Answer:
The solution of given equation is (2,5)
Step-by-step explanation:
The equations give to us are:
y - 3 = x
or
y = x + 3
y = x² - 6x + 13
We can find the solution of the given system of equations by substituting each point in both of the equations. The point which satisfies both of the equation will be the solution of the the system of given equation.
Substitute (2,5) in both equations
y = x+3
5 = 2+3
5 = 5
TRUE
y = x² - 6x + 13
5 = 2² -6(2) + 13
5 = 5
TRUE
Similarly, we can also check the rest of the points, which come as FALSE.
Therefore, the solution of given equation is (2,5)
Answer:
Answer is C
Step-by-step explanation:
14. Which graph shows the solution to the following system?
1
-x-2
y -
4
7
y = -x + 4
Answer:
Option (B)
Step-by-step explanation:
Equations of the lines shown in the graph are,
[tex]y=\frac{1}{4}x-2[/tex] and [tex]y=\frac{7}{4}x+4[/tex]
For equation (1),
[tex]y=\frac{1}{4}x-2[/tex]
Slope of the line = [tex]\frac{1}{4}[/tex]
And y-intercept of the line = -2
For equation (2),
[tex]y=\frac{7}{4}x+4[/tex]
Slope of this line = [tex]\frac{7}{4}[/tex]
And y-intercept of the line = 4
From the given graphs in the options,
Graph (B) shows the lines which show the y-intercepts as y = 4 and y = -2
Therefore, Option (B) will be the answer.
-402 + br – 11 = 0
Determine a possible value of b so that the quadratic has two complex solutions.
1)
12
2)
-14
3)
-16
4)
14
Answer:
2
Step-by-step explanation:
What is the value of x?
12 units
15 units
20 units
25 units
Need work shown please
Answer:
15=x
Step-by-step explanation:
a^2 + b^2=c^2
=9^2 +12^2 =x^2
=81 +144=x^2
=/225 =/x^2
=15=x
Answer:
x = 12
Step-by-step explanation:
Use the right triangle altitude theorem.
16/x = x/9
x^2 = 16 * 9
x^2 = 144
x = 12
GIVING BRANLIEST TO FIRST CORRECT ANSWER
Answer:
Step-by-step explanation:
y²+2by+b²-a²-6ad-9d²(y+b)²-(a²+2*3d*a+(3d)²)(y+b)²-(a+3d)²(y+b+a+3d)*(y+b-a-3d)Answer:
( y + b - a - 3d)(y + b + a + 3d).
Step-by-step explanation:
y^2 + 2by + b^2 - a^2 - 6ad - 9d^2
= y^2 + 2by + b^2 - (a^2 + 6ad + 9d^2)
= (y + b)^2 - (a + 3d)^2
This is the difference of 2 squares so we have
(y + b - (a + 3d))(y + b + (a + 3d))
= ( y + b - a - 3d)(y + b + a + 3d)
You are a young entrepreneur who ventures into selling milk tea. On the soft opening day, you sold all 50 glasses of classic and flavored milk tea, and bought in P4700. You need to determine how many glasses of classic milk tea and how many glasses of flavored milk tea were sold on that day if a glass of classic milk tea costs P100 and a glass of flavored milk tea is P80.
Answer:
35 glasses of classic milk tea
15 glasses of flavored milk tea
Step-by-step explanation:
You sold 50 glasses of classic and flavored milk tea.
c + f = 50
You made 4700 when classic tea costs 100 and flavored tea costs 80.
100c + 80f = 4700
Use this system of equation to solve. Use substitution. Rearrange the first equation so that it is equal to c. Then, plug the c-value into the second equation.
c + f = 50
c = 50 - f
100c + 80f = 4700
100(50 - f) + 80f = 4700
5000 - 100f + 80f = 4700
5000 - 20f = 4700
-20f = -300
f = 15
Plug the f-value into one of the equations and solve for c.
c + f = 50
c + 15 = 50
c = 35
35 glasses of classic milk tea and 15 glasses of flavored milk tea were sold.
58.30
The slope of the graph of the equation y2x-2 is 2. What is the y-intercept?
y-intercept =
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Answer:
the slope is 2 and the y intercept is -2
Step-by-step explanation:
y=2x-2
This is in the form y = mx+b where m is the slope and b is the y intercept
the slope is 2 and the y intercept is -2
Using the given points and line, determine the slope of the line. (-3, 0) and (2, 7) slope = - slope = - slope = slope =
Answer:
slope = [tex]\frac{7}{5}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (2, 7)
m = [tex]\frac{7-0}{2+3}[/tex] = [tex]\frac{7}{5}[/tex]
Answer:
7/5
Step-by-step explanation:
m=y2-y1/x2-x1
7-0=7
2-(-3)=5
7/5
A moth of a year is chosen at random what is the probability that the month starts with the letter j or the letter M? 5/24p
Answerr:
Step-by-step explanation:
Two prisms are similar with a scale factor of 1:4. Find the volume of the smaller prism given that the volume of the larger is 2400ft3.
The Volume of the smaller prism is 37.5 ft³.
What is a Prism?Prism is a three-dimensional structure that has identical polygon bases, and other faces are identical parallelograms.
The volume of the prism is determined by the formula
V = Bh
B is the base area and h is the height of the Prism.
The scale factor is given as 1/4, as the volume of the larger prism is given.
The volume of the larger prism is 2400 ft³
the side lengths will be multiplied by 1/4
Let the base area is for the larger prism the area for the smaller prism will be equal to
A = (1/16) a
The height of the larger prism is h.
Height of the smaller prism will be (1/4)h
The volume of the smaller prism = (1/16)*(1/4) Volume of the Larger Prism
The volume of the smaller prism = 2400 / (16*4)
The volume of the smaller prism = 37.5 ft³.
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Which inequality will have a shaded area below the boundary line?
A y-x>5
B. 2x-3y< 3
C. 2x-3y
D. 7x+ 2y<2
E. 3x+4y> 12
Answer:
D. 2y < 2
Step-by-step explanation:
To find the equation with shaded area below the boundary line, all we need to do is to examine each inequality and find the one which gives
+y < ( a constant)
We can leave out the x term for this.
For example:
A. y>5 clearly it is shaded above the line (because of the > sign)
B. -3y <3 => 3y > -3 so again it is shaded above
C. -3y is not even an inequality
D. 2y < 2 clearly it is shaded BELOW
E. 4y >12 clearly it is shaded above
See also attached diagram. The answer is represented by the purple area. All the other areas are shaded above the boundary line.
Find the missing segment
Answer:
? = 9.
Step-by-step explanation:
According to the AA Theorem, the two triangles are similar.
[tex]\frac{30}{30 + 5} =\frac{54}{? + 54}[/tex]
30 (? + 54) = 54 * 35
30? + 1620 = 1890
3? + 162 = 189
3? = 27
? = 9
Hope this helps!
1. fill in the blanks below and write and evaluate an example of a function part1: Ashley earns 17 per hour. define the variables and state which quantity is a function of the other. part 2: using the variables defined in part 1, write a function using notation that represents Ashley's income Part 3: Ashley's hours for the last two weeks were 35 hours and 29 hours. Using the function you wrote in Part II, determine her income for each of the two weeks. Show your work. (4 points) 37 Week 1: Ashley worked 35 hours. She earned __________. Week 2: Ashley worked 29 hours. She earned __________.
Answer:
See below
Step-by-step explanation:
Part 1 -
x: number of hours worked
y: total income
This is written as → y = f(x)
Part 2 -
y = 15*x
Part 3 -
f (35) = 15 × 35 = $525
f (29) 15 × 29 = $435
Week 1 - Ashley worked 35 hours with a total income of $525.
Week 2 - Ashley worked 29 hours with a total income of $435.
can somewon help me plz
Answer: s=36
Step-by-step explanation:
To solve for s, we can use our algebraic properties to solve.
[tex]\frac{1}{3}s+14=26[/tex] [subtract both sides by 14]
[tex]\frac{1}{3}s=12[/tex] [multiply both sides by 3]
[tex]s=36[/tex]
Answer:
The answer is s=36
Step-by-step explanation:
There is a equilateral triangle with sides of 13 inches, how do I find the area of that triangle?
Answer:
73.18
Step-by-step explanation:
equilateral triangle means all sides are the same
A=(√3/4)a^2
A=(√3/4)*13^2
A=73.18 inches square
Answer:
73.18 square inches.
Step-by-step explanation:
To find the area of an equilateral triangle, we use a certain formula.
Where the side length is represented by s, the area is (sqrt(3))/4 * s^2.
Since s = 13, you will have (sqrt(3))/4 * 13^2 = 1.732050808/4 * 169 = 292.7165865/4 = 73.17914662. You can round that to 73.18.
So, the area of the triangle is 73.18 square inches.
Remember to use your units when presenting your answer, and hope this helps!
In △ABC, AB = BC = 20 and DE ≈ 9.28. Approximate BD.
Answer:
BD = 5
Step-by-step explanation:
∠A = 60°
Since AB = 20 = BC, Then ∠B = 60° resulting in a equilateral triangle with ∠C = 60°. Then dividing ∠DAE into half gives 4 = angles of 15° yielding each secition of BC being equal to 20/4 = 5. Do i don't think DE ≈ 9.28 cannot occur.
Find the value of the discriminant (D) and describe the roots for the quadratic equation shown below.
y= ax + bx + c
y= x + 3x-4
A. D= -7 and the roots are irrational.
B. D = 22 and the roots are irrational.
C. D= 25 and the roots are rational.
D. D=5 and the roots are rational.
Answer: C
Step-by-step explanation:
y = ax + bx + c is the general equation for quadratic function. While the discriminant D is
D = b^2 - 4ac
You are given the equation:
y = x^2 + 3x - 4
Where a = 1, b = 3 and c = -4
Substitutes all the parameters into the discriminant D formula
D = 3^2 - 4 × 1 × -4
D = 9 - ( - 16 )
Open the bracket
D = 9 + 16
D = 25
Therefore, D = 25 and the roots are rational
the tens digit exceeds the units digit by 3. If the units digit is r what is the value of the number ?The next even integer that is larger than 2n, if 2n is an even integer.
Answer:
a) we know that:
the tens digit exeeds the units digit by 3, then if we have two digits
ab.
and b, the digit for units is equal to r.
then a, the digit for tens, is equal to r + 3.
Then, if r = 4, we have that the digit for tens is r + 3 = 7
and the number is 74.
b) if n is an integer, then we know that 2*n is an even number.
Now, the next even number is always 2 units away, then the next even number to 2*n is:
2*n + 2 = 2*(n + 1)
Which equation can be used to solve for the measure of angle ABC? tan(x) = tan(x) = sin(x) = sin(x) =
Answer:
A. tan(x) = 2.4/10
Step-by-step explanation:
The question is incomplete and lacks the required diagram. Find the question and diagram attached below.
Which equation can be used to solve for the measure of angle ABC? tan(x) = 2.4/10 tan(x) =10/2.4 sin(x) =10/10.3 sin(x) =10.3/10
We will use the SOH CAH TOA identity to calculate the equation needed to solve for angle ABC.
In a right angled triangle, the side facing the acute angle ABC is the opposite, the longest side is the hypotenuse and the third side (base) is the adjacent.
From the diagram shown;
AB = hypotenuse = 10.3cm
AC = opposite = 2.4cm
BC = adjacent = 10cm
To get the angle x, we can use the SOH and TOA identity.
SOH means sin<ABC = opp/hyp
Sin(x) = AC/AB = 2.4/10.3
TOA ≈ Tan(x) = opp/adj
Tan(x) = 2.4/10
The equation that can be used to solve for the measure of angle ABC are therefore sin(x) = 2.4/10.3 OR tan(x) = 2.4/10
Based on the given option,
tan(x) = 2.4/10 is the only correct answer.
Answer:
in short its A.
Step-by-step explanation:
EDGE 2021
Fill in the blanks please
Answer:
Step-by-step explanation:
MNOP is a parallelogram Given
PM // ON opposite sides of parallelogram are parallel
∠ NOM = ∠ONP Alternate angles theorem
MN // OP opposite sides of parallelogram are parallel
∠NOP =∠ MNO Alternate angles theorem
ON = ON common to both triangles ΔOMN & ΔONP
ΔOMN ≅ ΔONP ASA congruent
PM ≅ ON CPCT -Corresponding Part of Congruent triangle
2/3x + 2= 21/3 solve for x a. 0 b. 1/2 c -2 d. 2
Answer:
x = 7.5
Step-by-step explanation:
2/3x + 2= 21/3
Subtract 2 from each side
2/3x + 2-2= 21/3-2
2/3x = 21/3 - 6/3
2/3x =15/3
2/3x = 5
Multiply each side by 3/2 to isolate x
2/3x * 3/2 = 5 *3/2
x = 15/2
The table shows how an elevator 500 feet above the ground is descending at a steady rate. A two column table with 5 rows. The first column, time in seconds (t), has the entries, 0, 5, 10, 15. The second column, Height in feet h(t), has the entries, 500, 475, 450, 425. Which equation represents the height, h(t), of the elevator in feet, as a function of t, the number of seconds during which it has been descending?
Answer:
h(t)=-5t+-500
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
i took the test
The population of Peru is 10904 the population of Franklin is 25248. The population of Franklin is percent more than the population of Peru
Answer:
132%
Step-by-step explanation:
The population of Peru = 10904
The population of Franklin = 25248.
Difference = 25248-10904=14,344
Expressing as a percentage of the population of Peru
[tex]\dfrac{14344}{10904} X 100[/tex]
=132%
Therefore, the population of Franklin is 132% more than the population of Peru.
Two random samples were taken to determine how often people in a community listen to the local radio station each month. The first sample surveyed 15 people as they exited the bank on Main Street. The first sample found that the mean number of hours they listened to the radio each month was 20. The second sample surveyed every sixth person as they exited the only local grocery store until 100 people were surveyed. The second sample found that the mean number of hours they listened to the radio each month was 12. Which statements are true? Check all that apply. The second sample is random. The second sample is likely to be more representative of the population. The first sample is likely to be more representative of the population. The second sample will give a better representation because is it larger. The first sample will give a better representation because it is smaller. Community members are more likely to listen to the radio station an average of 12 hours a month than 20 hours a month.
Answer:
The answers to this question are 1,2,4,6. Hope this helps you
Step-by-step explanation:
Statements A, B, E, and F are true. The second sample was taken at random using a fair sampling technique.
What is the probability?Probability is synonymous with possibility. It is concerned with the occurrence of a random event.
Probability can only have a value between 0 and 1. Its simple notion is that something is very likely to occur. It is the proportion of favorable events to the total number of events.
The correct statement is as follows;
A) The second sample is random.
B) The second sample is likely to be more representative of the population.
D) The second sample will give a better representation because is it larger.
F) Community members are more likely to listen to the radio station an average of 12 hours a month than 20 hours a month.
The second sample was taken at random using a fair sampling technique.
Because the research using the larger data size is accepted rather than that of the smaller data, community members are more likely to listen to the radio station an average of 12 hours a month than 20 hours.
A research's sample size is a crucial consideration. Additionally, the second sample is probably a better indicator of the broader population.
Hence statements A, B, E, and F are true.
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Triangle STV has vertices S (-3, -2) , T (-4, 3) and V (-2, 3). If (x, y) arrow (x+2, y-3), what are the vertices of its image?
Answer:
see below
Step-by-step explanation:
The mapping tells you how to find the vertices of the image:
(x, y) ⇒ (x +2, y -3)
S(-3,-2) ⇒ S'(-3 +2, -2 -3) = S'(-1, -5) . . . . . matches choice D
T(-4, 3) ⇒ T'(-4 +2, 3 -3) = T'(-2, 0)
V(-2, 3) ⇒ V'(-2 +2, 3 -3) = V'(0, 0)
Answer:
D
Step-by-step explanation:
The Statue of Liberty weighs about 2.04 x 105 kg. The Washington Monument weighs about 9.07 x 107 kg. About how many more kilograms does the Washington Monument weigh than the Statue of Liberty?
Answer:
[tex]9.05 * 10^{7} kg[/tex]
Step-by-step explanation:
Given
[tex]Statue\ of\ Liberty\ =\ 2.04 * 10^5 kg[/tex]
[tex]Washington\ Monument\ =\ 9.07 * 10^7 kg[/tex]
To get the number of kilograms the Washington Monument weighs more than the Statue of Liberty, we simply calculate the difference;
Difference = Washington Monument - Statue of Liberty
[tex]Difference = \ 9.07 * 10^7 kg - \ 2.04 * 10^5 kg[/tex]
Expand [tex]10^7[/tex]
[tex]Difference = \ 9.07 * 10^{5+2} kg - \ 2.04 * 10^5 kg[/tex]
[tex]Difference = \ 9.07 * 10^{5} * 10^2 kg - \ 2.04 * 10^5 kg[/tex]
Take out the common factor in the above expression
[tex]Difference = 10^{5}\ (\ 9.07 * 10^2 kg - \ 2.04\ kg)[/tex]
[tex]10^2 = 100;[/tex] so we have
[tex]Difference = 10^{5}\ (\ 9.07 * 100 kg - \ 2.04\ kg)[/tex]
[tex]Difference = 10^{5}\ (\ 907 kg - \ 2.04\ kg)[/tex]
[tex]Difference = 10^{5}\ (904.96\ kg)[/tex]
Open bracket
[tex]Difference =904.96 * 10^{5} kg[/tex]
Write in standard form
[tex]Difference =9.0496 * 10^2 * 10^{5} kg[/tex]
[tex]Difference =9.0496 * 10^7 kg[/tex]
[tex]Difference =9.05 * 10^7 kg[/tex] (Approximated)
Hence, he Washington Monument weigh more than the Statue of Liberty by about [tex]9.05 * 10^{7} kg[/tex]
Answer:
it is d i just did the 4 quiestion assignment by the learning odessy
Step-by-step explanation:
Plz help me 2/3(6-9x)+15
Answer:
19-6x
Step-by-step explanation:
2/3(6-9x)+15
=4-6x+15
=19-6x
Answer:
19-6xSolution,
[tex] \frac{2}{3} (6 - 9x) + 15 \\ = \frac{2}{3} \times 6 - \frac{2}{3} \times 9x + 15 \\ = 4 - 6x + 15 \\ = 4 + 15 - 6x \\ = 19 - 6x[/tex]
Hope this helps...
Good luck on your assignment..
Calculate the area and the perimeter of the figure
Answer:
Area: 5 cm squared
Perimeter: 12 cm
Step-by-step explanation:
The area is Length times Width, and there is 5 different sqaures in the figure.Each sqaure has an area of 1 by 1, which is 1. 1 times 5 is 5. So the area is 5. You can get the perimeter by adding all the side lengths together, 2+3+2+1+1+1+1+1=12. The perimeter is 12. Hope this helps.
Line m passes through the points (-4, 3) and (-4, 7). What is the slope of the line that is parallel to line m?
Answer:
4x
Step-by-step explanation:
When you have a parallel line, the slope of the line is the same. So the slope of (-4,3),(-4,7)=4 would be the same as for example 4x+5
The diagram shows a 5 cm x 5 cm x 5 cm cube.
Calculate the length of the diagonal AB.
Give your answer correct to 1 decimal place.
Answer:
8.7 cm
Step-by-step explanation:
The question is a 2-two-step Pythagoras theorem. (c^2 = a^2 + b^2)
Consider as such, If I were to draw a diagonal line along the base of the cube what is the length of the diagonal line. To find out that we use the theorem. We can substitute a for 5 and b for 5 as well. So
a^2 +b^2 = c^2
5^2 + 5^2 = c^2
25 + 25 = c^2
√50 = c
Then since the line side of the cube is on a 3d angle we need to do the same process again but now using the imaginary diagonal line that we just calculated and the height (5).
a^2 +b^2 = c^2
√50^2 + 5^2 = c^2
50 + 25 = c^2
√75 = c
c = 8.6602...
when rounded to 1 d.p.
c = 8.7
Line AB is 8.7 cm long.
A restaurant offers 6 choices of appetizer, 8 choices of a main meal, and 5 choices of dessert. A customer can choose to eat just one course, or two different courses, or all three courses. Assuming all choices are available, how many different possible meals does the restaurant offer?
Answer:
377 choices
Step-by-step explanation:
From the above question, we are told that
A restaurant offers 6 choices of appetizer, 8 choices of main meal and 5 choices of dessert. A customer can choose to eat just one course, or two different courses, or all three courses.
Let us represent each choice by :
A = Appetizer = 6
M = Main meal = 8
D = Dessert = 5
a) The combination of the 3 choices together
AMD=6 × 8 × 5=240
b) AM= Appetizer and Main meal
= 6 × 8 = 48
c) AD= Appetizer and Dessert
= 6 × 5 = 30
d) MD = Main meal × Dessert
= 8 × 5 = 40
e) A,M,D (each alone)=
Appetizer + Main meal + Dessert
= 6 + 8 + 5
= 19
Assuming all choices are available, how many different possible meals does the restaurant offer?
This is calculated as:
AMD + AM + AD + MD + A,M,D
240 + 48 + 30 + 40 + 19
= 377 choices