Use substitution to solve the following system of equation
X =
y =
4x + y = 28
y = 3x
Answer:
x = 4
y = 12
Step-by-step explanation:
Replace all occurrences of y with 3x in each equation.
7x = 28
y = 3x
Divide each term in 7x = 28 by 7 and simplify.
x = 4
y = 3x
Replace all occurrences of x with 4 in each equation.
y = 12
x = 4
The solution to the system is the complete set of ordered pairs that are valid solutions.
(4,12)
The result can be shown in multiple forms.
Point Form:
(4,12)
Equation Form:
x = 4,y = 12
Hope I helped <3
62.3 is 60% of what number
Answer:103.83
Step-by-step explanation:
62.3/60=1.03831.0383 x 100=103.83Can you tell me what the answer is
The simplified form of the expression is ∛5/3x
What is an expression?Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given is an expression, [tex]\sqrt[3]{\frac{10x^{5} }{54x^{8} } }[/tex]
Simplifying, we get,
[tex]\sqrt[3]{\frac{10x^{5} }{54x^{8} } }\\= \sqrt[3]{\frac{10x^{3+2} }{2*27x^{3+3+2} } }\\= \frac{x}{3x^{2} } \sqrt[3]{\frac{10x^{2} }{2x^{2} } }\\= \frac{\sqrt[3]{5} }{3x}[/tex]
Hence, the expression is ∛5/3x
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Bob's gift shop sold a record number of cards for mother's day. One salesman sold 33 cards, which was 4% of the cards sold for mother's day. How many cards were sold for mother's day?.
Bob's gift shop sold a total of 825 cards for Mother's Day.
To calculate the total number of cards sold for Mother's Day, we can use the following formula:
Total Cards Sold = (Number of Cards Sold by Salesman) / (Percent of Cards Sold by Salesman)
In this case, the total number of cards sold for Mother's Day would be calculated as:
Total Cards Sold = (33 cards) / (4%)
Using the above formula, the total number of cards sold for Mother's Day would be 825 cards.
To arrive at this answer, we first converted 4% to a decimal by dividing it by 100. This gave us 0.04. We then divided 33 cards by 0.04 to get 825 cards.
Therefore, Bob's gift shop sold a total of 825 cards for Mother's Day.
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What is an equation of the line that passes through the points (8, 6) and
(-3,6)?
Answer:
y=6
Step-by-step explanation:
right!!
9) Consider the pattern of squares shown below: Which type of model, linear or exponential.
The given model is exponential.
Exponential function -The formula for an exponential function is f (x) = ax, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.
When b > 0 and b 1, an exponential function has the form f(x) = bx. The base is b, and the exponent is x, just like in any exponential expression. The development of bacteria is an illustration of an exponential function. Some germs multiply by two per hour.
As it is clear from the figure, 1 block has 2 boxes, then 4, 8.
So, it is in the form 2ⁿ.
∴ It is Exponential model.
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Complete question -
A scuba diver has a rope connecting the dive boat to an anchor on the ocean floor. The rope is 13 ft long. The water is 3 ft deep. How far is the anchor from a point directly below the boat?
Answer: 3 feet
It says the water is 3 feet deep, is it meant to say diver?
Rectangle abcd is dilated to form rectangle a′b′c′d′. what is the dilation factor? what is the center of dilation? select all that apply
Answer:
The answer is C
Step-by-step explanation:
The correlation coefficient, r, is a number between a. 0 and 1 b. 0 and [infinity]
c. -[infinity] and [infinity]
d. -10 and 10 e. 0 and 10 f. 0 and 100 g. -1 and 1
The correlation coefficient is measured on a scale that varies from +1 ≤ 0 ≤ -1.
What is correlation?Correlation is a statistical measure that expresses the extent to which two variables are linearly related.The sample correlation coefficient is defined as[tex]${\displaystyle {\begin{aligned}r_{xy}&={\frac {\sum x_{i}y_{i}-n{\bar {x}}{\bar {y}}}{ns'_{x}s'_{y}}}\\[5pt]&={\frac {n\sum x_{i}y_{i}-\sum x_{i}\sum y_{i}}{{\sqrt {n\sum x_{i}^{2}-(\sum x_{i})^{2}}}~{\sqrt {n\sum y_{i}^{2}-(\sum y_{i})^{2}}}}}.\end{aligned}}}[/tex]
where [tex]{\displaystyle s'_{x}}[/tex] and [tex]{\displaystyle s'_{y}}[/tex] are the uncorrected sample standard deviations of X and Y.
Given is a term as correlation coefficient.
The correlation coefficient is given by -[tex]$r =\frac{\sum\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)}{\sqrt{\sum\left(x_{i}-\bar{x}\right)^{2} \sum\left(y_{i}-\bar{y}\right)^{2}}}[/tex]
where -
[tex]r[/tex] = correlation coefficient
[tex]x_{i}[/tex] = values of the x - variable in a sample
[tex]\bar{x}[/tex] = mean of the values of the x-variable
[tex]y_{i}[/tex] = values of the y-variable in a sample
[tex]\bar{y}[/tex] = mean of the values of the y-variable
The correlation coefficient is measured on a scale that varies from +1 through 0 to -1. When one variable increases as the other increases the correlation is positive and when one decreases as the other increases it is negative.Therefore, the correlation coefficient is measured on a scale that varies from +1 ≤ 0 ≤ -1.
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What is SAS congruence rule of triangle?
The SAS (Side-Angle-Side) Congruence Rule states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.
The SAS (Side-Angle-Side) congruence rule is a method used to determine if two triangles are congruent. This rule states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
To determine if two triangles are congruent using the SAS rule, we must first identify the two sides and the angle in one triangle that are congruent to the two sides and the angle in the other triangle. This means that they must have the same measures in terms of length and angle.
Once we have identified the corresponding sides and angles, we can use the SAS rule to determine if the two triangles are congruent. If the two sides and the angle of one triangle are congruent to the two sides and the angle of another triangle, then the two triangles are congruent.
However, if the two sides and the angle of one triangle are not congruent to the two sides and the angle of another triangle, then the two triangles are not congruent. The SAS rule is a simple and effective way to determine if two triangles are congruent.
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Given the figure below, find the values of x and z.
►
75°
(8x+19)
Please help I’m really stressing
The two types of figures are open and closed, geometric figures respectively. Figures that don't end where they begin are said to be open figures.
what is geometric figures ?Closed geometric shapes are made up of points, line segments, circles, and curves. All around us, we can observe these types of shapes. Circle, rectangle, triangle, and other geometric shapes are a few examples. The triangle-shaped slices of a pizza are round.
Straight lines have been drawn on the floor, the door, the window, and the zebra crossing by the roadside in the classrooms. Even though angles are used in building construction, they also have connections to disciplines like physics and chemistry.
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Describe the graph of the line x = 5.
O horizontal line
O line with slope of 5
O crosses the y-axis
O vertical line
The line x= 5 is a vertical line that passes through the x-axis at the point
x = 5.
Option D is the correct answer.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
The equation of a line is x = 5.
This means,
(0, 5)
This is a vertical line that passes through x = 5 on the x-axis.
Thus,
x = 5 is a vertical line.
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2x+2y=4 and 3x+2y=7 please
Answer:
what is it you need to solve for, y? x?
Answer:
Step-by-step explanation:
(i)2x+2y=4
We take value of y=[tex]\frac{4-2x}{2}[/tex]
2x+2([tex]\frac{4-2x}{2}[/tex])=4
2x + [tex]\frac{8-4x}{2}[/tex]=4
[tex]\frac{4x+8-4x}{2}[/tex] =4 (4x-4x=0)
[tex]\frac{8}{2}[/tex]=4 -> 4=4=0
2x+2y=4 is 0
(ii)3x+2y=7
y=[tex]\frac{7-3x}{2}[/tex]
3x+2([tex]\frac{7-3x}{2}[/tex])=7
[tex]\frac{6x+14-6x}{2}[/tex]=7
[tex]\frac{14}{2}[/tex]=7
7=7=0
2. Brandon found that the number of snapper fish in an area can be represented by the formula
F = 1500(1.02)^t
where t represents the number of years since 2004. What is the y-intercept of this equation
and what does it represent?
The y-intercept represents the number of snapper fish in the area in 2004, which is the year that t = 0.
An area can be represented by the given formula:
[tex]F = 1500(1.02)^t[/tex]
where t represents the number of years since 2004.
The y-intercept of this equation is the point where the graph of the equation crosses the y-axis. In other words, it is the value of F when t is equal to 0.
Plugging in t = 0 into the equation above gives us:
F = 1500(1.02)⁰
= 1500(1)
= 1500
So the y-intercept of this equation is 1500.
Thus, the y-intercept reflects the amount of snapper fish caught in the area in 2004, the year t = 0.
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find and sketch the domain of the function. f(x, y) = ln(25 − x2 − 25y2)
The domain is the area enclosed by the circle, which is all the points inside the unit circle.
The domain of a function is the set of all possible input values (x, y) for which the function is defined and produces a valid output.
For f(x, y) = ln(25 − x2 − 25y2), the function is defined as long as 25 − x2 − 25y2 > 0. This is because the natural logarithm (ln) is only defined for positive numbers. To find the domain, we can set 25 − x2 − 25y2 > 0 and solve for x and y.
25 − x2 − 25y2 > 0
x2 + 25y2 < 25
x2 / 25 + y2 < 1
This is the equation of a unit circle centered at (0,0) with a radius of 1.
So the domain is the area enclosed by the circle, which is all the points inside the unit circle.
You can graph this on the x-y plane.
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It's the end of the school year, and your class of 250
students must decide the best place for the
yearbook signing party.
Everybody votes in a direct democracy!
☐ Select representatives for groups of students.
Why?
Plllls answer
Everybody votes in a direct democracy to select a place for the yearbook signing party.
What is direct democracy?Rules, institutions, and procedures known as "direct democracy" allow members of the public to vote directly on proposed constitutional amendments, laws, treaties, or policy decisions. Referendum and initiatives are the two most significant examples of direct democracy that are addressed in this primer.
Given:
It's the end of the school year, and your class of 250 students must decide the best place for the yearbook signing party.
To select the place:
They vote in direct democracy.
Because they have only 250 people.
And 250 people can have direct say.
Number of people is less.
So, selecting representatives would be not fair.
Therefore, everybody votes in a direct democracy.
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Which four statements describe the relationship represented by the model?
The four statemen that describes the relationship of the model
there are many possible masses of the cubethe mass of the cube is twice the mass of the cylinderWhen a cylinder has a mass of one the mass of the cube is twoIf the mass of the cylinder is s and the mass of the cube is c, 2s = cWhat is a model?A model refers to images, objects variables meant to depict a relation
In the model provided the relationship existing between the models is that the mass are equal hence there will be an equality sign to balance the relationship in the left and right hand side
examining the model shows that
3 cylinders = 1 cylinder + 1 cube
3 cylinders - 1 cylinder = 1 cube
2 cylinders = 1 cube
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Can someone answer this question really quick
The Bobcats football coach logged the following yardage gains and losses over four plays of a game.
1. Gain 25x yards.
2. Gain 0.9y yards.
3. Lose 12y yards.
4. Lose 5.2x yards.
What is the net yardage for these four plays?
Enter your answer as an expression, like this: 42x+53y
The net yardage the Bobcats football coach logged over four plays of game is 19.8x - 11.1y
How to find the net yardageThe net yardage is calculated using the addition and subtraction operation as follows
For the gains the calculation is as follows
= Gain 25x yards + Gain 0.9y yards.
= 25x + 0.9y
For the lose the calculation is as follows
= Lose 12y yards + Lose 5.2x yards.
= 5.2x + 12y
the net yardage is solved as follows
net yardage = gains - loses
net yardage = (25x + 0.9y) - (5.2x + 12y)
removing the parenthesis and rearranging
net yardage = 25x + 0.9y - 5.2x - 12y
net yardage = 25x - 5.2x + 0.9y - 12y
net yardage = 19.8x - 11.1y
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Find the derivative of the function. h(x) = 1 - x2 sin-1(x) -x2-x h'(x) = 1+x 1-x sin-1 x +1 -x2 +1
The derivative of the function h(x) = 1 - x^2 sin^-1(x) -x^2-x is h'(x) = - x^2/(sqrt(1-x^2)) - 2x - 1.
What is derivative ?
The derivative of a function is a measure of how much the output of the function changes with respect to the change in its input. It is represented by the symbol "d/dx" or "∂/∂x" and it is a fundamental concept in calculus.
First, we will apply the chain rule to the term -x^2 sin^-1(x)
Let u = sin^-1(x)
du/dx = 1/(sqrt(1-x^2))
so, -x^2sin^-1(x) = -x^2u
then dh/du = -x^2
then dh/dx = -x^2 * (du/dx) = -x^2/(sqrt(1-x^2))
Next, we will differentiate the rest of the function ,
h(x) = 1 - x^2sin^-1(x) - x^2 - x
h'(x) = - x^2/(sqrt(1-x^2)) - 2x - 1
So, the derivative of the function h(x) = 1 - x^2 sin^-1(x) -x^2-x is h'(x) = - x^2/(sqrt(1-x^2)) - 2x - 1.
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DD.13 Checkpoint: Problem solving with equations and inequalities aza
A skyscraper has a triangular window with an area of 42 square meters. The window's base is
2 meters shorter than twice the height.
Which equation can you use to find h, the height of the window in meters?
(2h-2)h = 42
(2h)h = 42
(2h-2)h = 42
Now, use the equation you picked to find h.
h =
Submit
(h-2)h = 42
↓
meters
NC
(2h + 2)(h - 2) = 42
(2h+
90
+ 2)h = 42
You ha
An equation that can you use to find h, the height of the window in meters is: A. 1/2(2h - 2)h = 42.
The height of the window in meters is equal to 7 meters.
How to calculate the area of a triangle?Mathematically, the area of a triangle can be calculated by using this mathematical expression:
Area of a triangle = 1/2 × b × h
Where:
b represents the base area of a triangle.h represents the height of a triangle.Since the window's base area is 2 meters shorter than twice the height, a mathematical expression which can be used to represent it is given by:
Base area, b = 2h - 2
Substituting the given parameters into the area of a triangle formula, we have the following;
Area of a triangle = 1/2 × b × h
42 = 1/2 × (2h - 2) × h
1/2(2h - 2)h = 42 [required equation].
Making the variable h the subject of formula, we have the following;
1/2(2h - 2)h = 42
Cross-multiplying, we have:
(2h - 2)h = 84
2h² - 2h = 84
2h² - 2h - 84 = 0
Dividing all through by 2, we have the following:
h² - h - 42 = 0
Next, we would solve the above quadratic function by using the factorization method;
h² - 7h + 6h - 42 = 0
h(h - 7) + 6(h - 7) = 0
(h + 6)(h - 7) = 0
h = -6 or 7 meters.
Therefore, the height of the window is 7 meters since it can't be negative.
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Select all the correct answers. Which expressions are equal to [tex]6^3 * 2^6/2^3[/tex] ?
Step-by-step explanation:
With bodmas rule
first should be solve divide
so 2^6/2^3=2^3
6^3*2^3=1728
Consider the following expression. 8y+3x+5 Select all of the true statements below.
Answer: What are the options??
Step-by-step explanation:
7:8 in its simpilest form
Answer:
7+8=15 that's the total
7\15 or 8\15
Answer: that is it’s simplest form
Step-by-step explanation:
solar panels use the sun's energy to generate power, a town wants to install 28th solar panels in an array, which what are all the possible ways the panels could be installed
The possible arrangements would be:
1 by 282 by 144 by 7What is an Arrangement?Combination refers to the various ways that certain objects or numbers can be arranged. If the set already has an order, rearranging its elements, or placing its members in a linear or sequential order.
Given that solar panels use the sun's energy to generate power. A town wants to install 28 solar panels in an array.
The possible arrangements would be:-
( 1 row having 28 panels in series )( 2 rows having 14 panels in each series.)( 4 rows having 7 panels in each series.)Read more about arrangements here:
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pls help with homework, due tommarow
can you explain how to do it also pls
The height of the cone is 16 feet.
How to find the height of the cone?A cone is a three-dimensional geometric shape.
The right cone has a slant height of 20 ft and the diameter of the base is 24 ft.
Therefore, the height of the cone can be found as follows:
Using Pythagoras's theorem,
c² = a² + b²
where
c is the hypotenuse sidea and b are the other legsThe slant height of the cone is the hypotenuse side of the detached right triangle. The radius and the height of the cone is the other legs of the detached right triangle.
Hence,
diameter = 24 ft
r = radius = 24 / 2 = 12 ft
Hence,
20² - 12² = h²
400 - 144 = h²
h = √256
h = 16 feet.
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PLEASE PLEASE HELP ME
The value of n in the vertical angles is 5 4 / 5.
What are vertical angles?Vertical angles are angles that are opposite of each other when two lines intersect each other.
Vertical angles share the same vertex. Vertically opposite angles are congruent to each other.
The measures of the two angles are 2n + 18 and 7n - 11. They are vertical angles.
Therefore, the two vertically opposite angles are congruent to each other. We will use the congruency to find the value of n in the equation.
2n + 18 = 7n - 11
2n - 7n = -11 - 18
-5n = -29
divide both sides by -5
n = -29 / -5
n = 29 / 5
Therefore,
n = 5 4 / 5
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A car can travel 75 miles on 4 gallons of gas at this rate,how many gallons of gas are needed to travel 300 miles?
Answer:
16 gallons of gas are needed to travel 300 miles
Step-by-step explanation:
75x4=300
4x4=16
Tyler’s distance times for a training run are suwon on the graph
Since Elena's distances and times for a training run are given by the equation y = 8.5x, Tyler’s pace per minute is equal to 8.2 miles per minute.
How to determine the rate of change?In order to determine Tyler’s pace per minute, we would have to determine the rate of change (slope).
Mathematically, the rate of change is also referred to as slope and it can be calculated by using this formula;
Rate of change (slope), m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)
Next, we would determine the rate of change with respect to Tyler’s pace per minute, with the following data points (0, 0) and (1, 8.2):
Rate of change (slope), m = (0 - 8.2)/(0 - 1)
Rate of change (slope), m = -8.2/-1
Rate of change (slope), m = 8.2.
Therefore, Tyler’s pace per minute is 8.2 miles per minute.
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Complete Question:
Tyler and Elena are on the cross country team. Tyler’s distances and times for a training run are shown on the graph. Elena's distances and times for a training run are given by the equation y = 8.5x, calculate Tyler’s pace per minute.
4. a driver is entering a round-about at 25 mph and it is icy. is the driver safer to be in the inside lane or the outer lane? explain your reasoning and how it relates to the equation for fc
The driver is safer in the inside lane. The equation for fc=mv^2 states that the force of centripetal acceleration increases with velocity, so the faster the driver goes, the greater the force of centripetal acceleration.
This means that in an icy roundabout, it is safer to drive in the inside lane since the inside lane has a lower speed limit and thus a lower force of centripetal acceleration.
The driver is safer in the inside lane of a roundabout when it is icy, as the equation for fc=mv^2 states that the force of centripetal acceleration increases with velocity, so the lower speed inside lane will have a lower force of centripetal acceleration.
The driver is safer in the inside lane. The equation for fc=mv^2 states that the force of centripetal acceleration increases with velocity, so the faster the driver goes, the greater the force of centripetal acceleration.
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Help aspp please thank you!!!
Answer: -2
Step-by-step
y = k*x
3 = k*-1
So k = -3
6 = -3 * x
6/-3 = -2
x = -2
