We have
[tex]\begin{gathered} 2x-6y=8\text{ (1)} \\ 5x-4y=31\text{ (2)} \end{gathered}[/tex]we must solve the system of equations
First, we will solve for x the first equation
[tex]\begin{gathered} 2x-6y=8 \\ 2x=8+6y \\ x=\frac{8}{2}+\frac{6}{2}y \\ x=4+3y \end{gathered}[/tex]Then, we must replace the value of x in the second equation
[tex]\begin{gathered} 5(4+3y)-4y=31 \\ 20+15y-4y=31 \\ 11y=11 \\ y=\frac{11}{11} \\ y=1 \end{gathered}[/tex]Finally, we replace the value of y in the equation that we solved for x
[tex]\begin{gathered} x=4+3(1) \\ x=4+3 \\ x=7 \end{gathered}[/tex]So, the correct ordered pair is (7, 1)
What is the acceleration of a 50 kg object pushed with a force of 500 newtons?10 m/s225,500 m/s2490 m/s225 m/s2
Let's use Newton's second law of motion:
F = m*a
Where:
F= Force = 500
m = mass = 50
a = acceleration
So:
500 = 50*a
Solve for a:
Divide both sides by 50:
500/50 = 50a/50
10 = a
a = 10m/s²
Using the image above, which of the following are opposite rays?A QP and PLB PL and PQC LP and QPD LQ and PQ
ANSWER
PL and PQ
EXPLANATION
We want to find which of the rays are opposite rays.
That means which of the rays are going in opposite direction and are the same length to one another.
We see different rays in the image. Some are going upward while some are going downward.
The ones going upward are:
LQ and PQ
The ones going downward are:
QL and PL
By observation, among all the options, we see that only PL and PQ are the same length and that are in opposite directions.
That means that the answer is PL and PQ
A cone has a height of 15 yards and a radius of 11 yards. What is its volume?Use a ~ 3.14 and round your answer to the nearest hundredth.cubic yardsSubmit+
Okay, here we have this:
Considering the provided information, we are going to calculate the volume of the cone, so we obtain the following:
We will substitute in the following formula for the volume of a cone:
[tex]V=\frac{1}{3}\pi R^2h[/tex]Replacing we obtain:
[tex]\begin{gathered} V=\frac{1}{3}\pi(11yd)^2\cdot(15yd) \\ V=\frac{1}{3}\pi121yd^2\cdot15yd \\ V=5yd\cdot121yd^2\cdot\pi \\ V=605\pi yd^3 \\ V=605(3.14)yd^3 \\ V=1899.7yd^3 \end{gathered}[/tex]Finally we obtain that the volume of the cone is approximately 1899.7yd^3.
A TV set is offered for sale for P1, 800 down payment, and P950 every month for thebalance for 2 years. If interest is to be computed at 6% compounded monthly, what isthe cash price equivalent of the TV set?
Answer:
The cash equivalent price of the tv set is P5849.37
Explanation:
The total amount paid monthly is:
The initial down payment of P1800 and 24 payments of P950 (2 years = 24 months)
Then, the price paid with interest is:
[tex]1800+24\cdot950=24600[/tex]
Now, the formula for the monthly compound interest is:
[tex]A=P(1+\frac{r}{12})^{12t}[/tex]Where:
A is the amount after t years
P is the initial amount (what we want to find)
R is the rate of compound in decimal
t is the number of years of compounding
In this case:
• A = 24600 (the total paid if compounded)
,• P is what we want to find
,• r = 0.06 ( to convert percentage to decimal, we divide by 100: 6%/100 = 0.06)
,• t = 24 (2 years)
[tex]\begin{gathered} 24600=P(1+\frac{0.06}{12})^{12\cdot24} \\ . \\ 24600=P\cdot1.005^{288} \\ . \\ P=\frac{24600}{4.2056} \\ . \\ P=5849.373 \end{gathered}[/tex]To the nearest cent, the cash price is 5849.37
Stanley marked two points on the grid below to show the locations of the fiction section, point F, and the travel section, point T, in a bookstore.
EXPLANATION
We need to calculate the distance between the points (x₁,y₁)=(-8,-3) and (x₂,y₂)=(-3,8) applying the distance equation as shown as follows:
distance=
[tex]\text{Distance}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substituting terms:
[tex]\text{Distance = }\sqrt[]{(-3-(-8))^2+(8-(-3))^2}[/tex]Adding numbers:
[tex]\text{Distance}=\sqrt[]{(5)^2+(11)^2}=\sqrt[]{(25+121)}=\sqrt[]{146}[/tex]The shortest distance is sqrt(146)
5) 5x + 7y + 3 is an example of a O monomial O binomial O trinomial O polynomial
Problem Statement
The question asks us for what the following expression is an example of
[tex]5x+7y+3[/tex]Solution
Monomial:
A monomial is an expression with only one term. For example:
[tex]x^2[/tex]Binomial:
A binomial is an expression with only two terms. For example:
[tex]2+3x[/tex]Trinomial:
A trinomial is an expression with 3 terms. For example:
[tex]5x+7y+3[/tex]Final Answer
Therefore, the answer is Trinomial
Thr sum of 2 numbers is 97.The greater number is three less then four times the lesser number.Find the numbers
need answer soon PLEASE!!!!
Answer:
Greater number: 77 Lesser number: 20
Step-by-step explanation:
Sooo
20 × 4 is 80
80 - 3 = 77
77 + 20 = 97
Answer:
77 & 20
Step-by-step explanation:
x+y=97
x=4y-3
4y-3+y=97
5y=97+3
5y=100
5 5
y=20
x=4y-3
x=4(20)-3
x=80-3
x=77
don't forget to follow , rate & like
Х о 1 2 3 4 у -5 4 13 22 31
We can take any 2 points both from x and y and use the equation of a line formula to find out the equation of the line represented by the points in the table.
Let's take the points:
[tex]\begin{gathered} (x_1,y_1)=(0,-5) \\ (x_2,y_2)=(1,4) \end{gathered}[/tex]The equation of a line formula is:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Let us plug in the points into this formula and do a little algebra to re-arrange the equation in the slope-intercept form, which is y = mx + b. The steps are shown below:
[tex]\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ y-(-5)=\frac{4-(-5)}{1-0}(x-0) \\ y+5=\frac{4+5}{1}(x) \\ y+5=\frac{9}{1}(x) \\ y+5=9x \\ y=9x-5 \end{gathered}[/tex]The slope-intercept form is given by:
[tex]y=9x-5[/tex]Where 9 is the slope and -5 is the y-intercept (y-axis cutting point)
Find an equation of variation in which y varies directly as x and y=28 when x=7. Then find the value of y when x=16.
Josslyn has nickels and dimes in her pocket. The number of nickels is three more than seven times the number of dimes let d represent the number of dimes. Write the expression for the number of nickels
to solve this we need to translate into math terms, so
Step 1
a) let d represents the number of dimes
let n represents the number of nickles
so
re write the expressions
[tex]\begin{gathered} number\text{ of dimes=d} \\ seven\text{ times the number of dimes = 7d} \\ \end{gathered}[/tex]The number of nickels is three more than seven times the number of dimes in other words you have to add 7 to seven times the number of dimes to obtain the number of nickles
hence
[tex]n=7d+3[/tex]therefore , the expression for the number of nickles is
[tex]7d+3[/tex]I hope this helps you
Round $43,569.14 the nearest dollar
To find:
Round $43,569.14 the nearest dollar
Solution:
The number after the decimal is less than 50. So, the amount $43,569.14 rounded to the nearest dollar is $43,569.
Thus, the answer is $43569.
For each ordered pair, determine whether it is a solution to the sytem of equations.
Given
We have the system of equations:
[tex]\begin{gathered} 3x\text{ - 2y = -4} \\ 2x\text{ + 5y = -9} \end{gathered}[/tex]The ordered pair that would be a solution to the given system of equations must satisfy both equations. There can only be one ordered pair and this can be obtained by solving the system of equations simultaneously
Using a graphing tool, the plot of the lines is shown below:
The point where the lines intercept is the solution to the system of equations.
Hence the ordered pair that is a solution is (-2, -1)
Answer:
(4,8) - No
(8, -5) - No
(0, 3) - No
(-2, -1) - Yes
pls help I've had a bad day and I've been trying to figure this out forever
the given expression is
4Ix-2I - 3
You roll a six-sided dice.Event A: Roll a 6. Event B: Roll a prime number. Find P(A or B) . Express your answer as a fraction in simplest form.
The probability of rolling a 6 is:
[tex]P(A)=\frac{1}{6}[/tex]There are 3 prime numbers between 1 and 6: 2, 3 and 5. Therefore, the probability of rolling a prime number is:
[tex]P(B)=\frac{1}{3}[/tex]Therefore, the probability of rolling a 6 or a prime number is:
[tex]P(AorB)=\frac{1}{6}+\frac{1}{3}=\frac{1}{2}[/tex]You're having a breakfast party for 483 of your closet friends and 271 like chocolate donuts. In a dozen donuts, the probability of getting a chocolate donut is 1/5. How many dozen donuts would you have to buy to ensure that all 271 people get a chocolate donut?
In a dozen donuts the probability of getting a chocolate donut is 1/5, meaning 1/5 of the 12 donuts are chocolate donuts.
Step 1.- Calculate how much 1/5 out of 12 is:
[tex]\frac{1}{5}(12)=\frac{12}{5}=2.4[/tex]In each dozen we would get 2.4 chocolate donuts
Step 2.- Calculate how many dozen are needed to get 271 chocolate donuts.
We divide 271 by 2.4 to get the answer:
[tex]\frac{271}{2.4}=112.92[/tex]Step 3: We round the answer to the nearest integer value, and we need 113 dozens of donuts to ensure that all 271 people get a chocolate donut.
Answer: 113
pls today I have it for tomorrow
Answer:
6/5 x 5/3 is 2
if that's what you need help with
step-by-step explanation
A hummingbird can travel up to 15 meters per second.What is the hummingbird's speed in miles per hour?1 mile ≈ 1609 meters Enter your answer, as a decimal to the nearest tenth, in the box. mph
SOLUTION
The speed of the hummingbird is giving as
[tex]\text{ 15meter/seconds }[/tex]Recall that
[tex]1\text{mile}\approx1609\text{ meters }[/tex]Hence
[tex]\begin{gathered} 15\text{meters will be }\frac{15}{1609}miles\text{ } \\ \\ \end{gathered}[/tex]Recall that
[tex]3600\text{ seconds =1hour }[/tex]Hence
the speed of the hummingbird in miles per hour will be
[tex]\begin{gathered} \frac{15}{1609}\times\frac{3600}{1}=\frac{54000}{1609}=33.56\text{miles per hour } \\ \\ \end{gathered}[/tex]Therefore the speed in miles per hour to the nearest tenth is 33.6mph
The florist charge $31.75 for eight roses and five carnations. For one rose and three carnations,it costs $5.75. What is the cost for each type of flower?
Let's use the variable x to represent the cost of one rose and y to represent the cost of one carnation.
If 8 roses and 5 carnations cost $31.75, we can write the following equation:
[tex]8x+5y=31.75[/tex]If 1 rose and 3 carnations cost $5.75, we can write a second equation:
[tex]x+3y=5.75[/tex]From the second equation, we have x = 5.75 - 3y.
Using this value of x in the first equation, we have:
[tex]\begin{gathered} 8(5.75-3y)+5y=31.75\\ \\ 46-24y+5y=31.75\\ \\ -19y=31.75-46\\ \\ -19y=-14.25\\ \\ y=0.75 \end{gathered}[/tex]Now, calculating the cost of one rose, we have:
[tex]x=5.75-3y=5.75-3\cdot0.75=5.75-2.25=3.5[/tex]Therefore the cost of one rose is $3.50 and the cost of one carnation is $0.75.
Which statement describes a key feature of the function g if g(x) =f(x)-7
The graph of the function f(x)=e^x is given.
To determine the function g(x),
g(x)=f(x)-7.
Then the graph of function g(x) is
Then from the graph above , the horizontal asymptote is y=-7.
Hence the correct option is D.
Hi I need help with this question. Melissa starts with four packages of balloons and 8 single balloons. Her brother gave her 20 more balloons and three more packages. She now has twice the number of balloons she started with. Write and solve an equation to find how many balloons are in a package. How many balloons did Melissa start with?
Okay, here we have this:
Let's take the packages as (x), so we obtain:
Melissa Starts with: 4x+8 ballons (1)
Her brother gave her: 3x+20 ballons (2)
And as she now has twice the number of balloons she started with. This mean that:
2(4x+8)=(3x+20)+(4x+8)
Let's clear x in this equation:
8x+16=3x+20+4x+8
8x+16=7x+28
8x-7x=28-16
x=12
Finally we obtain that in a package are 12 ballons, now let's calculate How many balloons did Melisa start with?:
Remember that Melissa Starts with: 4x+8 ballons, so replacing x with 12, we obtain that Melissa Starts with: 4(12)+8=48+8=56.
Finally we obtain that Melissa Starts with 56 ballons.
Please get help with this for I have tried many times to get the correct answers for each but still could not
A dilation of a point with a factor k is given by:
[tex](x,y)\rightarrow(kx,ky)[/tex]In this case the dilation factor is ; which means that we need to multiply each component of the vertexes by two. After doing this we get the following graph for the original and final polygon:
From the figure we can answer the questions.
a)
Longest side length of the original figrue: 3 units
Longest side lenght of the final figure: 6 units.
b)
Longest side length of the final figure = 2 x Longest side length of the original figure.
c)
For a positive scale final figure is always bigger than the original one, therefore, the stament is False.
d)
Any dilation creates a similar figure since we are not changing the angles, only the lengths. Therefore the statement is True
Which exponential expressions are equivalent to the one below? Check allthat apply.(3.7) 10A. 310 + 710B. (3:7)10O .C. 2110O d. 310.710
Given the exponential expression:
[tex](3\cdot7)^{10}[/tex]The equivalent expressions are:
[tex]\begin{gathered} (3\cdot7)^{10}=3^{10}\cdot7^{10} \\ (3\cdot7)^{10}=21^{10} \end{gathered}[/tex]So, the answer will be options C, D
2x = 5(2-y)y = 3(-x + 5)Solve system of equation using elimination method
The given system of equations is:
[tex]2x=5(2-y);y=3(-x+5)[/tex]Simplify to get:
[tex]\begin{gathered} 2x=10-5y \\ 2x+5y=10\ldots(i) \\ y=-3x+15 \\ 3x+y=15\ldots(ii) \end{gathered}[/tex]Multiply (ii) by 5 to get:
[tex]15x+5y=75\ldots(iii)[/tex]Subtract (i) from (iii) to get:
[tex]\begin{gathered} 15x+5y=75 \\ -2x-5y=-10 \\ 13x=65 \\ x=\frac{65}{13}=5 \end{gathered}[/tex]Substitute x=5 in (ii) to get:
[tex]\begin{gathered} 3(5)+y=15 \\ y=0 \end{gathered}[/tex]Solution set {5,0}.
Venus' orbital speed is approximately 210 kilometers in 6 seconds. Earth's orbital speed is approximately 270 kilometers in 9 seconds. Which planet travels at a faster speed per second?
We know that
• Venus' orbital speed is 210 kilometers in 6 seconds.
,• Earth's orbital speed is 270 kilometers in 9 seconds.
First, we have to divide the numbers to find the ratio
[tex]\begin{gathered} \frac{210}{6}=35 \\ \frac{270}{9}=30 \end{gathered}[/tex]As you can observe, Venus has greater speed because it's 35 kilometers per second.
Hence, the answer is Venus.For the polyhedron, use eular's foemula to find the missing number
Given:
Edges of the polyhedron, E = 10
Vertices, V = 5
A polyhedron is a three-dimensional figure.
Let's find the number of faces using Euler's formula.
To find the number of faces of the polyhedron, we have the Euler's formula:
V + F - E = 2
Substitute values into the formula:
5 + F - 10 = 2
Combine like terms:
F + 5 - 10 = 2
F - 5 = 2
Add 5 to both sides:
F - 5 + 5 = 2 + 5
F = 7
Therefore, the number of faces of the polyhedron is 7
ANSWER:
7 faces
Hello, May I please get some assistance with this homework question? I posted an image below Q2
Solving (a)
The two functions we have are:
[tex]\begin{gathered} f(x)=3x+3 \\ g(x)=x^2 \end{gathered}[/tex]We are asked to find the composite function:
[tex](f\circ g)(x)[/tex]Step 1. The definition of a composite function is:
[tex](h\circ k)(x)=h(k(x))[/tex]In this case:
[tex](f\circ g)(x)=f(g(x))[/tex]This means to plug the g(x) expression into the value of x of the f(x) function.
Step 2. Substituitng g(x) as the value for x in f(x):
[tex](f\circ g)(x)=f(g(x))=4(x^2)+3[/tex]Simplifying:
[tex](f\circ g)(x)=\boxed{4x^2+3}[/tex]Step 3. We also need to find the domain of this composite function.
The domain of a function is the possible values that the x-variable can take. In this case, there would be no issues with any x value that we plug as the x-value. Therefore, the domain is all real numbers.
The domain of fog is all real numbers.
Answer:
[tex](f\circ g)(x)=\boxed{4x^2+3}[/tex]The domain of fog is all real numbers.
Combine Like Terms -8w + 16x + 20w – 40x
Answer:
12w - 24x
Step-by-step explanation:
-8w + 16x + 20w - 40x
20w - 8w = 12w
-40x + 16x = 24x
Answer:
12w - 24xStep-by-step explanation:
Start by grouping terms that are alike. You can identify such terms by looking at the variables. Anything associated with x is considered a like term to another number associated with x.[tex]-8w+16x+20w-40x\\-8w+20w+16x-40x[/tex]
Add both like elements for each side.[tex]-8w+20w=12w\\12w+16x-40x\\16x-40x=-24x\\\bold{=12w-24x}[/tex]
Hope this helps!
Determine the slope (m) and y-intercept (b) of the line:y = 2x - 3A) m = 3, b = 2B) m = 2, b = -3C) m = -3, b = 2D) m = 2, b = 3
slope of line(m) = 2 and intercept on y axis is -2 that is 2 unit in negative y axis.
Equation of line in slope intercept form:
Slope:
Slope is known as tangent of an angle made by positive X-axis.
We know equation of line in slope and intercept form is,
y = mx + b
where,
m is slope of line
b is intercept on y axis
hence for the given equation,
y =2x - 3
slope (m) will be = 2
intercept on y axis (b) = -3
thus,
option (B) will be correct.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
The given function's f(t) = (t - 4)(t + 1)(t - 7), f-intercept is f(t) = 28 and the t-intercepts are t = - 1, 4, 7.
What are intercepts?A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the y-axis of the coordinate system in analytic geometry using the widely used convention that the horizontal axis represents a variable x and the vertical axis represents a variable y. Therefore, x = 0 is satisfied at these sites. The x-intercept and y-intercept are the points where a line crosses each axis.
An intercept is a location where an axis and a graph intersect. The x-intercept is the name given to this particular one.
Put t = 0 in the function f(t) = (t - 4)(t + 1)(t - 7)
f(t)= (0-4)(0+1)(0-7)
f(t) = (-4)(1)(-7)
f(t) = 28
So, the f-intercept is (0,28)
Put f(t) = 0 to find t- intercepts
0 = (t-4)(t+1)(t-7)
So, t - 4 = 0
t = 4
For t + 1 = 0
t = -1
For (t - 7) = 0
t = 7
So, the t intercepts are t = -1, 4, 7.
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What is the solution to the equation?3+√3x- 5 = x A. -2 and -7B.2 and 7C. -2D. 7
Given the equation:
[tex]3+\sqrt[\placeholder{⬚}]{3x-5}=x[/tex]Isolating the square root:
[tex][/tex]