The vertical line's equation is x = -7, and the horizontal line's equation Is y = 7.
Where the given coordinate is (--7, 7).
What do the vertical and horizontal lines represent?A vertical line is a straight, up and down line in a coordinate plane that is parallel to the y-axis. The horizontal line, on the other hand, is parallel to the x-axis and goes straight, left, and right.Here,
The value of x, is -7, will never change for a vertical line. This holds true for any y value. As a result, x = -7 is the equation for a vertical line passing through this point.
Similarly, the value of y, is 7, will never change for a horizontal line. This holds true for any x value. As a result, the equation for a horizontal line passing through this point is as follows: y =7
As a result, the vertical line's equation is x = -7 and the horizontal line's equation is y = 7.
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Renting a roller rink for your birthday costs $300 plus $9 per person. The total charge for your party was $534. Translate this information into an equation using x to represent the number of guests at your party.
The equation using x to represent the number of guests at your party is 300 + 9x = 534
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let x represent the number of guests at your party.
Here, renting a roller rink for your birthday costs $300 plus $9 per person. This will be:
300 + 9x = 534
Collect like terms
9x = 534 - 300
9x = 234
Divide
x = 234 / 9
x = 26
The number of guest is 26.
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At the start of a trip, a car's gas tank contains 12 gallons of gasoline. During the trip, the car consumes 10 gallons of gasoline. How much gasoline is left in the tank? Should you represent this amount with a positive or negative value? Why?
If the tank contains 12 gallons and then the car consumes 10, we can know how much gasoline is left by substracting 12 with 10:
12 - 10 = 2
Then, 2 gallons of gasoline is left in the tank
Since there is still gasoline because 12 is higher than 10, then we represent this amount with a positive value.
We can desribe 15x-10 as an expression.
We would describe 6x-2<35 as an
We can describe 15x-10 as an expression.
We would describe 6x-2<35 as an inequality.
What is an inequality?In mathematics, inequalities characterize the connection between two non-equal numbers. Inequality means being unequal. If two values are not equal, we use the "not equal symbol". However, various inequalities are employed to compare the numbers, whether they are less than or higher than.
An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. It is most commonly used to compare two numbers on the number line based on their size. In the illustration above, there's a less than sign. This means that it's an inequality.
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find the area of this question.
30pts.
Answer:
A=40, formula for area of a rectangle is a=L×W
Step-by-step explanation:
A=L×W = 10×4
f(x)=2x^3+ax^2-24x+1 has a local maximum at x=-4. find a
Step-by-step explanation:
ax2+2x3−24x+1=y
Step 2: Add -2x^3 to both sides.
ax2+2x3−24x+1+−2x3=y+−2x3
ax2−24x+1=−2x3+y
Step 3: Add 24x to both sides.
ax2−24x+1+24x=−2x3+y+24x
ax2+1=−2x3+24x+y
Step 4: Add -1 to both sides.
ax2+1+−1=−2x3+24x+y+−1
ax2=−2x3+24x+y−1
Step 5: Divide both sides by x^2.
ax2
x2
=
−2x3+24x+y−1
x2
a=
−2x3+24x+y−1
x2
Answer:
a=
−2x3+24x+y−1
x2
WILL GIVE BRAINLIEST
Answer:
1. Hyperbole
2. Center: (0,0)
3. Vertices: (-3, 0), (3, 0)
4. Foci: (-6, 0), (6, 0)
5. Asymptotes: y = [tex]\frac{\sqrt{18}}{3} }[/tex]x and y = [tex]-\frac{\sqrt{18}}{3} }[/tex]x
Step-by-step explanation:
PLS HELP WITH 15. (GIVING EXTRA POINTS)
Answer:
[tex]4^{6}[/tex] or 4096
Step-by-step explanation:
When the bases are the same, you add the exponents.
Answer:
Step-by-step explanation:
[tex]\boxed{\bf\\a^n*a^m=a^{n+m}}[/tex]
[tex]\displaystyle(4)^2\cdot(4)^4\cdot(4)^0=(4)^{2+4+0}=4^6=4096[/tex]
The graph of function f is shown. An exponential function on a coordinate plane passes through (minus 1, 7), (1, 2), (10, minus 1) and also intercepts the x-axis at 3 units and the y-axis at 4 units. Function g is represented by the table. x -1 0 1 2 3 g(x) 24 4 0 Which statement correctly compares the two functions? A. They have the same x- and y-intercepts. B. They have different x- and y-intercepts but the same end behavior as x approaches ∞. C. They have the same x-intercept and the same end behavior as x approaches ∞. D. They have the same y-intercept and the same end behavior as x approaches ∞.
f(x) = 2x³ - 4x + 6
f(3) =
Graph the cubic using its end behaviour and a few selected points.
The leading coefficient test requires one variable only
A bag contains 2 white balls, 6 orange balls and 2 red balls. If a ball is drawn, find the probability that it is a white or red ball.
First, let's calculate the total amount of balls:
[tex]2+6+2=10[/tex]Since there are 2 white balls and 2 red balls, the number of white or red balls is 4.
So the probability is:
[tex]p=\frac{red\text{ or }white}{total}=\frac{4}{10}=\frac{2}{5}[/tex]Correct option: A
A salesperson works 40 hours per week at a job where he has two options for being paid option a is an early wage of $19 option B is a commission rate of 8% sales how much does he need to sell in a given week to earn the same amount with each option
The salesperson needs to make weekly sales of $9,500 to earn the same amount with each option.
The amount he earns by option A can be calculated as follows;
As he works 40 hours per week and the hourly wage is $19; therefore the amount he will earn can be determined by multiplication as follows;
Option A earning: 40 × 19 = $760
Thus, the salesperson earns $760 through option A.
Consider x to be the amount of weekly sales;
As the commission rate is 8% of sales therefore 8% of x should be equal to $760 for the salesman to earn the same amount with both options.
(8/100)x = 760
0.08x = 760
x = 760 / 0.08
x = 9,500
Hence the salesman needs to make weekly sales of $9,500 to earn the same amount with both options.
Although there is a mistake in your question, you might be referring to this question;
A salesperson works 40 hours per week at a job where he has two options for being paid option a is an hourly wage of $19 option B is a commission rate of 8% sales how much does he need to sell in a given week to earn the same amount with each option
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can someone help me i will give brainlest :) 5, 6, 7, 8 only do those one's
Answer:
5. -2 > x
6. 4 [tex]\leq[/tex] x
7. 0 [tex]\geq[/tex] x
8. -3 < x
Step-by-step explanation:
Let S be any sample space, and E, F and G be any three events. Describe the event that E and G occur, but not the event F.
In the sample space, the annotation for the event where both E and G but not F occurs is given as:( E ∩ G ) ∩ Fc (Option B).
What are events in Math?An event is a specified set of results of a random experiment in probability theory. Because the sample space is the collection of all potential outcomes of a random experiment, another definition of an event is any subset of a sample space.
Colloquially, the sample space for a given set of events is the collection of all potential values for the events. Technically, a sigma-algebra is formed by the set of probable occurrences for a given random variate, and sample space is defined as the biggest set in the sigma algebra.
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Full Question:
Let S be any sample space, and E, F, and G be any three events. Describe the event that E and G occur, but not event F.
a) ( Ec ∪ G ) ∩ Fc
b) ( E ∩ G ) ∩ Fc
c) ( E ∪ G ) ∪ Fc
d) ( Ec ∪ Gc ) ∩ F
e) ( E ∩ G ) ∩ F
f) None of the above.
The annotation for the event in the sample space when E and G both occur but F does not is given as:( E ∩ G ) ∩ Fc which is the correct answer would be an option (B).
What are events in probability?In probability theory, an event is a predetermined group of outcomes from a random experiment. Another definition of an event is any subset of a sample space, which is the collection of all possible results of a random experiment.
We are allowed to use here for the necessary notation, though one way to indicate this is the complement of E U F U G. This would be the area in the sample space S that lies outside E, F, and G in a Venn diagram.
Thus, the annotation for the event in the sample space when E and G both occur but F does not is given as:( E ∩ G ) ∩ Fc
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The question seems to be incomplete the correct question would be
Let S be any sample space, and E, F, and G be any three events. Describe the event that E and G occur, but not event F.
a) ( Ec ∪ G ) ∩ Fc
b) ( E ∩ G ) ∩ Fc
c) ( E ∪ G ) ∪ Fc
d) ( Ec ∪ Gc ) ∩ F
e) ( E ∩ G ) ∩ F
f) None of the above.
Can you help me find the x and y of this triangle I don’t understand it
Answer: [tex]x=5\sqrt{3}, y=15[/tex]
Step-by-step explanation:
[tex]\sin 60^{\circ}=\frac{x}{10}\\\\x=10 \sin 60^{\circ}\\\\x=5\sqrt{3}\\\\\\\tan 30^{\circ}=\frac{5\sqrt{3}}{y}\\\\\sqrt{3}=\frac{y}{5\sqrt{3}}\\\\y=15[/tex]
A painter has three partially filled paint cans.1 7/8 gallonsthe second contains 1 1/5 gallonsand the third contains 1 3/4which anwer is closet to the total amount of paint?A.2B.3C.4D.5
A painter has three partially filled paint cans.
The first contains 1 7/8 gallons
The second contains 1 1/5 gallons
The third contains 1 3/4 gallons
The total amount of paint is the sum of these paint cans.
[tex]total=1\frac{7}{8}+1\frac{1}{5}+1\frac{3}{4}[/tex]Now let us add these mixed fraction numbers
[tex]\begin{gathered} total=1\frac{7}{8}+1\frac{1}{5}+1\frac{3}{4} \\ total=(1+1+1)+(\frac{7}{8}+\frac{1}{5}+\frac{3}{4}) \\ total=(3)+(\frac{7}{8}+\frac{1}{5}+\frac{3}{4}) \\ total=(3)+(1.825) \\ total=4.825 \end{gathered}[/tex]As you can see, 4.825 is closest to 5.
Therefore, the correct option would be D
Write an equation of a parabola with a vertex at the origin and a directrix at y=5
SOLUTION
The equation of the parabola is defined using
[tex]y=\frac{1}{4(f-k)}(x-h)^2+k[/tex]Since the vertex is at the origin the equation becomes
[tex]\begin{gathered} y=\frac{1}{4(f-0)}(x-0)^2+0 \\ y=\frac{1}{4f}x^2 \end{gathered}[/tex]Since the directrix is y=5
The distance from the focus to the vertex is equal to the distance from the vertex to the directrix
It follows
[tex]\begin{gathered} f-k=k-5 \\ f=-5 \end{gathered}[/tex]Thus the equation becomes
[tex]\begin{gathered} y=\frac{1}{4\times-5}x^2 \\ y=-\frac{x^2}{20} \end{gathered}[/tex]Therefore the equation of the required parabola is
[tex]y=-\frac{x^2}{20}[/tex]Answer: Y=-1/20x^2
Step-by-step explanation:
A box has a width of 12 cm and a length of 9 cm. the volume of the box is decreasing at a rate of 541 cubic cm per second, with the width and length being held constant. what is the rate of change of the height, in cm per second, when the height is 6 cm?
With the width and length being held constant, the height of the box decreases at rate 5 cm/s
Let:
l = length
w = wide
h = height
Then, the volume of the box is given by:
V = l . w. h
The length and the width are assumed to be constant. Hence, the derivative with respect to time is:
dV/dt = l . w dh/dt
Parameters given:
dV/dt = - 541 cm³/dt
l = 9 cm
w = 12 cm
Plug these parameters into the formula:
-541 = 12 . 9 . dh/dt
dh/dt = 5 cm/s
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Solve for u.u^2-u-12=0If there is more than one solution, separate them with commas.If there is no solution, click on "No solution."
we have the quadratic equation
[tex]u^2-u-12=0[/tex]we have that
a=1
b=-1
c=-12
Applying the formula to solve a quadratic equation
[tex]u=\frac{-(-1)\pm\sqrt{-1^2-4(1)(-12)}}{2(1)}[/tex][tex]u=\frac{1\pm7}{2}[/tex]The values of u are
u=4 and u=-3
therefore
The answer is
u=-3,4The product of 3x^5 and 2x^4 is
Options:
1) 5x^9
2) 5x^20
3) 6x^9
4)6x^20
Answer:
6x^9
Step-by-step explanation:
Hello!
Multiply the like terms:
3 and 2x^5 and x^4Multiply3x^5 * 2x^43*2*x^5*x^46*x^(5 + 4)6x^9The correct answer is the 3rd option, 6x^9.
The diagram shows a quadrilateral ABCD with each of its sides extended.
AB = AD
Show that ABCD is a kite. Give a reason for each stage of your working
(The diagram is attached)
Thanks, by neve124
It is to be noted that by the proof given below, the attached shape ABCD is a kite.
What is a kite in Euclidean Geometry?A kite is a quadrilateral having reflection symmetry across a diagonal in Euclidean geometry. A kite has two equivalent angles and two pairs of adjacent equal-length sides as a result of its symmetry.
The proof is as follows:
AB = AD [Given]
∠ADC = 115° [Angles on a Straight line]
That is 180 - 65 = 115°
∠BCD = 20° [Vertical Angles are equal]
∠ABC = (360 - (20+115+110))
= 115° [Angles in a quadrilateral]
Hence,
ABCD = Kite [Definition of a Geometric Kit]
That is
It two equivalent angles (∠ABC and ∠ADC)It also has two pairs of adjacent equal-length sides (that is |AD| ≈ |AB|.QED
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What is a correct congruence statement for the triangles shown?
Enter your answer in the box.
Answer:
ASA
Step-by-step explanation:
there are two congruent angles with an included side in between
Answer: Triangle RHS and NKW are congruent through the Congruence Theorem Angle-Side-Angle.
Step-by-step explanation:
The side HS is congruent to the side KW.
The angle H is congruent to angle K.
The angle S is congruent to angle S.
a 17 foot ladder is leaning against a wall. if the top slips down the wall at a rate of 2 ft/s, how fast will the foot be moving away from the wall when the top is 13 feet above the ground?
The foot will be moving at a rate of 2.373 ft/s away from the wall when the top is 13 feet above the ground.
From the question, we have the following;
Hypotenuse=17 foot
Height(y)=13 feet
Base(x)=(17^2-13^2)^1/2
=120^1/2 or sqrt(120)
The ladder against the wall is a right angle triangle, so we have:
x^2+y^2=17^2
x^2+y^2=289
Top slips down at 2ft/s
dy/dt=-2 ft/s, where height (y)=13ft
The foot will be moving horizontally(x), along the x axis, to find how fast the foot will be moving, we find dx/dt
Now, we take the derivative with respect to time:
=x^2+y^2=17^2
=2x(dx/dt)+2y(dy/dt)=0
Substitute the known values, y=13, x=sqrt(120), z=17, dy/dt=-2 ft/s
2(sqrt(120))(dx/dt)+2(13)(-2)=0
2(sqrt(120))(dx/dt)-52=0
We solve for dx/dt:
dx/dt=52/(2sqrt(120))
dx/dt=52/21.9089
dx/dt=2.373 ft/s
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The difference between two-fifth of a number and 9 is 7. Find the number.
Answer:
The number is 40.
Step-by-step explanation:
Step 1: Assume your variables
Consider the 'number' to be [tex]x[/tex].
Step 2: Create an equation(s)
The information in the question states that the difference between [tex]\frac{2}{5}[/tex] of [tex]x[/tex] and [tex]9[/tex], is [tex]7[/tex].
Representing this mathematically gives us:
[tex](\frac{2}{5}\times x) -9=7[/tex]
Step 3: Solve the equation
The equation we have is:
[tex](\frac{2}{5}\times x) -9=7[/tex]
So, let's solve it:
[tex](\frac{2}{5}\times x) -9=7\\\\\text{Add 9 to both sides:}\\(\frac{2}{5}\times x) -9+9=7+9\\\\\text{Simplify:}\\(\frac{2}{5}\times x)=16\\\\\text{Multiply by}~\frac{5}{2}~\text{on both sides:}\\\frac{5}{2}\times\frac{2}{5}\times x=16\times \frac{5}{2}\\\\\text{Simplify:}\\1\times x=\frac{80}{2}\\\\\text{Calculate:}\\x=40[/tex]
The equation of the line that is perpendicular to the line 5x + 6y = 18 and passes through the point (10,7)
Answer:
y = ( 6 / 5 )x - 5;
Step-by-step explanation:
Perpendicular Line Theoryy = - ( 1 / m )x + c;
AlgebraConvert dual intercept to standard form.
5x + 6y = 18;
Subtract 5x from both sides.
6y = - 5x + 18;
Divide both sides by 6.
y = ( - 5x + 18 ) / 6;
y = ( - 5x / 6 ) + ( 18 / 6 );
y = ( - 5 / 6 )x + 3;
Get the perpendicular line.
y = ( 6 / 5 )x + c;
Substitute the point.
7 = ( 6 / 5 )( 10 ) + c;
7 = 12 + c;
Subtract 12 from both sides.
- 5 = c;
c = - 5;
y = ( 6 / 5 )x - 5;
Use the long division method to find the result when 9x³ +30x² + 10x - 24 is
divided by 3x + 8. If there is a remainder, express the result in the form
q(x)+7(2).
Answer:
8
3x² + 2x - 2 - ----------
3x + 8
Step-by-step explanation:
3x² + 2x - 2
--------------------------------
3x + 8 | 9x³ + 30x² + 10x - 24
-9x³ - 24x² ↓
--------------------------------
6x² + 10x
-6x² - 16x ↓
-------------------------
-6x - 24
+6x + 16
----------------
-8
I hope this helps!
At a local print shop, 10 copies can be made for $4. At this rate, how much would it cost to make 75 copies?
Answer:
$30
Step-by-step explanation:
10 x 7 = 70
7 x 4 = 28
Since it's $4 to make 10 copies, it'll be $2 to make 5
28 + 2 = 30
$30 for 75 copies (a bad deal honestly)
Please mark Brainliest!!
Answer:
$30 dollars for 75 copies
Step-by-step explanation:
What we know:
$4 for every 10 copies.
How to figure out:
Divide 4/10 = .4 .4 is the cost per copy.
We do this because if it is 4 dollars per 10 copies, then we have to figure out the cost per copy. So we have to do how many dollars goes into each copy.
Now we know the cost of one copy we can multiply the amount of copies we need by the price of one.
75 x 0.4 = 30 30 is the price of 75 copies.
You have 8 times as many dimes as nickels. You have 18 dimes and nickels altogether how much money do you have in all?
For the given condition of dimes is 8 times of nickel and there are 18 dimes and nickels altogether, then total money is equal to $1.
As given in the question,
Let x be the number of dimes
Then number of nickels are 8x.
As per given condition,
Total number of dimes and nickels = 18
⇒ x + 8x = 18
⇒ 9x = 18
⇒ x= 2
Number of dimes =2
Number of nickels = 8(2)
= 16
Conversion:
1 dime = 0.10$
1 nickel = 0.05$
Total amount of money in dollars
= 2 ×(0.10) + 16× (0.05)
= 0.20 + 0.80
= 1.00
Therefore, for the given condition of dimes is 8 times of nickel and there are 18 dimes and nickels altogether, then total money is equal to $1.
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please help me ! please
Answer:
[tex] \sf {\large{4\pi }}[/tex]
Step-by-step explanation:
Circumference of a circle ⭕ = [tex] 2 \pi r [/tex]
Where,
r = d/2
d means diameter
r = 4/2 = 2
So, substitute to equation C = 2πr
C = 2πr
C = (2r)π
C = (2•2)π
C = 4π
what proportion of american households has at least one television? group of answer choices virtually all american households have at least one tv. except for adolescents who live in low-income, single-parent, or disadvantaged homes, the majority of american households have at least one tv. more than 50% of american households have at least one tv. virtually all middle-class and upper-class households have at least one tv; however, about 50% of lower-income families have a tv.
About 50% of Americans households have a tv except who live in low-income, single-parent, or disadvantaged homes
What is meant by Proportion?Proportion: Proportion is a central principle of architectural theory and an important connection between mathematics and art. It is the visual effect of the relationships of the various objects and spaces that make up a structure to one another and to the whole
Virtually all American households have at least one tv except for adolescents who live in low-income, single-parent, or disadvantaged homes, the majority of American households have at least one tv. More than 50% of American households have at least one tv.
however, about 50% of Americans households have a tv
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An electric current that alternates sinusoidally with a frequency of 60
cycles per second and is at maximum at t = 0.1 seconds can be described by
the equation
I(t) = 10cos(120πt - 12π) + 5,
where I is current in Amperes and t is time in seconds. What is the
approximate range of the current?
The current is defined as rate of flow of charge I = dq/dt.
The approximate range of the current is 299.5.
How to estimate the approximate range of the current?The current is defined as rate of flow of charge I = dq/dt
Let the equation be [tex]$q=\int i d t$[/tex]
Given: I(t) = 10 cos(120πt - 12π) + 5
We will substitute it in the above equation
q = [tex]$$\int[/tex] 10 cos(120πt - 12π) + 5 dt
now here limits of time is from t = 0.1 to t = 60 s
so here it will be given as
[tex]$\int 10 cos(120\pi t - 12\pi ) + 5 dt[/tex]
Rewrite using trig identities
[tex]$=\int_{0.1}^{60} 10 \cos (120 \pi t)+5 d t$$[/tex]
Apply the Sum Rule:
[tex]$\int f(x) \pm g(x) d x=\int f(x) d x \pm \int g(x) d x$[/tex]
substitute the values in the above equation, we get
[tex]$=\int_{0.1}^{60} 10 \cos (120 \pi t) d t+\int_{0.1}^{60} 5 d t$[/tex]
simplifying the equation,
[tex]$\int_{0.1}^{60} 10 \cos (120 \pi t) d t=0[/tex]
[tex]$\int_{0.1}^{60} 5 d t=299.5$[/tex]
= 0 + 299.5
= 299.5
Therefore, the approximate range of the current is 299.5.
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