Answer: (0,4) and (-1,-1)
Step-by-step explanation:
1) Plug in all of each equation
1a) (0,4)
3(0)-(4)<10
0-4< 10
-4< 10
2(0)+6(4)>=-8
0+24 >= -8
24>= -8
Works!
1b) (2,-1)
3(2)-4(-1)<10
6+4<10
10<10
Nope.
1c) (2,-2)
3(2)-4(-2)<10
6+8<10
14<10
Nope.
1d) (8,2)
3(8) -4(2) < 10
24 - 8 < 10
16<10
Nope.
1f) (-1,-1)
3(-1)-4(-1) < 10
-3 +4 < 10
1 < 10
2(-1)+6(-1)>=-8
-2+-6 >= -8
-8 >= -8
Works.
Please I need help right now
A mathematical function is a mathematical relationship where each input value (x) has a unique output value (y), which means that it is a relationship where every individual value for the independent variable always results in a specific predictable value for the dependent variable.
What is meant by mathematical function?A mathematical function is a mathematical relationship where each input value (x) has a unique output value (y), which means that it is a relationship where every individual value for the independent variable always results in a specific predictable value for the dependent variable.
The exact same number of elements from Y are assigned to each element of X via a mathematical function from a set X to a set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
A mathematical phrase, rule, or law that establishes the relationship between two variables, one of which is independent and the other dependent (the dependent variable)
The complete question is:
What is a mathematical function? After studying the vending machine examples, write a definition that communicates precisely what it means for a mathematical relationship to be a function.
To learn more about mathematical function refer to:
https://brainly.com/question/10283950
#SPJ13
i'll give you brainliest
The quadratic 3x^2+4x-9 has two real roots. What is the sum of the squares of these roots? Express your answer as a common fraction in lowest terms.
If the quadratic [tex]3x^2[/tex]+4x-9 =0 has two real roots, then the sum of the square of the these roots is 7.77
The polynomial is [tex]3x^2[/tex]+4x-9 =0
Here,
a = 3
b = 4
c = -9
Here the quadratic equation
= [tex]\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]
Substitute the values in the quadratic equation
= [tex]\frac{-4+/-\sqrt{4^2-4(3)(-9)} }{2(3)}[/tex]
The result will be
= [tex]\frac{-2+/-\sqrt{31} }{3}[/tex]
Therefore, the roots are
[tex]\frac{-2+\sqrt{31} }{3}[/tex] and [tex]\frac{-2-\sqrt{31} }{3}[/tex]
Square of the first root = [tex](\frac{-2+\sqrt{31} }{3} )^{2}[/tex]
= 1.414
Square of the second root = [tex](\frac{-2-\sqrt{31} }{3} )^2[/tex]
= 6.363
The sum of the square of the roots = 1.414+6.363
= 7.77
Hence, if the quadratic [tex]3x^2[/tex]+4x-9 =0 has two real roots, then the sum of the square of the these roots is 7.77
Learn more about quadratic equation here
brainly.com/question/1863222
#SPJ1
Measure of angle 1 = 110 degrees. You only need to type 110.
The unknown angles are as follows:
∠1 = 110°∠2 = 70°∠3 = 110°∠4 = 70°∠5 = 110°∠6 = 70°∠7 = 110°∠8 = 70°How to find angles?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, linear angles, alternate angles etc.
Therefore,
∠1 = 110 degrees(given)
∠2 = 180 - 110 (sum of angles on a straight line)
∠2 = 70°
∠3 = ∠1 (vertically opposite angles)
Vertically opposite angles are congruent.
Therefore,
∠3 = 110°
∠2 = ∠4 (vertically opposite angles)
∠4 = 70°
∠1 = ∠5 (corresponding angles)
Corresponding angles are congruent
∠5 = 110°
∠6 = ∠4(alternate angles)
Alternate angles are congruent.
∠6 = 70°
∠1 = ∠7 (alternate exterior angles)
∠7 = 110°
∠2 = ∠8(alternate exterior angles)
∠8 = 70°
learn more on angles here: https://brainly.com/question/18166236
#SPJ1
i'll give brainliest
Answer:
-40
Step-by-step explanation:
10/1*(-4) Set up equation
10/1 * -4 Open up parentheses
10/1 =10 Next, divide 10 by 1
10*-4 Now, multiply 10 and -4
-40 Answer
Answer:
-40
Step-by-step explanation:
Given expression
[tex]\dfrac{10}{1} \cdot (-4)[/tex]
When dividing and multiplying, follow the order of operations and work from left to right.
Divide the numbers
When dividing anything by 1, the quotient is the numerator:
[tex]\implies \dfrac{10}{1} \cdot (-4)=10 \cdot (-4)[/tex]
Multiply the numbers
When multiplying a positive number by a negative number, the product is always negative:
[tex]\implies 10 \cdot (-4)=-40[/tex]
Find the range, variance & standard deviation of the following sample dataset. Round all answers to the nearest tenth.
The following data represent the number of students from each school that attended a debate tournament: 75, 47, 50, 71, 64, 50, 52, 56, 53, 47, 55
Answer:
The range is 28
The variance is 90.855
The mean is 56.36
The median is 53
The sample standard deviation is 9.532
Step-by-step explanation:
the temperature outside must be between 32 degrees Fahrenheit is 95 degrees Fahrenheit and inclusively for students for students to be allowed to play outside during recess at an elementary school.write the compound inequality to show the temperature that are within the given range
The compound inequality which correctly shows the temperatures that are within the given range is; 32°F ≤ T ≤ 95.
What is the compound inequality which shows the temperatures that are within the given range?It follows from the task content that the temperature outside is said to be between 32 degrees Fahrenheit and 95 degrees Fahrenheit and inclusively.
On this note, it follows from the statement above that the upper limit of the temperature is; 95°F while the lower limit is; 32°F.
Therefore, the required compound inequality is;
32°F ≤ T ≤ 95.
Ultimately, the required compound inequality which shows the temperature that are within the given range is; 32°F ≤ T ≤ 95.
Read more on compound inequalities;
https://brainly.com/question/24761100
#SPJ1
3.7416573868 to nearest tenth
Explanation:
The tenths decimal place is right after the decimal point
7 is in the tenths place
The digit just to the right of 7 is 4
Since the 4 is not 5 or larger, this means we erase everything after the 7 and go with 3.7
If we had something like 3.76, then the 7 bumps up to 8 to get 3.8
Jai is 1.45 meters tall. At 11 a.m., he measures the length of a tree's shadow to be
39.55 meters. He stands 34.1 meters away from the tree, so that the tip of his shadow
meets the tip of the tree's shadow. Find the height of the tree to the nearest
hundredth of a meter.
오ㅜ
39.55 m-
(Diagram is not to scale.)
1.45 m
34.1 m-
By using triangles laws, we know that the height of the tree is 8.42 meters.
What are triangles?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.So, 1.45 m is Joshua's height.
Tree shadow length: L=31.65 mJoshua's distance from the tree is 26.2 meters.We must ascertain the tree's height.
BC = 26.2 mBD = 31.65mCD = BD-BCCD = 31.65-26.2=5.45 mEC = 1.45 mThe right triangles are all alike.
The ratio of the corresponding sides is equal when two triangles are comparable.
△ABD ≈ △ECDAB/EC = BD/CDNow, put values as follows:
AB/1.45 = 31.65/5.45AB = 31.65 × 1.45/5.45AB = 8.42mTherefore, by using triangles laws, we know that the height of the tree is 8.42 meters.
Know more about triangles here:
https://brainly.com/question/28889256
#SPJ13
The correct form of the question is given below:
Joshua is 1.45 meters tall. At 2 p.m., he measures the length of a tree's shadow to be 31.65 meters. He stands 26.2 meters away from the tree so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
Which of the following values are in the range of the function graphed below?
Check all that apply.
The range of the function is 1
As seen by the graph in the following figure
As can be seen, x's value falls between
nonetheless, y is equal to 1 for all values of x.
This holds true regardless of x's value.
Consequently, the function's range is 1.
To know more about graph refer to https://brainly.com/question/24313387
#SPJ9
The team's engagement score was 5.20 this month. the score has been improving at a rate of 8% per month. what was the score 3 months ago? 1.60 3.95 4.13 4.78 5.12
The score 3 months ago was 4.130.
What is rate of increase?
Rate of increase is defined the change in rate that describes how one quantity changes in relation to another quantity.
Assume the score 3 months ago was x. This means that the above can be expressed as:
Current score = x × ( 1 + rate) ^ number of months
5.20= x(1+8%)^3
5.20 = x(1.259)
x= 5.20/1.259
x= 4.130
therefore, the score was 4.130
To know more about rate of increase, visit:
https://brainly.com/question/20884505
#SPJ9
Write the word sentence as an inequality.
A number b multiplied by -5 is at most -30
The word sentence as an inequality phrase is -5[tex]\leq[/tex]30.
What is the inequality phrase?
An algebraic statement that uses the symbols less than (), less than or equal to (), larger than (>), or greater than or equal to () in place of the equal sign (=) is known as an inequality equation. How do you work out mathematical inequalities? Similar to how equations are solved, inequalities may be resolved by separating the variable and combining like terms.
Different types of inequalities
Equations that are linear
When the variables' highest exponent is power 1, inequality is said to be linear.
Triangle inequalities
A quadratic inequality is one in which the largest exponent is power 2, which is present in the inequality.
Learn more about inequality phrasehttps://brainly.com/question/11840365
#SPJ1
Two exponential functions, f(x) and g(x), are graphed on the same coordinate plane. Graph of f of x equals 2 to the x power going through points 0 comma 1 and 1 comma 2 and graph of g of x equals 2 to the x power plus 4 going through points 0 comma 5 and 1 comma 6. What effect does adding 4 to the parent function have on the transformed function? a Adding 4 to the parent function shifts the function down four units. b Adding 4 to the parent function shifts the function up four units. c Adding 4 to the parent function shifts the function right four units. d Adding 4 to the parent function shifts the function left four units.
Answer:
b Adding 4 to the parent function shifts the function up four units.
Step-by-step explanation:
The original function is y(x) = 2^x
Adding four is y(x) = 2^x + 4
We've simply told y to take whatever value is generated for x and add four to it.
So the new value for the same x would have 4 added to y: (x,y+4),
Point (1,2) would shift to point (1,6).
Adding four to the parent function will shift the entire graph up by 4. See ate attached graph.
Question 9
The preimage of M(-3,-5) under a translation is M'(6, -1).
Using the same translation, find the image of B', if B is (3,-2).
B'
By using the same translation applied to point M, the image of point B' is equal to (12, 2).
What is a translation?In Geometry, a translation can be defined as a type of transformation which moves every point of a geometric figure (object) in the same direction, as well as for the same distance.
Since the x-coordinate moved from a negative to a positive sign, we know that point M was translated to the right and then shifted down because it moved from a negative to a negative sign on the y-coordinate.
Next, we would determine the translation rule that was applied to point M:
(x, y) → (x + n, y - z)
-3 + n = 6
n = 6 + 3
n = 9.
-5 - z = -1
z = -5 + 1
z = -4
Now, we can determine the image of B':
(x, y) → (x + n, y - z)
Point B (3, -2) → Point B' (3 + 9, -2 - (-4)) = (12, 2).
Read more on translation here: brainly.com/question/16486008
#SPJ1
A star shape is made out of 5 congruent triangles. the peak of 1 triange is 25°. what are the sizes of the base angles?
Answer:
77.5
Step-by-step explanation:
180-25=155
155/2=77.5
Please help me with this. Show the solution as well. Thank you
Step-by-step explanation:
any ordered pair is a solution, if we can use its coordinates in the equation, and the equation stays true.
for x - 3y = 6
1. (3, -1)
3 - 3×-1 = 6
3 + 3 = 6
6 = 6
true, this is a solution.
2. (0, 2)
0 - 3×2 = 6
-6 = 6
false, this is not a solution.
3. (3, 1)
3 - 3×1 = 6
3 - 3 = 6
0 = 6
false, this is not a solution.
What is the y-intercept of the equation 4x + 5y = 20?
(0, 4)
(0, 5)
(4, 0)
(5, 0)
Answer:
(0,5)
Step-by-step explanation:
Answer:
(0, 4 )
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
4x + 5y = 20 ( subtract 4x from both sides )
5y = - 4x + 20 ( divide through by 5 )
y = - [tex]\frac{4}{5}[/tex] x + 4 ← in slope- intercept form
with y- intercept c = 4 or in coordinate form (0, 4 )
Find the value of each variable
Answer:
x = 58°
y = 74°
z = 106°
w = 42°
Step-by-step explanation:
Finding the value of unknown variables:
x + 32° = 90°
x = 90 - 32
[tex]\sf \boxed{\bf x = 58^\circ}[/tex]
x + y + 48 = 180 {Angle sum property of triangle}
58 + y + 48 = 180
y + 106 = 180
y = 180 - 106
[tex]\sf \boxed{\bf y = 74\°}[/tex]
y + z = 180 {Linear pair}
74 + z = 180
z = 180 - 74
[tex]\sf \boxed{\bf z = 106\°}[/tex]
32 +z + w = 180 {Angle sum property of triangle}
32 + 106 +w = 180
138 + w = 180
w = 180 - 138
[tex]\sf \boxed{\bf w = 42\°}[/tex]
Maria buys n pencils that cost p each, she pays with a $y note find in terms of n, p and y, the amount of change maria recieves. give your answer in cents
The amount of change Maria receives is 100y - np
What is Conversion rate ?
A conversion rate is the ratio between two currencies, most commonly used in foreign exchange markets, which designates how much of one currency is needed to exchange for the equivalent value of another currency.
Given,
The cost of each pencil is = p
Maria buys = n pencils
so, the cost of n pencils is = np
She pays for the n pencils is = $y
Now, in question given that we need to find answer in cents
so, We know 1$ = 100 cents
By that, $y = 100y
Maria received the change is = 100y - np
Therefore, the amount of change Maria receives is 100y - np
To read more about the Conversion rate.
https://brainly.com/question/25870256
#SPJ13
How many subsets does the set (1,2,3) have
Answer:
Answer down below!
Step-by-step explanation:
The set (1, 2, 3) would have 8 sets in total
PLS HELP!!!
Zane deposited $3,000 in an account earning 11% interest compound annually. To the nearest cent, how much will he have in 4 years?
Answer:4554.21
Step-by-step explanation:
Two parallel lines are cut by a transversal. Suppose <1 and <2 are alternate interior angles and that m<1=4(x+2) and m<2=2x+24. What is the m<2?
The value of m∠2 will be equal to 40°.
Transversal may be defined as a line which cuts two different lines which lie on the same plane at two different points. Alternate interior angles may be defined as the angles which are formed when a transversal cut the two different lines. These angles lie on the interior of the parallel lines, but they are on the opposite side of the transversal. If two parallel lines are cut by a transversal, then their alternate interior angles are equal. Thus, m∠1 = m∠2
4(x + 2) = 2x + 24
4x + 8 = 2x + 24
2x = 16
=> x = 16/2
=> x = 8
Now, m∠2 = 2x + 24
m∠2 = 2×8 + 24
m∠2 = 40° which is the required answer.
Learn more about Alternate Interior Angles at:
brainly.com/question/20344743
#SPJ1
Boris's art class is 8 hours long. How long is his class in minutes?
Answer:
480 minutes
Step-by-step explanation:
that's your answer
Answer:
480 minutes.
Step-by-step explanation:
8×60=480.
HELP PLEASE!!!!!!!
A rectangle is 32ft by 8ft. Ross dilated the rectangle and the dimensions of the image were 80ft by 20ft. What was the scale factor used?
The scale factor of the dilation = 2.5
The original dimensions of the rectangle:
Length = 32 ft
Width = 8 ft
The dimensions of the rectangle after dilation:
Length = 80 ft
Width = 20 ft
Dilation is a transformation where the dimensions of the figure is enlarged by multiplying with a number. This number multiplied with all dimensions of the original figure is called its scale factor.
So the new dimension of the figure will be scale factor times the original dimensions of the figure.
Thus the scale factor can be defined as the ratio of larger dimension to the smaller dimension of a figure.
Hence the scale factor used here is the ratio of new length to the original length or the ratio of new width to the original width of the rectangle.
That is, scale factor = 80/32 = 20/8 = 2.5
Learn more about dilation https://brainly.com/question/3457976
#SPJ1
Look at this set of ordered pairs:
(7, -17)
(5,3)
(7,3)
Is this relation a function?
yes
no
The given relation is not a function.
What is function?
A function is a relationship between inputs where each input is related to exactly one output.
Given that, (7, -17) , (5. 3) , (7, 3)
Here 7 is connected with two elements i.e. -17 and 3 but the condition of a function is that one element must be related to only one element of another set.
Hence, the given relation is not a function.
To learn more about function using the given link
https://brainly.com/question/10439235
#SPJ9
Help pls
Explain how to simplify ((a^3)^4)^-2 using the properties of exponents.
Answer: a^24
Hope this helps you!
graph this function f(x) = -7x - 64
The graph of the function f(x) = -7x - 64 will be a straight line.
A function may be defined as an expression in which for every input variable x there is only one output variable y. The input variable is called independent variable and output variable is called dependent variable. The function f(x) = -7x - 64 is in the form of linear equation in one variable as it is expressed in the form of f(x) = ax + b where a, b are coefficients and x are the independent variable. When we plot this function, we compare it from the slope intercept form of line that is y = mx + c where m is slope and c is y intercept. It will be a straight line having a negative slope which is equal to -7 and the y intercept will be equal to -64 as compared from slope intercept form. The graph of the function plotted is attached below. For x intercept we put f(x) = 0, so we get x intercept equal to -64/7. Coordinates of x intercept is (-64/7, 0) and that of y intercept is (0, -64).
Learn more about Linear Equation at:
brainly.com/question/28307569
#SPJ1
Match the financial activities to their relevant management type within the wealth management phase. (Cash management or Credit and debt management)
keeping an emergency
fund
reducing credit use
spending plans
stop credit misuse
debt reduction
cash reserve
recording income and
spending
paying off credit cards
Each financial activities should be matched to their relevant management type within the wealth management phase as follows:
Cash management:
Keeping an emergency fund.Spending plans.Cash reserve.Recording income and spending.Credit and debt management:
Reducing credit use.Stop credit misuseDebt reduction.Paying of credit cards.What is wealth management?Wealth management can be defined as an investment advisory service that is designed and developed to provide advices and solutions to meet the needs of a wide array of affluent clients, especially by combining other financial services.
The phases of financial activities.Generally speaking, there are three (3) distinct phases of a person's financial activities and these include the following:
Wealth accumulationWealth preservationWealth distribution.Read more on debt management here: https://brainly.com/question/7066178
#SPJ1
Answer:
Cash management:
- keeping an emergency fund
- spending plans
- cash reserve
- recording income and spending
Credit and debt management:
- paying off credit cards
- stop credit misuse
- reducing credit use
- debt reduction
Step-by-step explanation:
correct on plato
Evaluate compositions of function. Let f(x) = 3x + 2, g(x) = -x2, and h(x) = x-2/5. Find the indicated value. (SHOW WORK PLEASE))
The indicated numeric values for the composite functions are given as follows:
1. f(g(-3)) = -25.
2. g(f(2)) = -64.
3. h(f(-5)) = -3.
4. g(g(-3)) = -81.
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is according to the following rule:
(f ∘ g)(x) = f(g(x)).
It means that the output of the inside function serves as the input for the outside function. Hence, to calculate f(g(-3)), for example, we calculate g(-3), then we calculate the numeric value of function f(x) at x = g(-3).
For this problem, the functions are given as follows:
f(x) = 3x + 2.g(x) = -x².h(x) = (x - 2)/5.For item 1, the numeric values are found as follows:
g(-3) = -(-3)² = -9.f(g(-3)) = f(-9) = 3(-9) + 2 = -27 + 2 = -25.For item 2, the numeric values are found as follows:
f(2) = 3(2) + 2 = 6 + 2 = 8.g(f(2)) = g(8) = -(8)² = -64.For item 3, the numeric values are found as follows:
f(-5) = 3(-5) + 2 = -15 + 2 = -13.h(f(-5)) = h(-13) = (-13 - 2)/5 = -3.For item 4, the numeric values are found as follows:
g(-3) = -(-3)² = -9.g(g(-3)) = g(-9) = (-9)² = -81.More can be learned about composite functions at https://brainly.com/question/10687170
#SPJ1
Johnathan is hosting a barbeque for 7 of his friends. He wants to buy twice as many sausages as burgers and the same number of buns as sausages and burgers combined.
Buns come in a packet of 6
Sausages come in a pack of 10
Burgers come in a pack of 8.
What is the smallest number of packets of buns that Johnathan could buy?
The smallest number of packets of buns that Jonathan could buy is 4.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
We have,
Buns come in a packet of 6
Sausages come in a pack of 10
Burgers come in a pack of 8.
Sausage = 2 x burgers ____(1)
Buns = Sausages + Burgers _____(2)
The smallest number of packets of buns can be calculated when only one packet of Burgers is bought.
So,
Burgers = 1 pack = 8
From (1) and (2),
Sausage = 2 x 8 = 16
Buns = 16 + 8 = 24
Buns = 24
This can be put in 4 packets.
Thus,
The smallest number of packets of buns that Jonathan could buy is 4.
Learn more about expressions here:
https://brainly.com/question/10978794
#SPJ1