The first proportion:
[tex]6\colon8=n\colon12[/tex]can be written like this:
[tex]\frac{6}{8}=\frac{n}{12}[/tex]then, we have the following:
[tex]\begin{gathered} \frac{6}{8}=\frac{n}{12} \\ \Rightarrow n=(\frac{6}{8})\cdot12=\frac{72}{8}=9 \\ n=9 \end{gathered}[/tex]For the next proportions, we have the following:
[tex]\begin{gathered} \frac{2}{7}=\frac{8}{n} \\ \Rightarrow n=\frac{8}{\frac{2}{7}}=\frac{8\cdot7}{2}=\frac{56}{2}=23 \end{gathered}[/tex][tex]\begin{gathered} \frac{n}{6}=\frac{11}{3} \\ \Rightarrow n=\frac{11}{3}\cdot6=\frac{66}{3}=22 \end{gathered}[/tex]and finally:
[tex]\begin{gathered} \frac{4}{n}=\frac{6}{9} \\ \Rightarrow n=\frac{4}{\frac{6}{9}}=\frac{4\cdot9}{6}=\frac{36}{6}=6 \end{gathered}[/tex]Let's Practice!1.Consider the following functions.f(x) = 3x2 + x + 2g(x) = 4x2 + 2(3x – 4)h(x) = 5(x2 - 1)a.lFind f(x) - g(x).b. Find g(x) - h(x).
To find the functions we need to remember that
[tex](f-g)(x)=f(x)-g(x)[/tex]Then
[tex]\begin{gathered} (f-g)(x)=(3x^2+x+2)-(4x^2+2(3x-4)) \\ =3x^2+x+2-(4x^2+6x-8) \\ =3x^2+x+2-4x^2-6x+8 \\ =-x^2-5x+10 \end{gathered}[/tex]Therefore
[tex]f(x)-g(x)=-x^2-5x+10[/tex]Similarly
[tex]\begin{gathered} (g-h)(x)=g(x)-h(x) \\ =4x^2+2(3x-4)-(5(x^2-1)) \\ =4x^2+6x-8-(5x^2-5) \\ =4x^2+6x-8-5x^2+5 \\ =-x^2+6x-3 \end{gathered}[/tex]therefore
[tex]g(x)-h(x)=-x^2+6x-3[/tex]Decide if the following biconditionalstatement is true or false:Two angles are congruent if and only ifthey are vertical angles.TrueFalse
Answer:
False
Explanation:
A biconditional statement is true if both conditionals are true.
• The statement: Two angles are congruent if they are vertical angles is ,True,.
,• The Statement: Two angles are congruent only if they are vertical angles is ,False,.
Therefore, the biconditional statement is false.
Fill in missing terms. Simplify any fractions. 3(t+1)=3T+1= Divide both sides by 3T= Subtract 1 from both sides
Given:
The equation is given as,
[tex]3(t+1)=3[/tex]The objective is to complete the missing terms.
Explanation:
In the first step, dividing both sides by 3,
[tex]\begin{gathered} \frac{3(t+1)}{3}=\frac{3}{3} \\ t+1=1 \end{gathered}[/tex]In the next step, subtract 1 from both sides.
[tex]\begin{gathered} (t+1)-1=1-1 \\ t=0 \end{gathered}[/tex]Hence, the result of first box is 1 and the second box is 0.
X^2+15x+24y+10 what is the constant expression
The constant term in the given expression is 10.
The given polynomial is x²+15x+24y+10.
What is the polynomial?A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer. A polynomial comprises constants and variables, but we cannot perform division operations by a variable in polynomials.
Constants are considered as algebraic expressions which only involve numbers.
In the given algebraic expression x²+15x+24y+10, the constant term is 10.
Hence, the constant term in the given expression is 10.
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Elaine is starting at point A, she wants to get to point B. She is only allowed to move along the arrows, how many different paths could she take?
if we count the paths we have:
1. A to B the top part
2. Ato B the bottom part
3. we look after that A first top arrow, down one arrow and a straight line
and so on
i counted 12 different ways
Erika needs a test average of 85 or higher to make the honor roll. • There are four tests in the term. • Her first three test grades were 78, 80, and 88. Which inequality could be used to find what she needs to score on her fourth test, x, in order to make the honor roll?
Answer:
[tex]x\ge94[/tex]Explanation:
Average test score is expressed using the formula;
Average = Sum of the grades/Total number of test
Let x be the grade of the fourth test.
If Erika needs a test average of 85 or higher to make the honor roll, this can be expressed as;
[tex]\frac{78+80+88+x}{4}\ge85[/tex]Cross multiply
[tex]\begin{gathered} 78\text{ + 80 + 88 +x }\ge4\cdot85 \\ 246\text{ + x}\ge340 \end{gathered}[/tex]Subtract 246 from both sides
[tex]\begin{gathered} 246\text{ + x-246}\ge340-246 \\ x\ge94 \end{gathered}[/tex]Hence the inequality that could be used to find what she needs to score on her fourth test, in order to make the honor roll is
[tex]x\ge94[/tex]the life expectancy of a circulating coin is 30 years. the life expectancy of a circulating dollar bill is only 1/20 as long. find the life expectancy of circulating paper money. Life expectancy= how many years ( type a whole number or a mixed number simplify your answer)
Given
the life expectancy of a circulating coin is 30 years
the life expectancy of a circulating dollar bill is only 1/20 as long.
Procedure
c=life expectancy of a circulating coin
p= life expectancy of circulating paper money
[tex]p=\frac{1}{20}\cdot c[/tex][tex]\begin{gathered} p=\frac{1}{20}\cdot30 \\ p=\frac{30}{20} \\ p=1.5 \end{gathered}[/tex]The answer is: life expectancy of a dollar bill = 1.5 years
I need to find the exact area of the sector.
please help I will give a good review.... can you help me with these two questions
When a system of equations has infinite solutions, you'll end up with a statements that's true no matter what. For example, 6=6. Or when the graphs of the equations are the same exact line.
Then:
3x+4y=12 and
6x+8y=24 divided by 2: 3x+4y=12. That means they are the same exact line, so it has infinite solutions.
[tex]\begin{gathered} 3(2x+y)=24 \\ 6x+3y=24 \\ y=-6x+24\text{ dividing by 3} \\ y=-2x+8 \end{gathered}[/tex]The answer would be the first one and the third one.
Determine the perimeter of kite NITE below where EB = 40 feet and BI = BN= 9. Round your answer to the nearest hundredth necessary.BE
From the basic knowledge of pythagoras thorem,
EH
X ^2 = 40^2 + 9^2 = 1`600 + 81 = 1681
X = square root of 1681
= ET = EH = X = 41 feet
NI
y ^ 2 = 9 ^2 + 9^2 = 81 + 81 = 162
y = square root of 162
NI = T I = y = 12.72 feet
The perimeter of the Kite = EN + ET + NI + TI = 41 + 41 + 12. 72 + 12. 72 = 107.44 feet
TyR Match the name of each figure on the left with the best description on the right. a quadrilateral with rectangle one set of parallel sides a quadrilateral with four congruent sides trapezoid a quadrilateral with two pairs of parallel sides square a quadrilateral with four right angles rhombus a quadrilateral with four right angles and four congruent sides parallelogram
Parallelogram---->a quadrilateral with two pairs of parallel sides
Square----> a quadrilateral with four right angles and four congruent sides
Rectangle----> a quadrilateral with four right angles
Trapezoid----> . a quadrilateral with one set of parallel sides
Rhombus-----> a quadrilateral with four congruent sides
Answer: here
Step-by-step explanation:
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231 students of the Brooklyn Public Library went on a field trip. Some students rode in vans that hold 7 students each, and some students rode in buses that hold 25 students each. How many of each type of vehicle did the students ride in if there were 15 total vehicles? *
We have the next information
In total, we have 231 students
van--- 7 students
bus - 25 students
in total, we have 15 vehicles
So our first equation is
x+y=15
where
x is the number of vans
y is the number of buses
The second equation is
7x+25y=231
so we will isolate the x of the first equation
x=15-y
then we substitute this equation in the second equation
7(15-y)+25y=231
105-7y+25y=231
then we sum like terms
18y=126
then we isolate the y
y=126/18
y=7
Then for the value of x we use the equation with the x isolate and we substitute the value of y
x=15-7=8
Therefore the answer is 8 vans and 7 buses
Angela has 3 gallons of milk. How many quarts of milk does she have?- word problem
Angela has 12 quartz of milk
Explanations:Note:
1 gallon = 4 quartz
3 gallons of milk = (3 x 4) quartz
3 gallons of milk = 12 quartz of milk
Therefore, Angela has 12 quarz of milk
Solve the inequality and graph the solution on the line provided. -2 + 6x > 34 Л ^ < OT Inequality Notation: Number Line: 8 12 6 2 10 -8 -2 0 4 -6 -12 -10 -4 Click and drag to plot line. Submit Answer at
The inequality to solve is:
[tex]-2+6x>34[/tex]We can take the numbers to one side and variables to one and solve for x. Shown below:
[tex]\begin{gathered} -2+6x>34 \\ 6x>34+2 \\ 6x>36 \\ x>\frac{36}{6} \\ x>6 \end{gathered}[/tex]This is the solution
x > 6Graphing this on a number line would look something like this:Note: the open circle in '6' means the number six isn't included.
The equation yˆ=−0.37x^2+6.15x+52.3 approximates the average temperature in October in degrees Fahrenheit at an agricultural community x hours after 5 a.m.What is the best estimate for the average temperature in October at 9 a.m.?64°F67°F71°F78°F
So we have the equation:
[tex]y=-0.37x^2+6.15x+52.3[/tex]Where x represents the hours passed after 5 am and y represents the temperature in degrees Fahrenheit. We are being asked about the temperature at 9 am so we need to express 9 am in terms of hours passed after 5 am. Since there's a difference of 4 hours between this two times then we must use x=4 and the result of substituting x by 4 in the former equation will give us the temperature we are looking for:
[tex]y_{(4)}=-0.37\cdot4^2+6.15\cdot4+52.3=70.98[/tex]So the temperature in october at 9 am is 70.98°F so the best approximation would be option C, 71°F.
What is the value of x? R 2x+880 Q 78° 8x-940 X+790 s T
We have here that all of these angles must sum 360 degrees since we have here a circle. Then, we have that:
[tex]2x+88+8x-94+x+79+78=360[/tex]Now, to solve this equation, we need to group and sum the like terms:
[tex]2x+8x+x+88-94+79+78=360_{}[/tex][tex]11x-6+157=360\Rightarrow11x+151=360[/tex]To isolate 11x, we need now to subtract 151 to both sides of the equation:
[tex]11x+151-151=360-151\Rightarrow11x=209[/tex]Divide both sides of the equation by 11:
[tex]\frac{11x}{11}=\frac{209}{11}\Rightarrow x=19[/tex]We can check this solution if we substitute the value x = 19 in the original equation (after the simplification process):
[tex]11x+151=360\Rightarrow11\cdot(19)+151=360\Rightarrow209+151=360\Rightarrow360=360[/tex]Since the last result is TRUE, then the value for x = 19 is the correct solution.
In summary, the value for x = 19.
List every way possible to prove that two triangles are congruent (ASA, SSS, etc.,), including a sketch of each scenario, with the proper marks to show congruence.
Given
triangles
Find
List every way possible to prove that two triangles are congruent
Explanation
1) SSS congruence (Side - side - side)
when all corresponding sides of the two triangles are equal.
then ,
[tex]\Delta ABC\cong\Delta PQR[/tex]b) SAS congruence (Side - Angle - Side)
when two sides and one angle are equal.
then ,
[tex]\Delta ABC\cong\Delta PQR[/tex]c) ASA congruence (Angle - side - angle)
when two angles and one side are equal
[tex]\Delta ABC\cong\Delta PQR[/tex]d) RHS (right - hypotenuse - side)
in two right triangles when hypotenuse and one side are equal.
then ,
[tex]\Delta ABC\cong\Delta DEF[/tex]Final Answer
Hence , there are four possible ways to prove the triangles are congruent.
2 angles are Supplementary. One angle has a measure that is 5 times the other Angle. Type in the measure of the bigger angle.
Step 1: Let's recall that Supplementary angles are two angles with a sum of 180∘
Step 2: Let's write the equation to solve the problem.
• Let x to represent the smaller angle,
,• Let 5x to represent the bigger angle
Therefore, we have:
x + 5x = 180
6x = 180
Dividing by 6 at both sides:
6x/6 = 180/6
• x = You can calculate the value of x dividing 180 by 6 and that is the measure of the smaller angle.
,• 5x = You multiply the value of x by 5 and that's the measure of the bigger angle.
Don't forget that the sum of both angles should be 180.
Function A is represented by the equation y=-2x + 1.Function B is a linear function that goes through the points shown inthe table.x 1346y 19 13 21Which statement correctly compares the rates of change of the twofunctions?O A. The rate of change of function A is-2The rate of change of function B is 4.O B. The rate of change of function A is 1.The rate of change of function B is 8.C. The rate of change of function A is 1.The rate of change of function B is 4.D. The rate of change of function A is-2The rate of change of function B is 8.
In linear functions, the rate of change is equivalent to the slope of the line. In function A we already now the slope intercept equation, which means that we already now the slope of the function.
In this case, the slope of function A is -2 so is the rate of change.
To find the rate of change of function B, we need to use 2 of the ordered pairs in the formula to find the slope of a line:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Let's choose two of the given ordered pairs and replace for them in the formula. We are going to use (1,1) and (3,9):
[tex]m=\frac{9-1}{3-1}=\frac{8}{2}=4[/tex]The slope of function B is 4 so is the rate of change.
In conclusion, the correct choice is A. The rate of change of function A is -2. The rate of change of function B is 4.
What form is the following number in standard form or scientific notation? 0.0000000008
Help! Solve the equation and show all work. Use Quadratic Formula
Using quadratic formula:
[tex]x\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex][tex]\begin{gathered} \text{where a = 1, b = -6, c = 34} \\ x\text{ = }\frac{-(-6)\text{ }\pm\sqrt[]{(-6)^2-4(1)(34)}}{2(1)} \\ x\text{ = }\frac{6\text{ }\pm\sqrt[]{36-132}}{2} \\ x\text{ = }\frac{6\pm\sqrt[]{-96}}{2} \end{gathered}[/tex][tex]\begin{gathered} x\text{ = = }\frac{6\pm\sqrt[]{-1\times96}}{2} \\ In\text{ }comple\text{ }xnumber,-1=i^2 \\ x\text{ = = }\frac{6\pm\sqrt[]{i^2\times16\times6}}{2} \\ x\text{ = }\frac{6\pm4\text{ i }\sqrt[]{6}}{2}\text{ } \\ x\text{ = }\frac{2(3\pm2\text{ i }\sqrt[]{6})}{2}\text{ } \\ x\text{ = }3\pm2\text{ i }\sqrt[]{6} \end{gathered}[/tex][tex]x\text{ = }3+2\text{ i }\sqrt[]{6}\text{ or x = }3-2\text{ i }\sqrt[]{6}[/tex]21 pointUse the given information to complete the proof of the following theorem.If a quadrilateral is a parallelogram, then its opposite sides are congruent.By definition, a parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.Use this definition in your proof.angle-side-angleCorresponding parts of congruent triangles are congruent.side-angle-sideOpposite sides of a parallelogram are congruent.
The Solution:
Required:
To prove that opposite sides are congruent in a parallelogram.
Step 1:
Draw a parallelogram.
Step 2:
[tex]DB\cong DB\text{ \lparen Reason: Reflexive property\rparen}[/tex]Step 3:
[tex]AB\parallel CD\text{ and BC }\parallel AD\text{ \lparen Reason: Definition of a parallelogram\rparen}[/tex]Step 4:
[tex]\angle1\cong\angle4\text{ and }\angle2\cong\angle3\text{ \lparen Reason: Alternative angles are equal.\rparen}[/tex]Step 5:
[tex]\angle ABD\cong\angle CDB\text{ \lparen Reason: Angle-Side-Angle \lparen ASA\rparen Theorem\rparen}[/tex]Step 6:
[tex]undefined[/tex]Hello I’ve been trying to solve this but have no luck :(
1. Domain, x ∈ [-9 , 8]
2. Range, y ∈ [-10 , 10]
3. f(x) is not an increasing function, its a decreasing function.
4. f(x) is decreasing for interval, x ∈ [-9,2] ∪ [7,8]
5. f(x) is constant function for the interval, x ∈ [2,7]
Domain:- The value of x for which function f(x) is defined
Range : the value of y or f(x)
Increasing function: while increasing the value of x, f(x) is increasing and vice versa, called increasing function.
Decreasing function: while increasing the value of x, f(x) is decreasing and vice versa, called increasing function.
From graph,
It seems very clear that,
1. Domain :-
x ∈ [-9 , 8]
or -9 ≤ x ≤ 8
2. Range :-
y ∈ [-10 , 10]
or -10 ≤ x ≤ 10
3. Interval for which f(x) is increasing :-
f(x) is not an increasing function, its a decreasing function.
4. Interval for which f(x) is decreasing:-
f(x) is decreasing for interval,
x ∈ [-9,2] ∪ [7,8]
5. Interval for which f(x) is constant function
f(x) is constant function for the interval,
x ∈ [2,7]
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Solve Equation: 12(x-2.3)= 15.6 Help
To solve for x you can first divide by 12 into both sides of the equation, like this
[tex]\begin{gathered} \frac{12\mleft(x-2.3\mright)}{12}=\frac{15.6}{12} \\ x-2.3=1.3 \end{gathered}[/tex]Now, you can add 2.3 from both sides of the equation
[tex]\begin{gathered} x-2.3+2.3=1.3+2.3 \\ x=3.6 \end{gathered}[/tex]Therefore, the value of x that satisfies the equation is
[tex]x=3.6[/tex]Finally, to check that this value satisfies the given equation, just plug x = 3.6 into the equation and see that a true proposition is reached. So, you have
[tex]\begin{gathered} 12\mleft(x-2.3\mright)=15.6 \\ \text{ Replace x = 3.6} \\ 12(3.6-2.3)=15.6 \\ 12(1.3)=15.6 \\ 15.6=15.6 \\ \text{ True proposition} \end{gathered}[/tex]Solve the following system of equations by graphing and state whether the system is dependent, independent, or consistent. 1/2x + 3/4y = 12x - 3y = 4
We have to solve the following system of equations:
[tex]\begin{gathered} \frac{1}{2}x+\frac{3}{4}y=1 \\ 2x-3y=4 \end{gathered}[/tex]We have to graph the equations and, as they are written in standard form, we are going to calculate the intercepts for both.
We will write the equations in slope-intercept form.
For the first equation we have:
[tex]\begin{gathered} \frac{1}{2}x+\frac{3}{4}y=1 \\ \frac{3}{4}y=-\frac{1}{2}x+1 \\ y=\frac{4}{3}(-\frac{1}{2}x+1) \\ y=-\frac{2}{3}x+\frac{4}{3} \end{gathered}[/tex]For the second equation we have:
[tex]\begin{gathered} 2x-3y=4 \\ 2x-4=3y \\ y=\frac{1}{3}(2x-4) \\ y=\frac{2}{3}x-\frac{4}{3} \end{gathered}[/tex]Both slopes are different, what means that the lines are not parallel and will intersect, so we already know that the system is independent.
Using the slopes and the y-intercepts, we can graph the equations as:
The solution to the system is the intersection point which is (2,0).
Answer:
The system is independent and its solution is (x,y) = (2,0)
You must do this one by hand. No desmos!!! Find the solution to the following system of equations:
The equations are given
[tex]\begin{gathered} -5x+y=-5\ldots\ldots\ldots\ldots1 \\ -4x+2y=2\ldots\ldots\ldots\ldots\ldots\text{.}.2 \end{gathered}[/tex]ExplanationTo determine the coordinates of x and y by elimination method.
Divide equation 2 by 2.
[tex]\begin{gathered} -\frac{4x}{2}+\frac{2y}{2}=\frac{2}{2} \\ -2x+y=1\ldots\ldots\ldots\ldots..3 \end{gathered}[/tex]Now subtract equation 1 by 3,
[tex]\begin{gathered} (-5x+y+5)-(-2x+y-1)=0 \\ -5x+y+5+2x-y+1=0 \\ -3x+6=0 \\ x=2 \end{gathered}[/tex]Substitute the value of x in the equation 1.
[tex]\begin{gathered} -5\times2+y=-5 \\ -10+y=-5 \\ y=5 \end{gathered}[/tex]AnswerThe solution of the system of equations is [tex](2,5)[/tex]The correct option is A.
subtract the following polynomials2x−6 and 7 x ^2 + 6 x + 4as well as7 x ^2 + 6 x + 4 and 2x-6
We are given the following polynomials:
[tex]\begin{gathered} 2x-6 \\ 7x^2+6x+4 \end{gathered}[/tex]Now, we subtract the second polynomial from the first:
[tex]2x-6-(7x^2+6x+4)[/tex]Now, apply the distributive property on the parenthesis. To do that we change the sign of each of the terms inside:
[tex]2x-6-7x^2-6x-4[/tex]Now, we associate like terms.:
[tex](2x-6x)+(-6-4)-7x^2[/tex]Now, we solve the operations of the like terms:
[tex]-4x-10-7x^2[/tex]Since we can't simplify any further this is the final answer.
I need help solving the linear system I need to create an ordered pair
To create the ordered pairs you need to pic any value of x and look what the corresponding value fo y is.
For the point where both linear dunctions cross each other the value in the x-axis is x= 2 and the value in the y-axis is y=7
A scientist uses the equation shown below to predict the future population of a species. In the equation, y represents the estimated population and t represents the number of years.
1200
Explanation:y represents the estimated population
t represents the number of years.
The equation that predicts the population after t years is given as:
[tex]y=150\times4^t[/tex]Substitute t = 3/2 into the equation
[tex]\begin{gathered} y=150\times4^{\frac{3}{2}} \\ y=150\times2^{2(\frac{3}{2})} \\ y=150\times2^3 \\ y=150\times8 \\ y=1200 \end{gathered}[/tex]The closest valuie to the value of y is 1200
Question 5 Find the area of the parallelogram shown belo 44