The solution of the system of equations 2xy = z, 4x + z = 4y, y = x + 1 are:
x = 1, y = 2, z = 4 and;
x = - 2, y = - 1, z = 4.
Consider the system of equations,
2xy = z ------------(1)
4x + z = 4y ------------(2)
y = x + 1 -------------(3)
Substituting equation (3) in equation (2),
4x + z = 4y
4x + z = 4( x + 1)
4x + z = 4x + 4
z = 4
Substituting equation (3) in equation (1),
2xy = z
2x( x + 1 ) = z
2x² + 2x = 4
x² + x = 2
Hence, x = 1, - 2
Therefore,
When x = 1,
y = x + 1 = 2
When x = - 2, y = x + 1 = - 1
So, the solution for the system of the equations are x = 1, y = 2, x = 4 and x = - 2, y = - 1, z = 4.
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the greater roadrunner bird can run 14 miles per hour that's 7 times faster than an ostrich can walk how fast does an ostrich walk Solve using skip counting
Answer:
14•7=98
Step-by-step explanation:
think its help have a good day
If $14,000 is invested at 8% interest compounded quarterly, find the interest earned in 12 years.
Using the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where:
P = Principal = $14000
r = interest rate = 8% = 0.08
t = time = 12
n = Number of times interest is compounded = 4
Therefore:
[tex]\begin{gathered} A=14000(1+\frac{0.08}{4})^{4\cdot12} \\ A=36218.99 \end{gathered}[/tex]Let f(x) = 2x + 7 and g(x) = 3(2x +7). The y-intercept of g is Choose... the y-intercept of f, and the x-intercept of g is Choose... the x-intercept of f.
The y-intercept of .f(x) = 2x + 7 is 7; its x-intercept is -7/2.
The y-intercept of .f(x) = 2x + 7 is 7; its x-intercept is -21/6.
What is the Y-intercept and the X-intercept of a Function?A function is expressed in slope-intercept form as .f(x) = mx + b, where the y-intercept is represented by the value of b.
On the other hand, to determine the value of the x-intercept for a function, .f(x) = mx + b, substitute .f(x) = 0 into the equation .f(x) = mx + b and solve for the value of x in the equation.
Find the y-intercept and the x-intercept of .f(x) = 2x + 7:
y-intercept of the function (b) = 7
To find the x-intercept, substitute .f(x) = 0 into f(x) = 2x + 7:
0 = 2x + 7
Subtract 7 from both sides
0 - 7 = 2x + 7 - 7
-7 = 2x
Divide both sides by 2
-7/2 = 2x/2
-7/2 = x
x = -7/2
Therefore, the x-intercept is: -7/2.
Find the y-intercept and the x-intercept of g(x) = 3(2x +7):
g(x) = 3(2x +7)
g(x) = 6x + 21
The y-intercept is: 21.
Find the x-intercept by substituting g(x) = 0 into g(x) = 6x + 21:
0 = 6x + 21
-21 = 6x
-21/6 = 6x/6
-21/6 = x
x = -21/6.
x-intercept is: -21/6.
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I sent a pic to the app and it gave me an answer my class hasn't gone over and so I need someone to walk through the equation with me. The instructions say "solve the systems by elimination".
The linear system:
[tex]\begin{gathered} \frac{1}{4}x+4y=2+\frac{3}{4} \\ 3x+\frac{1}{2}y=9+\frac{1}{4} \end{gathered}[/tex]Let's follow the steps to solve this linear system.
1) Multiply one equation by a constant to set up the elimination of one of the variables.
You can multiply equation 2 by - 8:
[tex]undefined[/tex]Selecting all the correct answers. Which represents the inverse of this statement? Is the inverse true or false?
Given: A statement- A number is negative if and only if it is less than 0.
p: A number is negative.
q: A number is less than 0.
Required: To find the inverse of the given statement and state if it is true or false.
Explanation: The inverse of the statement will be-
A number is positive if and only if it is greater than 0.
p: A number is positive.
q: A number is greater than 0.
The statement is always true since a positive number is always greater than 0.
Now p and q both are true since any positive number is greater than 0 and any number greater than 0 is always a positive number.
Hence we can write
[tex]\text{\textasciitilde}p\leftrightarrow\text{\textasciitilde}q\text{ }[/tex]The inverse of the given statement is true.
Final Answer: Option D and Option F are correct.
x = the number of small bottles
y = the number of large bottles
The inequality in standard form that describes the situation is 15x + 20y ≥ 554.
What is the inequality equation?Here are inequality signs and what they mean:
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
If the ounces of water have to be at least 554 ounces, it means that the water taken can be equal or greater than 554 ounces. Thus the sign to be used is ≥.
The total ounces of water taken if a function of the capacity of small bottles and the number of small bottles taken and the capacity of large bottles and the number of large bottles taken.
(capacity of a small bottle x number of small bottles) + (capacity of large bottles x number of large bottles) ≥ 554 ounces
15x + 20y ≥ 554
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Save Submit Melanie and Joseph are raising money for their class trip to the zoo. They each need $30 to pay for the trip and are selling boxes of cookies for $4 each to earn the money. Joseph has sold 5 boxes and Melanie has sold 3 boxes. How much more money does Melanie need than Joseph? A) $10 B) $12 $18 DY $8
Save Submit Melanie and Joseph are raising money for their class trip to the zoo. They each need $30 to pay for the trip and are selling boxes of cookies for $4 each to earn the money. Joseph has sold 5 boxes and Melanie has sold 3 boxes. How much more money does Melanie need than Joseph? A) $10 B) $12 $18 DY $8
Joseph -------> has sold 5 boxes
5*($4)=$20 --------> need 30-20=$10
Melanie -------> has sold 3 boxes
3*($4)=$12 ------> need 30-12=$18
therefore
18-10=$8
answer is $8brain's tent is a triangular prism how much fabric was used make the tent
We can think of the tent as the sum of two rectangles (both sides) and two triangles (front and back)
Each ofthe rectangles are 12ft lenght and 8.6ft height, so their area is:
Area of the rectangle = 12x8.6 = 103.2 square feet, since they are two, 103.2 x 2 = 206.4 square feet
Each of the triangles have a base of 10ft and a height of 7 ft, so their area is:
Area of the triangle = (10 x 7)/2 = 70/2 = 35, since they are also two, 35 x 2 = 70 square feet
Total area of the tent = 206.4 + 70 = 276.4 square feet
Answer:
276.4 square feet
Jason likes to play video games. His parents allow him to play for 20 minutes plus 10 min for each half hour he does chores or studies. He can never play for more than 90 min/day.
The function f(x) = 20 + 10x models the number of minutes per day Jason could play where x represents the number of half hour increments he has done chores or studied. What is the practical range of the function?
Answer:
f(7)=20+10x
Step-by-step explanation:
The retail price for Jamaican allspice is $4.69 per ounce. You buy 8 ounces of allspice on sale for $4.62 per ounce. How much money do you save?
Answer:
Step-by-step explanation
56 cents
Explanation: The deal is 7 cents less per ounce, you need to buy 8 ounces, multiply 7 by 8, equaling 56 cents
Which statement is true about the function f(x)=√=-x?
O The domain of the graph is all real numbers.
O The range of the graph is all real numbers.
O The domain of the graph is all real numbers less than or equal to 0.
O The range of the graph is all real numbers less than or equal to 0.
Answer:
jfi6+_4655vud
Step-by-step explanation:
hiTeugdCan you please help me out with this I’m stuck
Given
Find
the value of x
Explanation
given m is parallel to n.
so, these are corresponding angles.
hence
[tex]\begin{gathered} 4x-23=2x+17 \\ 2x=17+23 \\ 2x=40 \\ x=20 \end{gathered}[/tex]so, x = 20
Final Answer
The value of x is 20
Estimate each sum 22+ 23 + 19 + 20 + 18 + 19 + 22
Please help it’s due tonight I will give a brainlist
24.8 %
The percentage of profit / selling price markup = 24.8 % , by rounding to nearest tenth.
What is profit?If the selling price is higher than the cost price, the difference between the two is referred to as profit. If the selling price is less than the cost price, the difference is referred to as the loss.Given this,
The seller's cost price is 210 dollars.
The seller's selling price is 279.30$.
We know that ,
Profit = selling price - cost price.
so, Profit = 279.30$ - 210$
= 69.3$.
To find the profit,
Profit /Selling Price Markup = (Profit/Selling Price)*100 .
-=> (69.3 / 279.30) x 100 = 24.81%
This is rounded to 24.8 %. ( by converting to nearest tenth).
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Alex can eat 8 hotdogs in 11
12 minutes. At this rate,
how many hotdogs can
Alex eat in three
minutes?
Answer:
Step-by-step explanation: It is a rate problem. If Alex can eat 8 hotdogs in 12 mins, you just divide 12/4=3 mins. Then, divide the hotdogs. 8/4=2
So: Alex can eat 2 hotdogs in 3 minutes
x/-6≥-20help meeee[tex] \frac{x}{ - 6 } \geqslant - 20[/tex]
We need to solve an inequality given in the form:
[tex]\frac{x}{-6}\ge-20[/tex]So we need to isolate "x" on one side to the inequality symbol.
In order to do that, we need to multiply both sides by the number "-6" (which will cancel out the denominator that "x" has). Bit we need to recall that when we multipkynor divide by a negative number boths sides of an inequality, the symbol flips direction. having that in mind, we proceed to multiply and solve for "x":
[tex]\begin{gathered} \frac{x}{-6}\ge-20 \\ x\leq(-20)\cdot(-6) \\ x\leq120 \end{gathered}[/tex]So the answer is: all real x-values less than or equal to 120.
If we need to give the answer in graphic form, we draw a number line with the origin (0), and mark on the right of it a point that we name "120". Then we highlight the line from the point 120 towards the left, and we make sure that we draw a solid dot on the 120 point mark to indicate that the point is included in the set.
Last year, Yoko had $10,000 to invest. She invested some of it into an account that paid 10% simple interest per year, and she invested the rest in an account that paid 6% simple interest per year. After one year she received a total of $640 in interest. How much did she invest in each account?
Final answer:
At 10% interest, $1 000 was invested.
At 6% interest, $9 000 was invested.
Let "x" be the amount invested at 10%. The annual interest for this investment would be $ 0.1x
Now, the investment at 6% is (10 000 - x), and it would have an annual interest of 0.06(10 000 - x)
We will use the following equation to solve for this
[tex]interest_1+interest_2=totalinterest[/tex]interest 1 = 0.1x
interest 2 = 0.06(10 000 - x)
total interest = 640
Substitute these values
[tex]interest_1+interest_2=totalinterest[/tex][tex]0.1x+0.06(10000-x)=640[/tex]Solve for x
[tex]0.1x+0.06(10000-x)=640[/tex][tex]0.1x-0.06x=640-\lbrack(0.06)(10000)\rbrack[/tex][tex]0.04x=640-600[/tex][tex]0.04x=40[/tex]Divide both sides by 0.04
[tex]\frac{0.04x}{0.04}=\frac{40}{0.04}[/tex][tex]x=1000[/tex]Since the investment at 6% is equal to 10000-x,
[tex]interest_2=10000-x[/tex][tex]=10000-1000[/tex][tex]=9000[/tex]Final answer:
At 10% interest, $1 000 was invested.
At 6% interest, $9 000 was invested.
To check,
[tex]0.1x+0.06(10000-x)=640[/tex][tex]0.1(1000)+0.06(10000-(1000))=640[/tex][tex]640=640[/tex]Write an equation in standard form of the line that passes through the point (-2,0) and has the slope of m=-2.
The equation in standard form of the line is y+2x+4 = 0.
A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.
Y = mx + c represents the expression of a straight line with slope m and intercept c on the y-axis.Given the variety of geometries in modern mathematics, the idea of a line is directly related to how the topology is described. In analytic geometry, for example, a line in the plane is frequently described as the collection of points whose coordinates satisfy a particular linear equation, whereas in a more abstract context, such as contact geometry, a line may be an autonomous object, separate from the points.We know that the standard form a straight line equation is given by
y-q = m(x-p) where (p,q) is a point on the line and m is the slope.
Therefore
y-0 = -2(x-{-2})
or, y = -2x -4
or, y + 2x + 4 = 0
Therefore the equation of the straight line is y + 2x + 4 = 0 .
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At a dinner table, the meal cost $22 and a sales tax of $1.87 was added to the bill. How much would the sales tax be on a $66 meal? What is the tax rate for the meals in this city?
Calculate the percentage for the tax rate
using this analysis
[tex]1.87\cdot\frac{100}{22}=8.5[/tex]The tax rate for meals in this city is 8.5%
Calculate the tax for the $66 meal.
[tex]66\cdot0.085\cdot=5.61[/tex]The tax for a $66 meal should be $5.61
In the diagram, the length of segment VS is 39 units.What is the length of segment TV?14 unitsnQ19 units3x + 438 unitsR50 units2x + 56x - 3Save and ExitNextSubmUnmark this question
From the diagram we know that:
[tex]\begin{gathered} TR=RV \\ TS=\text{VS} \end{gathered}[/tex]Therefore:
[tex]6x-3=39[/tex]Solving for x we get:
[tex]\begin{gathered} 6x=42 \\ x=7 \end{gathered}[/tex]Then:
[tex]\begin{gathered} TV=TR+RV=2RV=2(2x+5)=2(2\cdot7+5) \\ TV=2(19)=38 \end{gathered}[/tex]Answer: 38 units.
Superior Segway Tours gives sightseeing tours around Chicago, Illinois. It charges a one-time fee of $55, plus $15 per hour. What is the slope of this situation? 10 15 55 70
The linear equation that represents this situation is given by
y=15x+55
therefore
The slope is 15
How would I begin to find the equation for this? I will post picture of problem below if I can figure out how to upload photo. It's a graph. I have 10 extra credit of these to do...teachers always make extra credit on things we've never even seen before, ugh. Thanks in advance!
The equation of the parabola is y = (x + 2)² - 2, and the value of f(-1) is -1 after plugging x = -1 in the function.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
From the graph the vertex form of the parabola:
(-2, -2)
h = -2
k = -2
The vertex form of the parabola:
y = a(x - h)² + k
y = a(x + 2)² - 2
Plug x = 0
y = 2
a = 1
y = (x + 2)² - 2
Or
f(x) = (x + 2)² - 2
f(-1) = (-1 + 2)² - 2
f(-1) = -1
Thus, the equation of the parabola is y = (x + 2)² - 2, and the value of f(-1) is -1 after plugging x = -1 in the function.
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A plane flying horizontally at an altitude of 1 mi and a speed of 590 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it has a total distance of 5 mi away from the station. (Round your answer to the nearest whole number.)
Two students were competing to have the
highest amount of sales at a bake sale.
Together they made $132. If each
student had made $15 more in sales, one
student would have made twice as much
as the other student.
How much money did the winning
student make, in dollars?
Amount of money made by thee winning student as per the given conditions is equal to $93.
As given in the question,
Let x dollars be the money made by winning student
And y be the amount made by other student
As per given conditions:
x + y = $132 ___(1)
x + 15 = 2(y+15)
⇒ x +15 = 2y +30
⇒ x-2y =15 ____(2)
Multiply (1) by 2 and add it to (2)
2x +2y = 264
x - 2y = 15
3x = 279
⇒x =$93
Hence, y = 132 -93
= $39
Therefore, amount of money made by thee winning student as per the given conditions is equal to $93.
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Are you able to help? If you are thank you
From the graph of the function, the polynomial has the next roots: -2 (double), -1 (simple), and 3 (simple). Then, its equation is:
[tex]\begin{gathered} y=(x-(-2))^2(x-(-1))(x-3) \\ y=(x+2)^2(x+1)(x-3) \end{gathered}[/tex]What is anequation of the line that passes through the points (-7,3) and (-4,3)?
y = 3
Explanation:Equation of line formula:
y = mx + b
m = slope
b = y-intercept
Points: (-7,3) and (-4,3)
we apply the slope formula:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\begin{gathered} x_1=-7,y_1=3,x_2=-4,y_2\text{ = }3 \\ m\text{ = }\frac{3-3}{-4-(-7)}=\frac{0}{-4+7} \\ m\text{ = 0/3} \\ m\text{ = 0} \end{gathered}[/tex]To get c, we use any of the points in the equation of line
Using point (-7, 3) = (x, y)
y = mx + b
3 = 0(-7) + b
3 = 0 + b
3 = b
The equation of line for the given points:
y = 0(x) + 3
y = 0 = 3
y = 3
Hence, the equation is y = 3
[tex]e^x^-^3=(1/e^6)^x^+^2[/tex] e^x-3=(1/e^6)^x+2
The value of x in the given equation is -9/7.
Here, we are given an equation as follows-
[tex]e^{x-3} =(1/e^{6} )^{x+2}[/tex]
The expression on the right hand side can further be simplified as follows-
[tex]e^{x-3} =(e^{-6} )^{x+2}[/tex]
[tex]e^{x-3} =(e )^{-6(x+2)}[/tex]
now since the bases on both sides are equal to e, we can simply equate the powers to form the following equation-
x - 3 = -6(x + 2)
Now, we solve the equation to find the value of x as follows-
x - 3 = -6x + -6*2
x - 3 = -6x -12
x + 6x = -12 + 3
7x = -9
x = -9/7
Thus, the value of x in the given equation comes out to be -9/7.
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Seven cards are chosen from a well-shuffled deck of 52 playing cards. In how many selections do at least 3
Jacks occur?
Using the combination formula, it is found that there are 193 selections that contain at least 3 Jacks.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula, involving factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In the context of this problem, we have that the possibilities with at least 3 Jacks are given as follows:
3 Jacks from a set of 4, and one non Jack from a set of 48.4 Jacks from a set of 4.Hence the number of selections with at least four jacks is calculated as follows:
[tex]T = C_{4,3}C_{48,1} + C_{4,4}[/tex]
T = 4 x 48 + 1
T = 193.
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twice the sum of a circles radius and a squares side length is no more than 100 feetI have to translate English into algebra I need help can you help me please
Are these fractions equivalent or nonequivalent?
9/19
3/4
Click on the correct answer.
