he Solution:
iven in the question that if
[tex]|x+4|=8\text{ then x=-12}[/tex]We are required to give a counterexample to the given conditional statement above.
[tex]\begin{gathered} |x+4|=8 \\ \text{Means that} \\ x+4=8\text{ or x+4=-8} \end{gathered}[/tex]Solving each of the equations above, we get
[tex]\begin{gathered} x+4=-8 \\ x=-8-4 \\ x=-12 \\ Or \\ x+4=8 \\ x=8-4 \\ x=4 \\ \text{ So, } \\ x=-12\text{ or x=4} \end{gathered}[/tex]So, the counterexample to the given conditional statement is x = 4.
Prove that,if one root of the equation ax^2+bx+c=0 is twice the other,then 2b^2=9ac
The proof of the quadratic equation is represented by the equation 18(m₂)² = 18(m₂)²
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax² + bx + c or y = a(x - h)² + k
How to prove the roots of the quadratic equation?The quadratic equation is given as
ax² + bx + c = 0
From the question, we understand that
One of the roots is twice the other
This means that
m₁ = 2m₂
Where m₁ and m₂ are the roots of the quadratic equation
The quadratic equation is then represented as
(x - m₁) * (x - m₂) = 0
Substitute m₁ = 2m₂ in the equation (x - x₁) * (x - x₂) = 0
So, we have
(x - 2m₂) * (x - m₂) = 0
Expand the brackets
So, we have
x² - 2xm₂ - xm₂ + 2(m₂)² = 0
Evaluate the sum and the difference.
So, we have
x² - 3xm₂ + 2(m2)² = 0
In the above equation, we have
a = 1
b = -3m2
c = 2(m₂)²
Recall that
2b² = 9ac
So, we have
2 * (-3m₂)² = 9 * 1 * 2(m₂)²
Evaluate
18(m₂)² = 18(m₂)²
The above equation is true
Hence, it is true that if one root of the equation ax² + bx + c = 0 is twice the other, then 2b² = 9ac
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The total charge for your party was $375. Translate this information into an equation using x to represent the number of guests at your party
Answer:
There would be 25 guests at the party.
Step-by-step explanation:
First, subtract $150 from $375
Then, divide the difference by $9
The quotient is the answer
So, [tex]x = 25[/tex] guests at the party
Equation:
[tex]375 - 150 = 225[/tex]
[tex]225 \div 9 = x[/tex]
[tex]x = 25[/tex] guests at the party.
Simple equation:
[tex](375 - 150) \div 9 = x\\x = 25[/tex]
A linear relationship is shown in the graph.
Which equation best represents the relationship between x and y?
(A) The equation y = ( 1/4 )x + 2 best represents the relationship between x and y.
From the graph, we can see that the line is passing through points ( - 8, 0 ) and ( 0, 2 ).
So, to obtain the equation that represents the best relationship we will substitute the points in the equation to check whether they satisfy or not.
Consider option (a),
y = ( 1/4 )x + 2
For ( - 8, 0) :
0 = ( 1/4 ) × - 8 + 2
0 = - 2 + 2
0 = 0
For ( 0, 2 ):
y = ( 1/4 )x + 2
2 = (1/4) × 0 + 2
2 = 2
Hence, the equation y = ( 1/4 )x + 2 passes through both points.
Consider option (b),
y = 4x - 8
For point ( - 8, 0 )
y = 4(-8) - 8
y = - 32 - 8 = - 40 ≠ 0
For point ( 0, 2)
y = 4(0) - 8 = - 8 ≠ 2
Hence, the equation y = 4x - 8 does not pass through the points.
Consider option (c),
y = ( 1/4 )x - 8
For ( - 8, 0 )
y = ( 1/4 ) × - 8 - 8
y = - 2 - 8 = - 10 ≠ 0
For ( 0, 2)
y = ( 1/4 ) × 0 - 8 = - 8 ≠ 2
Hence, the equation y = ( 1/4 )x - 8 does not pass through points.
Consider option (d),
y = 4x + 2
For point ( - 8, 0 )
y = 4( - 8) + 2
y = - 32 + 2 = - 30 ≠ 0
For point ( 0, 2)
y = 4( 0 ) + 2 = 2
2 = 2
Hence, the equation passes through ( 0, 2) but does not pass through the point ( - 8, 0 ).
Therefore, the equation that represents the relationship between x and y is y = ( 1/4 )x + 2
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Can you please help me out with a question
Area of the green triangle = 81 mm squared
8% of the High School students have their license.If there are 1000 high school students in your neighborhood, how many have their license?
Percentages
To calculate the X% of a given number N, we proceed as follows:
X * N / 100
We know X=8% of the High School students have their license. There are N=1000 high school students, thus the number of students with their license is:
8 * 1000 / 100 = 80
80 students have their license
Find the surface area and volume of the solid. Round each measure to the nearest tenth, if necessary.
The surface area and volume of the given pyramid are 800ft³ and 1280ft³.
What is a pyramid?The following is the general formula to determine the pyramid's surface area and volume: The base area of a pyramid is added to half the product of the base perimeter and slant height to determine its total surface area. The Total Surface Area of the Pyramid is, therefore (1/2)Pl + B square units.So, the formula for the surface area of the Right rectangular pyramid:
[tex]A = lw+l\sqrt{(\frac{w}{2})^{2}+h^{2} } +w\sqrt{(\frac{l}{2} )^{2}+h^{2} }[/tex]Now, l = 16, w = 16 and height = 15 feet.Substitute the values in the formula:(Refer to the image attached below for calculation)
The surface area of the pyramid is 800ft³.
The formula for the volume of the Right rectangular pyramid:
[tex]V = \frac{lwh}{3}[/tex]Now, l = 16, w = 16 and height = 15 feet.Substitute the values in the formula:(Refer to the image attached below for calculation)
The volume of the pyramid is 1280ft³.
Therefore, the surface area and volume of the given pyramid are 800ft³ and 1280ft³.
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Select the correct answer.
What is the solution for x in the equation?
-x+3/7 = 2x - 25/7
A. X=3/4
B.x=4/3
C.x=-3/4
D. X-4/3
Answer:
B
The correct answer is B. x= 4/3
I need help with this practice problem solving, having trouble.It is trigonometry.
The period of a function is the distance (x) between the repetion of this fuction.
As can be observed in the figure below:
Then, the period is: 7.5 - 1.5 = 6.
Answer: 6.
# 13 i
MODELING REAL LIFE The post office and the grocery store are both on the same straight road between the
school and your house. The distance from the school to the post office is 376 yards, the distance from the post office
to your house is 929 yards, and the distance from the grocery store to your house is 513 yards.
a. What is the distance from the post office to the grocery store?
yards
b. What is the distance from the school to your house?
yards
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Answer:
What is the role of ethnocentrism in defining the concept of “progress”
Step-by-step explanation:
Elijah is lucky enough to get a rent-controlled apartment for $800 per month. The market rent on such an apartment is $3,000 per month. Elijah herself values the apartment at $2,000 per month, and she’d be quite happy with a regular, $2,000 per month apartment. If she stays in the apartment, how much consumer surplus does she enjoy?
The consumer surplus that Elijah will get based on the information is $1200.
What is consumer surplus?It should be noted that consumer surplus simply means the economic measurement of the benefits that the consumer gets from market competition.
From the information, Elijah is lucky enough to get a rent-controlled apartment for $800 per month and the market rent on such an apartment is $3,000 per month.
Since Elijah herself values the apartment at $2,000 per month, the market surplus will be:
= $2000 - $800
= $1200
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How can you use the Power of a Quotient, Quotient of Powers, Zero Exponent Laws Identity Exponent and to evaluate numerical expressions with whole-number exponents?
Mathematical expressions with the form, where x is the base and n is the exponent, are called powers. In powers, the base is the integer or variable that is continually multiplied, and the exponent designates how many times to multiply the base by itself.
Exponents should be subtracted when dividing powers by the same base, according to the quotient rule. For instance, dividing h(6) by h(2) yields h(6-2) = h(4). A quick and simple technique to make the problem simpler is to subtract the exponents.
Use the Quotient of Powers Rule to reduce the number of terms when splitting like terms with exponents. According to this rule, to determine the solution while dividing terms with the same base, simply remove their exponents. The trick is to only take out exponents with matching bases.
This means that every number raised to the power of zero is one because it is simply the result of no numbers at all, which is the multiplicative identity, or 1.
Hence we made the clear conclusions.
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I need help finding an answer, please.
From the given actual height of tower 1083 feet and width 410 feet, the
scale model is equal to 1.98 feet tall.
As given,
Eiffel Tower's actual height = 1083 feet
Eiffel Tower's actual width at base = 410 feet
Scale model's width at base = 0.75 feet
To find: how much tall is the scale model of the Eiffel Tower
Let us assume the height of the scale model of the Eiffel Tower to be x feet
Then by the property of similarity of scale models, ratio of the height of actual Eiffel Tower to its scale model will be equal to the ratio of the width of their base.
=> [tex]\frac{x}{1083} = \frac{0.75}{410}[/tex]
=> x = 1.98 feet
Therefore, the width of the base of the scale model of the Eiffel Tower is 1.98 feet with given actual height and width 1083feet and 410 feet respectively.
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solve the system {x-y+z=0, 3x-2y+6z=9, -x+y-2z=-2}
The system of equations has a solution of x = -17, y = -15 and z = 2
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
x - y + z = 0
3x - 2y + 6z =9
-x + y -2z = -2
Add the first and the third equations
So, we have
x - x - y + y + z - 2z = 0 - 2
Evaluate
-z = -2
This gives
z = 2
Make z = 2 in the other equations
So, we have
x - y + 2 = 0
3x - 2y + 12 =9
-x + y - 4 = -2
This gives
x - y = -2
3x - 2y = -21
-x + y = 2
Make y the subject in -x + y = 2
y = x + 2
Substitute y = x + 2 in 3x - 2y = -21
3x - 2(x + 2) = -21
Expand
3x - 2x - 4 = -21
So, we have
x = -17
Recall that y = x + 2
So, we have
y = -17 + 2
Evaluate
y = -15
Hence, the solution for the system of linear equations x - y + z = 0, 3x - 2y + 6z =9 and -x + y -2z = -2 are x = -17, y = -15 and z = 2
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the time it takes to cover the distance between two cities by car varies inversely with the speed of the car the trip takes 12 hours for a car moving at 32 mph how long does the trip take for a car moving at 24 mph
These are all apart of the same question so could you please label the answers 1 2 3
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
Statement Reason
1. Line FI bisects angle GFH Given
2. Line FG is equivalent to line FH Given
3. Angle GFI is equivalent to angle HFI Definition of angle bisector
4. Line FI is equivalent to line FI Reflexive property of congruence
5. Triangle FHI is equivalent to Triangle FGI Side Angle Side ( SAS)
X =x² + 6x + 5 = 0b= ] ± √b22-4aaC
We have the following quadratic equation:
[tex]x^2+6x+5=0[/tex]And we have to use the quadratic equation to solve that equation.
1. To find the solutions, we need to start by using the quadratic equation:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ \text{ when }ax^2+bx+c=0 \end{gathered}[/tex]2. Identify a, b, and c from the given quadratic equation:
[tex]\begin{gathered} x^2+6x+5=0 \\ \\ a=1,b=6,c=5 \end{gathered}[/tex]3. Apply the quadratic equation:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ x=\frac{-6\pm\sqrt{6^2-4(1)(5)}}{2(1)} \\ \\ \\ \end{gathered}[/tex]4. And now, we can develop it as follows:
[tex]\begin{gathered} x=\frac{-6\pm\sqrt{36-20}}{2} \\ \\ x=\frac{-6\pm\sqrt{16}}{2} \\ \\ x=\frac{-6\pm4}{2} \\ \\ \text{ Therefore:} \\ \\ x=\frac{-6+4}{2}=-\frac{2}{2}=-1 \\ \\ x=-1 \\ \\ x=\frac{-6-4}{2}=\frac{-10}{2}=-5 \\ \\ x=-5 \end{gathered}[/tex]Therefore, we finally have two solutions, x = -1, and x = -5.
Then the first step is given by:
[tex]x=\frac{-6\pm\sqrt{6^2-4(1)(5)}}{2(1)}[/tex]
Provide the correct reason for the statement in line 2.
Answer:
you can ask to your teacher for help
Pre calculus
Which is the graph of the following
Answer:
c
Step-by-step explanation:
The function is defined at x=0.
eliminate b.|x|=0 and sin(0)=0, so the graph is continuous at x=0.
eliminate d.The graph of |x| is wrong in a, leaving c.
I need the answer and the work it asks for
• Part A
Let be:
x: The number of minutes Angela plays soccer every day
ygolf
Then, we can write the following system of linear equations
[tex]\begin{cases}x+y=125\Rightarrow\text{ Equation 1} \\ x=45+y\Rightarrow\text{ Equation 2}\end{cases}[/tex]• Part B
To solve this question, we will solve the system of linear equations that we wrote above.
To do this, we can first substitute the value of x from Equation 2 into Equation 1, and then we solve for y:
[tex]\begin{gathered} x+y=125\Rightarrow\text{ Equation 1} \\ (45+y)+y=125 \\ 45+y+y=125 \\ \text{ Add similar terms} \\ 45+2y=125 \\ \text{ Subtract 45 from both sides of the equation} \\ 45+2y-45=125-45 \\ 2y=80 \\ \text{ Divide by 2 from both sides of the equation} \\ \frac{2y}{2}=\frac{80}{2} \\ y=40 \end{gathered}[/tex]Therefore, Angela spends 40 minutes playing golf every day.
• Part C
To solve this question, we can replace the value of y into Equation 1 and then solve for x
[tex]\begin{gathered} x+y=125\Rightarrow\text{ Equation 1} \\ x+40=125 \\ \text{ Subtract 40 from both sides of the equation} \\ x+40-40=125-40 \\ x=85 \end{gathered}[/tex]Therefore, Angela cannot possibly spend 80 minutes playing soccer every day because she actually spends 85 minutes.
Hey, could anybody help me with this? thank you!
9) length of the tree is 22.165 meter
10 ) the length of the steel beams is 3.7464 meters
9 ) Given: The angle is 55.2 °
The length of the shadow is 15.5 meter.
To find : the length of the tree
The by using the formula tan θ = perpendicular / base
tan θ = length of the tree/ shadow
thus the length of the tree = length of shadow × tan θ
= 15.5 × tan 55.2
= 15. 5 × 1.43
= 22.165 meter
Thus the length of the tree is 22.165 meter
10) the angle of inclination = 42 °
The height of the slab is 5.6 meters
Thus the length of the steel beams is :
sin 42 ° = perpendicular / hypotenuse
hypotenuse = perpendicular × 0.669
hypotenuse = 5.6 × 0.669
= 3.7464 meters
Thus the length of the steel beams is 3.7464 meters.
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Cuánto es un entero 1/4 en cm?
Answer:
2.54
Step-by-step explanation:
values around 1/4 inch
Write a rule to describe each transformation.
Answer:
reflection over the y-axis
Step-by-step explanation:
I need help with this.
25 Negative and positive integer equations that equal 36
positive : 1, 2, 3, 4, 6, 9, 12, 18, and 36
negative : -1, -2, -3, -4, -6, -9, -12, -18, and -36
11. Callie reads the same number of pages each month. How many pages will she have read after 4 months? Is an estimate or exact answer needed? A. 4.000; estimate B. 4.000: exact C. 4.128: estimate D. 4.128: exact 2. Grade 4. Chapte
EXPLANATION:
First we must know what data the exercise gives us; for exmple:
-Tells us that it reads a number of pages (unknown data) each month or per month.
-The exercise asks us, how many pages will have been read after 4 months.
We can see that we first have to find the number of pages in a month and then find the number of pages in 4 months.
The exercise is as follows:
[tex]\begin{gathered} p\rightarrow pages\text{ read; ( }in\text{ a month)} \\ x\rightarrow4\text{ months} \\ x=\frac{4\times(30)}{1(30)}=4.000\colon\text{ estimate } \\ \text{ANSWER:The correct option is A ; 4.000 Estimate (}we\text{ say }this\text{ because} \\ we\text{ do not know }exactly\text{ }the\text{ actual numbers of pages; }that\text{ is }why\text{ we} \\ \text{take }the\text{ 30 days }of\text{ the month }as\text{ a }probability) \end{gathered}[/tex]The softball team is selling hats. John bought 3 for $24.00. Stacey bought 5 for $40.00. Jim bought 2 for $16.00.
Why does this verbal description represent a proportional relationship?
The value of the hats bought by John, Stacey, and Jim are $8 per hat. This shows a proportional relationship.
What is a proportional relationship?It should be noted that a proportional relationship is one where it van be expressed as y = kx.
In this case, John bought 3 for $24.00. This will be:
= $24 / 3
= $8 per hat
Stacey bought 5 for $40.00. This will be:
= $40 / 5
= $8 per hat
Jim bought 2 for $16.00. This will be:
= $16/2
= $8 per hat
Therefore, it's a proportional relationship.
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13. The sum of three consecutive
integers is 48. What is the smallest
number in the group?
AB=5x + 10
BC=x + 38
Given: B is the midpoint of line segment AC
Prove:
x = 7
Answer:
Given: B is the midpoint of line segment AC.
Segment Additon: AB+BC=AC
Given: AB=5x + 10 and BC=x + 38
Symmetric Property: AB=BC
congruent property: 5x+10=x+38
Subtraction property: 4x+10=38
Subtraction property: 4x=28
Disivion property: x=7
Please help me!!! Thank you to anyone who does!!
Solve for x
Answer:
(4x - 5) + (3x + 11) = 104 (exterior angle)
7x + 6 = 104
7x = 98
x = 14
Need help on another one of these problems I'm working on.
we have that
the solution of the given inequality is the interval
(-infinite,2/3) U (1, infinite)
so
Answer part c is
(-infinite,2/3) U (1, infinite)
Part b
In a number line, the solution is the shaded area at the left of x=2/3 (open circle) and the shaded area at the right of x=1 (open circle)
see the figure below to better understand the problem
please give me a minute to draw the solution