Answer:
(a) D = 5/8 in
(b) A = 31.2 cm
(c) B = 8 ft
(d) C = 3 m
Explanation:
If two triangles are similar, their corresponding sides are proportional, so we can always use the following equation:
[tex]\frac{A}{B}=\frac{C}{D}[/tex]Therefore, for row (a), we can write the following equation:
[tex]\frac{5\frac{1}{2}}{1\frac{1}{4}}=\frac{2\frac{3}{4}}{D}[/tex]So, changing the mixed number by decimals and solving for D, we get:
[tex]\begin{gathered} \frac{5.5}{1.25}=\frac{2.75}{D} \\ 5.5D=2.75(1.25) \\ 5.5D=3.4375 \\ \frac{5.5D}{5.5}=\frac{3.4375}{5.5} \\ D=0.625 \end{gathered}[/tex]Then, for row (a), D = 0.625 = 5/8
In the same way, we can write and solve the following equation for row (b)
[tex]\begin{gathered} \frac{A}{23.4}=\frac{20.8}{15.6} \\ \frac{A}{23.4}\times23.4=\frac{20.8}{15.6}\times23.4 \\ A=31.2 \end{gathered}[/tex]For row (c), we get:
[tex]\begin{gathered} \frac{12}{B}=\frac{9}{6} \\ 12(6)=9(B) \\ 72=9B \\ \frac{72}{9}=\frac{9B}{9} \\ 8=B \end{gathered}[/tex]For row (d), we get:
[tex]\begin{gathered} \frac{4.5}{3.6}=\frac{C}{2.4} \\ \frac{4.5}{3.6}\times2.4=\frac{C}{2.4}\times2.4 \\ 3=C \end{gathered}[/tex]Therefore, the answers are:
(a) D = 5/8 in
(b) A = 31.2 cm
(c) B = 8 ft
(d) C = 3 m
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)
In the above graph of y = f( x ), find the slope of the secant line through the points ( -4, f( -4 ) ) and ( 1, f( 1 ) ).
Answer:
slope = 3 / 5
Explanation:
First, let us note from the graph that
[tex]f(-4)=1[/tex]and
[tex]f(1)=4[/tex]Therefore, the two points that lie on the secant line are
[tex]\begin{gathered} (-4,1) \\ (1,4) \end{gathered}[/tex]The slope of the line (the secant) passing through these two points is
[tex]slope=\frac{4-1}{1-(-4)}[/tex][tex]=\frac{3}{5}[/tex][tex]\boxed{slope=\frac{3}{5}\text{.}}[/tex]Hence, the slope of the secant is 3/5.
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]what are the solutions of the equation 2x ^ 2 equals 18 use a group of related function whose group answers the question
The given expression is :
[tex]2x^2=18[/tex]Simplify the equation for x :
[tex]2x^2=18[/tex]Divide both side by 2 :
[tex]\begin{gathered} \frac{2x^2}{2}=\frac{18}{2} \\ x^2=9 \end{gathered}[/tex]taking square root on both side :
[tex]\begin{gathered} x^2=9 \\ \sqrt[]{x^2}=\sqrt[]{9} \\ x=\pm3 \end{gathered}[/tex]Answer :
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]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]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 help with this practice problem solving My attempted answer is in the pic, though I am not sure if I am correct or not
Solution
To convert from polar coordinate to rectangular coordinate,
[tex]\begin{gathered} (r,\theta)\to(r\cdot\cos \theta,r\cdot\sin \theta) \\ \\ \Rightarrow(3\sqrt[]{5},-\frac{\pi}{8})\to(3\sqrt[]{5}\cdot\cos (-\frac{\pi}{8}),3\sqrt[]{5}\cdot\sin (-\frac{\pi}{8})) \\ \\ \Rightarrow(3\sqrt[]{5}\cdot\cos (-\frac{\pi}{8}),3\sqrt[]{5}\cdot\sin (-\frac{\pi}{8}))=(6.20,-2.57) \end{gathered}[/tex]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.
Find the value of r in the equation below.11 = = 12
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]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.
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.
Add the rational expressions and type your answer in simplest form. When typing your answers, type your terms with variables in alphabetical order without any spaces between your characters. \frac{\left(c+2\right)}{3}-\frac{\left(c-4\right)}{4} The numerator is AnswerThe denominator is Answer
Solve the operation between rationals, proceed as if they were numerical fractions:
[tex]\begin{gathered} \frac{c+2}{3}-\frac{c-4}{4} \\ \frac{4(c+2)-3(c-4)}{12} \\ \frac{4c+8-3c+12}{12} \\ \frac{c+20}{12} \end{gathered}[/tex]According to this:
The numerator is c+20
The denominator is 12
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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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
how do I find a unit rate for graphs
Unit rate of graph can be calculated by finding the slope of the graph or by dividing it's change in 'y' to the change in 'x' .
Generally, for linear graph unit rate can be calculated by finding it's slope but for curve graph it can be done by dividing it's change in 'y' to the change in 'x'.
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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
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.
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 form is the following number in standard form or scientific notation? 0.0000000008
Find the midpoint for G(9, 7) , H(10, -7)
we have G(9, 7) , H(10, -7)
The formula to calculate the midpoint between two points is equal to
[tex]m(\frac{x1+x2}{2},\frac{y1+y2}{2}_{})[/tex]substitute the given coordinates
[tex]m(\frac{9+10}{2},\frac{7-7}{2}_{})[/tex][tex]m(9.5,0_{})[/tex]what is the slope of the line below?Show your work.
To be able to determine the slope, let's identify at least two points that pass through the graph and use it in the following formula:
[tex]\text{ Slope (m) = }\frac{y_2-y_1}{x_2-x_1}[/tex]Let,
Point A: x1, y1 = -4, -4
Point B: x2, y2 = 4, -4
We get,
[tex]\text{ Slope (m) = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\text{ = }\frac{-4\text{ - (-4)}}{4\text{ - (-4)}}[/tex][tex]\text{ = }\frac{-4\text{ + 4}}{4\text{ + 4}}[/tex][tex]\text{ = }\frac{0}{8}\text{ = 0}[/tex][tex]\text{ Slope (m) = 0}[/tex]Therefore, the slope of the line is 0.
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
Represent the following expressions as a power of the number a (a≠0): (a^5*a/a^-3)^-1
PLS HELP
We can simplify the given expression:
((a⁵*a)/(a⁻³) )⁻¹
To get:
a⁻⁹
How to simplify the expression?There are some properties we need to use:
xᵃ*xᵇ = xᵃ⁺ᵇ(xᵃ)ᵇ = xᵃ*ᵇx⁻ᵃ = 1/xᵃOur expression is:
((a⁵*a)/(a⁻³) )⁻¹
First we can simplify the numerator:
a⁵*a = a⁵⁺¹ = a⁶
((a⁶)/(a⁻³) )⁻¹
Using the third property we can also rewrite the denominator:
(1/a⁻³) = a³
Replacing that we get:
((a⁶)/(a⁻³) )⁻¹ = ((a⁶)*a³ )⁻¹ = (a⁶⁺³)⁻¹ = a⁻⁹
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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.
When solving the radical equation 2 + 20 + 11 = I, the values I =-1 and I = 7 are obtained. Determine if either of these values is a solution of the radical equation. Select the correct two answers. (1 point) Since substituting I = -1 into the original equation resulted in a true statement, I= -1 is a solution to this equation. Since substituting I = 7 into the original equation resulted in a false statement, I = 7 is a not solution to this equation. Since substituting I=-l into the original equation resulted in a false statement, r=-1 is not a solution to this equation. Since substituting I=7 into the original equation resulted in a true statement, I=7 is a solution to this equation.
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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in looking for 450% of 80 I am not sure what I am looking for
Given the expression 450% of 80, we are to evealuate it.
You must know that of means multiplication
Hence the expression becomes;
[tex]450\text{\%}\times\text{ 80}[/tex]Simplify:
[tex]\begin{gathered} =\frac{450}{100}\times80 \\ =\text{ }\frac{45}{10}\times80 \\ =45\times8\text{ } \\ =\text{ 360} \end{gathered}[/tex]Hence 450% of 80 will give 360
What is next in sequence 2 and 1/4, 2 and 3/4, 3 and 1/4 come in 3 and 3/4,
Given:
[tex]2\frac{1}{4},2\frac{3}{4},3\frac{1}{4},3\frac{3}{4},.......[/tex]Required:
To find the next term in the given sequence.
Explanation:
Clearly the given sequence is in arithmetic.
Therefore,
[tex]a_5=a+(n-1)d[/tex]Here,
[tex]\begin{gathered} a=2\frac{1}{4} \\ =\frac{9}{4} \\ \\ n=5 \\ \\ d=2\frac{3}{4}-2\frac{1}{4} \\ =\frac{11}{4}-\frac{9}{4} \\ =\frac{2}{4} \end{gathered}[/tex][tex]\begin{gathered} a_5=\frac{9}{4}+(5-1)\frac{2}{4} \\ \\ =\frac{9}{4}+2 \\ \\ =\frac{17}{4} \\ \\ =4\frac{1}{4} \end{gathered}[/tex]Final Answer:
The next term in the sequence is 4 1/4.