2(x² - 6x + 2x - 12)
y = 2(x² - 4x - 12)
y = 2x² - 8x - 24.
2) Complete the square to find the vertex.
y = 2([x² - 4x)] - 24
y = 2[(x - 2)² - 4] - 24
y = 2(x - 2)² - 8 - 24
y = 2(x - 2)² - 32
The vertex: (2, -32)
or you can use this: x = -b/2a
x = -(-8)/2(2)
x = 8/4
x = 2
Substitute the value into the original equation for y.
y = 2(2)² - 8(2) - 24
y = 2(4) - 16 - 24
y = 8 - 16 - 24
y = -32
Vertex: (2, -32)
Answer:
(2, -32)
Step-by-step explanation:
The vertex of the graph of a quadratic equation is on the line of symmetry, halfway between the x-intercepts. It can be found by evaluating the equation at that point.
Line of symmetryThe given function is written in factored form, so the x-intercepts are easy to find. They are the values of x that make the factors zero:
(x +2) = 0 ⇒ x = -2
(x -6) = 0 ⇒ x = 6
The midpoint between these values of x is their average:
x = (-2 +6)/2 = 4/2
Then the x-coordinate of the vertex, and the equation of the line of symmetry is ...
x = 2
VertexUsing this value of x in the quadratic relation, we find the y-value at the vertex to be ...
y = 2(2 +2)(2 -6) = 2(4)(-4)
y = -32
The coordinates of the vertex are (x, y) = (2, -32).
f (1/2)pi = cos(1/2) pi
the answer to this equation should be 0 but i’m not sure how to do the work could someone help/ explain
Answer:
Step-by-step explanation:
1/2 pi is an angle ( in radians)
in degrees its 90 degrees.
cos 90 = 0.
Consider the relation given by the graph below.
a) Is the relation a function? Why or why not?
b) Determine the domain and range of the graph.
The given relation is function, because the curve of y = p(x) has its exist for every x in its domain(-6, 3) and the range of the function is lies between (-1, 9).
Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent while Y is dependent variable.
As Clearly the shows in the graph the structure is decreasing, increasing and then decreasing. And implies, curve is continuous in its limits and for every x (-6,3) there is exist in range of y(-1, 9).
Thus, The given relation is function, and domain is (-6, 3) and the range of the function is lies between (-1, 9).
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Write the equation of the line that passes through the point (-8,-3) with : slope of -1/4
Answer:
In slope-intercept form:
[tex]y = - \frac{1}{4} x - 5[/tex]
In standard form:
[tex]x + 4y = - 20[/tex]
Step-by-step explanation:
[tex] - 3 = - \frac{1}{4} ( - 8) + b[/tex]
[tex] - 3 = 2 + b[/tex]
[tex]b = - 5[/tex]
[tex]y = - \frac{1}{4} x - 5[/tex]
[tex] - 4y = x + 20[/tex]
[tex] - x - 4y = 20[/tex]
[tex]x + 4y = - 20[/tex]
How many integers in the set of all integers from 1 to 200, inclusive, are not the cube of an integer
Cubing of integers from 1 to 5 will have their cubes in the interval 1 to 200. There are such 5 positive numbers (1,2,3,4,5).
To calculate the variety of integers, locate and subtract the integers of the hobby after which subtract 1. As evidence of the concept, calculate the wide variety of integers that fall between five and 10 on more than a few lines. We realize there are four (6, 7, 8, 9).
All entire numbers are integers (and all herbal numbers are integers), however now not all integers are whole numbers or natural numbers. as an example, -five is an integer but not an entire variety or a natural quantity. An integer is an entire variety (not a fractional number) that can be fine, bad, or 0. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.forty three, 1 3/four, three.14, . 09, and five,643.1.
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A board game allows players to trade game pieces of equal value. The diagram shows two fair trades. The hotel is worth $2400. How much is a car worth?
Answer:
Step-by-step explanation:
For two functions, a(x) and b(x), a statement is made that a(x) = b(x) at x = 2. What is definitely true about x = 2? (2 points) Group of answer choices Both a(x) and b(x) have a maximum or minimum value at x = 2. Both a(x) and b(x) have the same output value at x = 2. Both a(x) and b(x) cross the x-axis at 2. Both a(x) and b(x) cross the y-axis at 2.
The statement that is definitely true about x = 2 is Both a(x) and b(x) have the same output value at x = 2.
How to find the statement that is true about the functions a(x) = b(x) at x = 2?If we have two functions a(x) and b(x), a statement is made that a(x) = b(x) at x = a, this implies that the values of the functions a(x) and b(x) are equal at x = a.
Given that the two functions a(x) and b(x), a statement is made that a(x) = b(x) at x = 2.Then the statement that is definitely true about x = 2 is Both a(x) and b(x) have the same output value at x = 2.
So, the statement that is definitely true about x = 2 is Both a(x) and b(x) have the same output value at x = 2.
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can you help me I am stuck
Answer:
False, False, True
Step-by-step explanation:
Matrix addition or subtraction can only be performed on two matrices if they are the same dimensions. The number of rows for both must match, and the number of columns for both must match. If either is different, they cannot be combined with addition or subtraction.
So, the first two questions are false because the first number from each pair doesn't match (and neither does the second number from each pair, but we just need one mismatch for it to fail).
The last question is true because both of the first numbers are a 3, and both of the second numbers are a 4.
Help me please find the value of x then find the measure of each unknown angle
The value of x is 103.
The value of x is 59.
The value of x is 134.
The value of x is 12
The value of x is 50
The value of x is 135
What is the value of x?
The sum of angles on a straight line add up to 180 degrees.
180 - 77 = 103
180 - 121 = 59
180 - 46 = 134
12 x + 36 = 180
12x = 180 - 36
12x = 144
x = 12
24 + 3x + 6 = 180
3x = 180 - 24 - 6
3x = 150
x - 50
[tex]\frac{x}{3}[/tex] + 99 + 36 = 180
[tex]\frac{x}{3}[/tex] = 180 - 36 - 99
[tex]\frac{x}{3}[/tex] = 45
x = 45 x 3
x = 135
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A spinner is spun that has 15 equal-sized sections numbered 1 to 15. What is the probability the spinner lands on a multiple of five?
Answer:
1/5
Step-by-step explanation:
P(event) = # of favorable outcomes / # of total outcomes. Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40 ... and there are 3 multiples of 5 within 1 to 15. So the # of favorable outcomes is 3. # of total outcomes is 15 because there are 15 equal-sized sections.
P = 3/15 = 1/5
ken needs to order 8 new uniform for the soccer team. Each uniform cost $14 and a pair of shorts. The cost of the shorts, c is unknown. 2 equivalent expressions for the cost of 8 uniforms
The equivalent expressions for the costs are 8 * (14 + c) and 112 + 8c
How to determine the total cost?The given parameters are:
Number of uniform = 8
Cost of each = $14
The cost of the uniforms and the shorts is then calculated as:
Cost = Number of uniforms * (Cost of uniform + Cost of short)
This gives
Cost= 8 * (14 + c)
Expand
Cost = 112 + 8c
Hence, the equivalent expressions for the costs are 8 * (14 + c) and 112 + 8c
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cho Q(x)=x^2+mx-12.Biết Q(-3)=0.tìm nghiệm còn lại
Answer: m=-1.
Step-by-step explanation:
[tex]Q(x)=x^2+mx-12\ \ \ \ Q(-3)=0\ \ \ \ \ m=?\\Q(-3)=(-3)^2+m*(-3)-12=0\\9-3m-12=0\\-3m-3=0\\3m=-3\ |:3\\m=-1.[/tex]
Coordinate Geometry Use the graph. Write each
ratio in simplest form.
33. BD
AC
AE
EC
34. A
35. slope of EB
36. slope of ED
8
6
D
O
y
E
6
LO
33) [tex]AC=6[/tex] and [tex]BD=6[/tex], so [tex]AC/BD=1[/tex]
34) By the distance formula,
[tex]AE=\sqrt{(-2-4)^2 + (8-0)^2 }=10\\[/tex]
Also, EC = 8. So, [tex]AE/EC = 5/4[/tex].
35) [tex]\frac{8-0}{4-2}=4[/tex]
36) [tex]\frac{8-0}{4-8}=-2[/tex]
Name the variable in each algebraic expression
4y+12
Answer:
y is the variable in that expression.
will give brainliest plus 10 points
Answer:
The distance is 7.3 units.
Step-by-step explanation:
Two given points: (-3, 1) and (4, -1)
[tex]\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Here given:
x₂ = 4x₁ = -3y₂ = -1y₁ = 1Applying the formula:
[tex]\sf d = \sqrt{(4 - (-3))^2 + (-1 - 1)^2}[/tex]
[tex]\sf d = \sqrt{(7)^2 + (-2)^2}[/tex]
[tex]\sf d = \sqrt{49 + 4}[/tex]
[tex]\sf d = \sqrt{53} \ \approx \ 7.28 \ \approx \ 7.3 \ (rounded)[/tex]
Answer:
7.3
Step-by-step explanation:
The distance of a line segment between two points (x1, y1) and (x2, y2) is given by the formula
[tex]d = \sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]
If we look at the graph,
the leftmost point of the line is at (-3, 1). Let's call this (x1, y1)
the rightmost point is at (4, -1). Let's call this (x2, y2)
Substituting these values into the distance formula gives us
[tex]d = \sqrt{(4-(-3)^2 + (1-(1)^2} \\ \\d = \sqrt{(7)^2 + (-2)^2} \\ \\d = \sqrt{49 + 4} \\\\d = \sqrt{(x2-x1)^2 + (y2-y1)^2}\\\\d = \sqrt{53} = 7.28[/tex]
Rounded to one decimal place, this is 7.3
Volume=
Please help thankss
Answer:
Volume = 64
Step-by-step explanation:
To find the volume of the cube use the formula.
Formula: l×b×h
l=length
b=base
h=height
Use the information given to solve using the formula.
4×4×4=64
The volume of this cube is 64.
Hope this helps!
If not, I am sorry.
Two circles, each of radius 5 units, are drawn in the coordinate plane with their
centers (0, 0) and (8, 0) respectively. How many points where both coordinates are
integers lie within the intersection of these circles, including its boundary?
The points where both coordinates are integers lie within the intersection of these circles, including its boundary are 8 points.
To answer the question, we need to find the equation of the circles.
What is the equation of a circle?The equation of a circle with center (h, k) and radius r is
(x - h)² + (y - k)² = r²
Equation of first circle
Given that the first circle has
center (0, 0) and radius, r = 5,Its equation is
(x - 0)² + (y - 0)² = 5²
x² + y² = 25 (1)
Equation of second circle
Given that the second circle has
center (8, 0) and radius, r = 5,Its equation is
(x - 8)² + (y - 0)² = 5²
x² - 16x + 64 + y² = 25 (2)
Point of intersection o the circlesTo find the point of intersection of both circles, subtracting (1) from (2), we have
x² - 16x + 64 + y² = 25 (2)
-
x² + y² = 25 (1)
-16x + 64 = 0
-16x = -64
x = -64/-16
x = 4
Substituting x = 4 into (1), we have
x² + y² = 25
4² + y² = 25
16 + y² = 25
y² = 25 - 16
y² = 9
y = ±√9
y = ±3
So, the circles intersect at (4,-3) and (4, 3).
So, all the points that lie within their points of intersection where both coordinates are integers including their points of intersection are
(4, -3), (3, -2), (2, -1), (1, 0), (0, 1), (1, 2), (2, 3) and (3, 4).So, there are 8 points.
So, all the points where both coordinates are integers lie within the intersection of these circles, including its boundary are 8 points.
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Area=
I need some help solving this question I'm stuck. Thanks
Answer: 36 square units
Work Shown:
area = base*height/2
area = 12*6/2
area = 72/2
area = 36
The base and height are always perpendicular to each other. The triangle formula above applies to obtuse triangles, as well as any other type of triangle. It might help to rotate the triangle so that side IJ is at the bottom rather than the top.
sin 3x + 2cos^2 (3x) = 1
Recall the Pythagorean identity,
[tex]\sin^2(x) + \cos^2(x) = 1[/tex]
Then we can rewrite the equation as
[tex]\sin(3x) + 2 \cos^2(3x) = 1[/tex]
[tex]\sin(3x) + 2 (1 - \sin^2(3x)) = 1[/tex]
[tex]1 + \sin(3x) - 2 \sin^2(3x) = 0[/tex]
Factorize the left side.
[tex](1 + 2 \sin(3x)) (1 - \sin(3x)) = 0[/tex]
Then we have
[tex]1 + 2\sin(3x) = 0 \text{ or } 1 - \sin(3x) = 0[/tex]
[tex]\sin(3x) = -\dfrac12 \text{ or } \sin(3x) = 1[/tex]
Solve for [tex]x[/tex]. We get two families of solutions:
[tex]3x = \sin^{-1}\left(-\dfrac12\right) + 2n\pi \text{ or } 3x = \pi - \sin^{-1}\left(-\dfrac12\right) + 2n\pi[/tex]
[tex]\implies 3x = -\dfrac\pi6 + 2n\pi \text{ or } 3x = \dfrac{7\pi}6 + 2n\pi[/tex]
[tex]\implies \boxed{x = -\dfrac\pi{18} + \dfrac{2n\pi}3} \text{ or } \boxed{x = \dfrac{7\pi}{18} + \dfrac{2n\pi}3}[/tex]
and
[tex]3x = \sin^{-1}(1) + 2n\pi[/tex]
[tex]\implies 3x = \dfrac\pi2 + 2n\pi[/tex]
[tex]\implies \boxed{x = \dfrac\pi6 + \dfrac{2n\pi}3}[/tex]
(where [tex]n[/tex] is any integer)
HURRY ANSWER NOW PLS
Which scenario is modeled by the equation (x) (0.6) = 86 dollars and 46 cents?
A. A picnic table is on sale for 60 percent off. The sale price of the picnic table is x, $144.10.
B. A picnic table is on sale for 40 percent off. The sale price of the picnic table is x, $144.10
C. A picnic table is on sale for 60 percent off. The original price of the picnic table is x, $144.10.
D. A picnic table is on sale for 40 percent off. The original price of the picnic table is x, $144.10
Using proportions, the scenario modeled by the equation 0.6x = 86.46 is:
D. A picnic table is on sale for 40 percent off. The original price of the picnic table is x, $144.10.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
When a product is 40% off, 100 - 40 = 60% of the original price x is paid, hence the expression for the price is:
0.6x.
In this problem, the expression is:
0.6x = 86.46
x = 86.46/0.6
x = 144.1.
Hence option D is correct.
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(Please help, quickly if possible.)
Which types of dilation are the given scale factors?
Select Expansion or Contraction to correctly describe the type of dilation for each given scale factor.
(See image attached for details.)
A scale factor is a contracting scale such that x < 1, where x is the scale factor.
For example, if the scale factor x is less than 1, then it must be decreasing in size, and thus be contracting in size.
But, if the scale factor is greater than 1, then it is expanding in size and increasing.
1) -5 is expanding. It is greater than one.
2) -1/4 is contracting. It is less than one.
3) 3.5 is expanding. It is greater than one.
4) 6/7 is contracting. It is less than one.
A medical researcher has two petri dishes containing viruses. Dish B has a population density of 1.2 viruses per square millimeter. Dish A has an area of about 2,826 square millimeters.
If both petri dishes have the same population density, approximately how many viruses are in Dish A?
2,355 viruses
3,391 viruses
23,550 viruses
33,912 viruses
The population of viruses in the dish A is 3,391 viruses.
What is the population?Population density measures the amount of organisms in 1 square millimeters of a place (in this case the dish)
Population density = population / area
Population = population density x area
1.2 x 2826 = 3,391 viruses
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Find the GCF of the monomials: 32x^2 and 24x^2y
Answer:
8x^2
Explanation:
First, do prime factorization of each of the coefficients:
32 ⇒ 2^5
24 ⇒ 2^3, 3
The greatest common factor (GCF) of the coefficients is 2^3 = 8.
Next, find the GCF of the variables:
x^2
x^2, y
The GCF of the variables is x^2.
Finally, multiply the GCF of the coefficients by the GCF of the variables to get:
8x^2
Answer: 4x^2
Step-by-step explanation: I took the test and got this answer right
The amount of soda in a half-liter bottle follows a normal distribution. Assume μ = 500 ml and σ = 10 ml. A government auditor will fine the company if a random sample of 5 bottles has a sample mean under 490 ml. Find the probability the company will be fined.
The probability that the company will be fined is 0.1587.
How to illustrate the probability?From the information given, it was assumed that μ = 500 ml and σ = 10 ml.
Also, the random sample of 5 bottles has a sample mean under 490 ml.
Here, the probability will be:
= P(x < 490)
= P[(z < (490 - 500)/10]
= P (z < -10/10)
= P(z < -1)
Looking at this under the z table, the probability will be 0.1587
The probability is 0.1587.
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can you pls helpppp lol there’s the picture igs
Using the bisection concept, it is found that the measure of angle PQR is of 130º.
What is a bisection?A bisection divides an angle into two equal angles. In this problem, the angles are given as follows:
(3x + 5)º.(2x + 25)º.Hence the value of x is given as follows:
3x + 5 = 2x + 25
x = 20º.
Hence the measure of angle PQR is given as follows:
m<PQR = 3x + 5 + 2x + 25 = 5x + 30 = 5 x 20º + 30º = 130º.
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