1.On the accompanying grid, sketch the graphs of y = 2^x and 3y = 7x + 3 over the interval
-3 ≤ x ≤ 4. Identify and state the coordinates of all points of intersection.
Answers
As a result, the coordinates of the equations y = 2x and 3y = 7x + 3 throughout the range of -3 ≤ x ≤ 4 are (-3,-6) and (-3,8), respectively.
what are coordinates ?When it comes to geometry, a coordinate system is a technique that uses one or more integers or coordinates to specify the exact location of points or other geometrical objects on a manifold, such as Euclidean space. Locating a point or item on a two-dimensional plane requires the usage of pairs of integer coordinates. Two numbers known as the x and y coordinates serve as a description of a point's location on a 2D plane. a collection of figures that signify exact locations. Most often, the figure contains two numerals. The first number denotes the distance from front to rear, and the second number denotes the distance from top to bottom. In (12.5), for example, there are 12 units below and 5 above.
given
y = 2^x and 3y = 7x + 3 over the interval -3 ≤ x ≤ 4.
as x = -3
y = 2^x= 2^-3 = -8
y = 8
3y = 7x+3
3y= 7*-3 +3
3y = -21 + 3
y = -6
As a result, the coordinates of the equations y = 2x and 3y = 7x + 3 throughout the range of -3 ≤ x ≤ 4 are (-3,-6) and (-3,8), respectively.
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Related Questions
Describe and correct the error a student made in writing the exponential function.
Starting value 6
Constant ratio - 1/3
f(x) = 6(1/3)^x
f(x)=2^x
Answers
The correct equation of exponential function is [tex]f(x) = 6 * (\frac{1}{3} )^x[/tex]
What is an exponential function?
An exponential function is one that has the formula f (x) = [tex]a^{x}[/tex], where x is a variable and a constant that serves as the function's base and must be greater than 0.
Given,
starting value = 6
constant ratio = 1/3
The general form of an exponential function
[tex]f(x) = ab^{x}[/tex]
where a = starting value i.e when x = 0
b = rate of change in exponential equation
So substituting our given values in the above equation, the exponential function is
[tex]f(x) = 6 * (\frac{1}{3} )^x[/tex]
Now the value 6 can be divided by 3 only if the value of x = 1
[tex]f(1) =\frac{6}{3} = 2[/tex]
If x = 5, then equation becomes,
[tex]f(5) = 6 * (\frac{1}{3} )^5 = \frac{2}{81}[/tex]
So we cannot simply divide 6 by 3 without considering the value of x.
Therefore the correct equation of exponential function is
[tex]f(x) = 6 * (\frac{1}{3} )^x[/tex]
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17. An isosceles triangle has congruent sides of 20 cm. The base is 12 cm. Find
the height of the triangle.
Answers
The height of the triangle is 19.36cm.
What is an isosceles triangle?
An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having precisely two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.
Here, we have
Given: An isosceles triangle has congruent sides of 20 cm. The base is 12 cm.
An isosceles triangle has two congruent sides. The height of an isosceles triangle is also the median and the perpendicular bisector of the triangle dividing the base in half and forming two congruent right triangles.
we use the Pythagorean theorem to solve for the triangle's height.
a² + b² = c²
5² + h² = 20²
h² = 400 - 25
h² = 375
h = 19.36cm
Hence, the height of the triangle is 19.36cm.
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i need help please i don’t get thus
Answers
According to the solving the lengths of right angle triangle using Pythagorean theorem x = 6, y = 3
How does the Pythagorean theorem work?A fundamental relationship in Euclidean geometry between a right triangle's three sides is known as the Pythagorean theorem or Pythagoras' theorem. According to this rule, the area of the square with the hypotenuse side is equal to the sum of the areas of the squares with the other two sides.
According to the given information:The following is one way to perform the calculation. It may not be the best way.
c = b/cos(α)
= 6
a = √c2 - b2
= √62 - 5.192
= √9.0639
= 3.01063
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At the independent record company where Chase works, the vinyl format has been experiencing a resurgence in popularity. Record sales are increasing by 6% each year. If 260,090 records were sold this year, what will annual sales be in 4 years?
If necessary, round your answer to the nearest whole number.
Answers
The annual sales is 322,511.6 in 4 years.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
Record sales are increasing by 6% each year.
And, 260,090 records were sold this year.
Now, We have;
Record sales are increasing by 6% each year.
Hence, After 4 years;
The annual sales = 260,090 + 4 × 6% of 260,090
= 260,090 + 4 × 6/100 × 260,090
= 260,090 + 62,421.6
= 322,511.6
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Answer:328,358
Step-by-step explanation:
Pleaseeeee help me i need the full answer for everything single one please I WILL GIVE MORE POINTS
Answers
Answer:
Step-by-step explanation:
it depends on where each point is on each chart because they can't be blank
The square above has an area of 100. If Q is the
midpoint of AC and R is the midpoint of BD, what
is the area of the shaded area?
Answers
Therefore , the solution of the given problem of surface area comes out to be area of the shaded area equals 50.
The definition of surface areaThe surface area of an object is an estimate of the entire amount of space it takes up. A three-dimensional shape surface area refers to the entire area surrounding it. The overall area of a muti shape is its surface area. The surface area of a cuboid can be calculated by adding the faces of each of its six rectangular sides. The following equation could be used to name the box's dimensions: Surface (SA) equals 2lh, 2lw, and 2hw. The surface area of a three-dimensional shape represents the overall area.
Here,
Square has an area of 100 a 2 = 100 a=10
QC=(1/2) AC=10/2=5,
BR=(1/2), and BD=10/2=5.
CD=AB=10=AC=BD
size of the triangle QCD is defined as: =(1/2)QCCD
= >(1/2)510=25.
size of the triangle ABR is =(1/2) ×AB×BR
=>( 1/2 ) ×10×5=25
Area of the darkened area equals area of square 2 area of triangles,
which is 100 (25+25)=50.
Area of the shaded area equals 50.
Therefore , the solution of the given problem of surface area comes out to be area of the shaded area equals 50.
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A decimal number is represented by (3 x 110) + (5 x 1100) + (8 x 11000).
Question 1
Which decimal is represented by the given expansion?
Responses
A 35.835.8
B 0.03850.0385
C 0.3580.358
D 3.58
Answers
125y - 5 -50y pls help lol
Answers
Answer:
The expression is a mathematical representation of an algebraic problem. The final form of the expression would be 75y -5 after combining like terms.
Here's the breakdown of the steps:
125y - 5 - 50y = (125-50)y -5 = 75y - 5
So the final simplified form of the expression is 75y -5.
Tim went 8 miles east and 15 miles north. Jan went 5 miles west and 12 miles north. How far apart are they?
Answers
Answer:
30miles
Step-by-step explanation:
As you can see in the graph, the distance between tim and jan is creating 2 right triangles
You can solve this using pythagoras theorem,
Triangle (1) :
[tex] x^{2} = {5}^{2} + {12}^{2} \\ {x} = \sqrt{{5}^{2} + {12}^{2} } \\ = \sqrt{169 } \\ = 13[/tex]
X (1) = 13 miles
Triangle (2):
[tex] {x}^{2} = {15}^{2} + {8}^{2} \\ x = \sqrt{ {8}^{2} + {15}^{2} } \\ = \sqrt{289} \\ = 17 [/tex]
X(2) = 17 miles
Now, the distance = x(1) + x(2)
= 13 + 17
=30 miles
Therefore, Tim and Jan are 30 miles apart
Enter the Correct 4 Character LETTER Code (Capital letters and no spaces) *
Please help
<3
Answers
Answer:
rawr :)
Step-by-step explanation:
Determine the graph that represents a function. On a coordinate plane, a circle is shown that crosses the x-axis at (negative 5, 0), the y-axis at (0, 5), the x-axis at (5, 0), and the y-axis at (0, negative 5). On a coordinate plane, a parabola opens to the left. It crosses the y-axis at (0, 3) and (0, negative 3), and the x-axis at (9, 0). On a coordinate plane, a straight line with a positive slope crosses the y-axis at (0, negative 2) and the x-axis at (1.2, 0).
Answers
Answer: The graph that represents a function is the parabola that opens to the left.
This can be determined by the following characteristics of the graph:
It is a parabola because it opens to the left and has a vertex on the y-axis.
It crosses the y-axis at (0, 3) and (0, negative 3), which means that it is symmetric about the y-axis, and also it crosses the x-axis at (9, 0) which means that it is a function.
A circle is not a function because, for any value of x, there are two different values of y that can be plotted on the graph (i.e. the point (5,0) and (-5,0) produce two different y values)
A straight line with a positive slope is not a function because, for any value of x, there is only one value of y that can be plotted on the graph.
So the parabola is the graph that represents a function.
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
PLEASE HELP ASAP!!!
I'd really appreciate the help, thanks in advance.
The questions below can be solved using the relation between angular size, physical size and distance. For the questions below, provide a complete solution with explanation.
1. Find the Sun's diameter. The sun has an angular diameter of about 0.5° and an average distance from the Earth of about 150 million km. What is the sun's approximate physical diameter? Compare your
answer to the actual value of 1 390 000 km.
2. Find a Star's Diameter. The supergiant star Betelgeuse (in the constellation Orion) has a measured angular diameter of 0.040 arcsecond from Earth and a distance from Earth of 720 light-years. What is the actual diameter of Betelgeuse? Compare your answer to the size of our Sun and the Earth-Sun distance.
Answers
The physical diameter of the sun will be 1309000km and the percentage of difference between the diameters will be 5.8%.
How to calculate the diameter?From the information, the sun has an angular diameter of about 0.5° and an average distance from the Earth of about 150 million km. The angular diameter in radians will be:
= 0.5π / 180
= 0.008727 radians
Distance from the sun = 150 × 10^6
The physical diameter of the sun will be:
= 150 × 10^6 × 0.008727
= 1309000km
The difference between the diameters will be:
= 1390000 - 1309000
= 8.1 × 10^4.
The percentage of difference will be:
= (8.1 * 10^4) / 1390000 × 100
= 5.8%
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Suppose f(x)=2x-8, evaluate f(7) =
Answers
Answer:
6
Step-by-step explanation:
f(x)=2x-8
f(7)=2(7)-8
f(7)=6
Answer:
Step-by-step explanation:
f(7)=2x-8
f(7) = (2)(7)-8
f(7) = 14-8
f(7) = 6
In a triploid of genotype B/b/b, what proportion of gametes will be B? A) 1/2 B. 1/3 C.1/8
D. 1/4
E. 1/6
Answers
Answer:
I think it’s D
Step-by-step explanation:
trust
what is 2 over x to the power of 2 equivilent to
Answers
The equivalent exponential expression for this problem is given as follows:
(2/x)² = 4/x².
How to obtain the equivalent exponential expression?The expression for this problem is defined as follows:
(2/x)².
We have a fraction that is squared, meaning that both the numerator and the denominator are squared, hence:
2² = 4.x².This means that the equivalent exponential expression for this problem is given as follows:
(2/x)² = 4/x².
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Make use of one of De Morgan's laws to write the given statement in an equivalent form.
She did not visit France and she did not visit Italy.
Answers
The statement "She did not visit France and she did not visit Italy" using De Morgan's laws will be C. She did not cost France if a only if she did not visit Italy.
What is De Morgan law about?The complement of the product of all terms is equal to the complement of each term added together. Similarly, the product of the complements of each term equals the complement of the sum of all the terms.
The intersection of their complements is the complement of the union of two sets, and the union of their complements is the complement of the intersection of two sets.
In conclusion, the correct option is C.
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I am looking for a hard equation that equals to number 41.
Answers
Answer:
[tex]\bf x+23=64[/tex]
Step-by-step explanation:
you can try x+23=64
Let's solve it:-
[tex]\sf x+23=64[/tex]
Subtract 23 from both sides:-
[tex]\sf x+23-23=64-23[/tex]
[tex]\bf x=41[/tex]
__________________
Hope this's what you're looking for!
Have a great day!
Answer:
How about this:
290 / 8 * 2 - 31.5
Step-by-step explanation:
I dunno if that's hard enough, but there you go!
Zara part 2.4 pounds of grapes in the watermelon that cost $5.28. The total cost of the food was $7.32 which describes a way to determine X the price per pound for the grapes?
Answers
The way to determine x, which is the price per pound of the grapes is B. Subtract 5.28 from 7.32 and then divide the difference by 2.4.
How to find the price per pound ?To find the price per pound of the grapes, you first needed to find the price of the grapes alone, without the cost of the watermelons.
This price of the grapes can be found by the formula :
= Total cost of fruit - Cost of watermelon
= 7. 32 - 5. 28
= $ 2. 04
Then, you can find the cost of each pound of grapes by the formula :
= Cost of grapes / Pounds of grapes purchased
= 2. 04 / 2 . 40
= $ 0. 85
In summary, you can find the price per pound of the grapes when you Subtract 5.28 from 7.32 and then divide the difference by 2.4.
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The full question is:
Zara bought 2.4 pounds of grapes and a watermelon that cost $5.28. The total cost of the fruit was $7.32. Which describes a way to determine x, the price per pound for the grapes?
Divide 7.32 by 2.4 and then subtract 5.28 from the quotient. Subtract 5.28 from 7.32 and then divide the difference by 2.4. Solve for x in the equation 2.4x - 5.28 = 7.32. Solve for x in the equation 2.4 (x + 5.28) = 7.32.the width of a rectangle is 9yds less . The area is 36sq yards
Answers
Answer:
17
Step-by-step explanation:
fhxc. t thug g h y yxhxg yxtzt
Use the distributive property to write an equivalent expression. Then
evaluate the expression.
(9+3)
Equivalent Expression
=
Answers
The equivalent expression of 2/5(s+20) is 2/5s+8 and expression (9+3)=12.
what are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, nected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between which math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now,
Given expression 2/5(s + 20)
Using distributive property
2/5s+2/5*20
2/5s+2*4
2/5s+8
and (9+3)=12
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Right question:-
Use the distributive property to write an equivalent expression for 2/5(s + 20). Then evaluate the expression (9+3).
The highest temperature ever recorded for a person with a fever who survived was 115 degrees. Alternatively, the lowest temperature ever recorded on a patient who survived was 56.7 degrees. If the average temperature is 98.6 degrees, which extreme temperature was furthest from the norm? How much further?
Answers
Answer:
The lowest temperature recorded is the furthest away from the average norm by 41.9 degrees.
Step-by-step explanation:
115-98.6= 16.4
98.6-56.7= 41.9
4. To which set of numbers does the number belong? (1 point)
√51
Orational numbers
O irrational numbers
O integers
Onatural numbers
Answers
What is the equation of a circle with a radius of 4 and a center located at (2,3)
Answers
Answer:
x² + y² - 4x - 6y - 3 = 0
Step-by-step explanation:
Formula for equation of circle when the radius r and centre (a,b) is given:
(x-a)² + (y-b)² = r²
(x-2)² + (y-3)² = 4²
Expanding the brackets;
x² - 4x + 4 + y² - 6x + 9 = 16
x² + y² - 4x - 6x + 4 + 9 = 16
x² + y² - 4x - 6x + 13 = 16
x² + y² - 4x - 6x + 13 - 16 = 0
x² + y² - 4x - 6x - 3 = 0 Ans.
Tyshawn bought 7 chicken wings for $16.10. How much does each wing cost?
Answers
Answer: Each chicken wing costs $2.30 ✅
Step-by-step explanation:
To find out how much each wing cost, we need to divide the total cost of the wings by the number of wings.
We can use the formula:
Cost per item = Total cost / Number of items
In this case:
Cost per wing = $16.10 / 7 wings
To find the cost of each wing we divide 16.10 by 7.
$16.10/7 = $2.30
Each chicken wing costs $2.30
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Answer:
[tex]\huge\boxed{\sf \$ 2.3}[/tex]
Step-by-step explanation:
Given that,
7 chicken wings = $16.10
Using unitary method.Divide both sides by 7
1 chicken wing = $16.10/7
1 chicken wing = $2.3[tex]\rule[225]{225}{2}[/tex]
Scale factor from smaller to larger of THIS triangle
Answers
The scale factor in the image depicting a similar triangle is solved to be
1.4When are triangles said to be similar?The term similar triangles as used in geometry means that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence when the size of the triangles are in equal proportions and the size of the angles are equal then the triangles are said to be similar triangles
Examining the figure shows the scale factor is sought as follows
using side 28
let the scale factor form smaller to larger be k
k = length of larger side / length of smaller side
k = 28 / (28 - 8)
k = 28 / 20
k =1.4
The scale factor is 1.4
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Solve for n and simplify your answer. -20=-4/3 n
Answers
I took the test earlier today
Brandon wants to use the Distributive Property to figure this problem out. What should be his next step?
8 × (10 + 7)
Answers
Answer: (8*10) + (8*7)
Step-by-step explanation: This would be distributing the 8 to both numbers while still adding the two products
Answer: 136
Step-by-step explanation:
When you do distributive Property, you are multiplying everything right before the parenthesis, with everything inside the parenthesis.
8 x (10 + 7)
1. Multiply 8 by 10 to get 80
2. Multiply 8 by 7 to get 56
Now you have: (80 + 56)
3. Add the numbers
80 + 56 = 136
8. Use the bar diagram to write an equation. Then
solve for x.
X
Total
7
X
5
X
Answers
Answer: 12, 16, 20, and 320.
Step-by-step explanation:
The value of x can be solved as follows, take note of the numbers you will need to drag to complete the equations:
4x + 12x = 320 (segment addition postulate)
16x = 320 (combining like terms)
x = 20 (dividing both sides by 16)
We would end up with the value of x, which equals 20.
Numbers that we end up using are: 12, 16, 20, and 320.
6y=-18x 24 solve for y
Answers
Suppose f(x)=−3x^2+ 6x +3 find f(-2) +f(2)
Answers
Answer:
-18
Step-by-step explanation: