GeometryQuestion 5•For what values of the variables must ABCD be a parallelogram?
Answers
SOLUTION:
For parallelograms; opposite sides are congruent;
Thus;
[tex]\begin{gathered} 2y-12=y-2 \\ solving\text{ for y} \\ 2y-y=12-2 \\ y=10 \end{gathered}[/tex]The shorter opposite sides must be equal too, thus;
[tex]\begin{gathered} 2x+1=y+3 \\ substitute\text{ in y = 10} \\ 2x+1=10+3 \\ 2x+1=13 \\ 2x=12 \\ x=6 \end{gathered}[/tex]Thus, for the figure to be a parallelogram, x = 6 and y = 10
Related Questions
1. A cylindrical jar has a radius of 6 inches and a height of 10inches. The jar is filled with marbles that have a
volume of 20 in³. Use 3.14 for pi. Show work. Complete sentences.
a. What is the volume of the jar?
V= πr ² h
Answers
Using the formula of volume of cylinder, the volume of the jar is 1130.4 cube inches.
In the given question we have to find the volume of the jar.
From the question,
A cylindrical jar has a radius of 6 inches
So r=6 inches
A cylindrical jar has a height of 10 inches
So h=10 inches
The jar is filled with marbles that have a volume of 20 cube inches.
As we know that the volume of cylinder is
V=πr^2h
where V= volume of cylinder
r = radius
h= height
π=3.14
Putting the value
V=3.14*(6)^2*10
V=3.14*36*10
V=1130.4 cube inches
To learn more about volume of cylinder link is here
brainly.com/question/16134180
#SPJ1
The graph of f(x) = 2x is shown on the grid. (First attachment)
The graph of g(x) = (One-half)x is the graph of f(x) = 2x reflected over the y-axis. Which graph represents g(x)? (The rest of the attachments are the options)
Answers
The graph that represents the function g(x) = (1/2)^x is given as follows:
The last graph.
How to obtain the rule for function g(x)?The parent function f(x) has the definition presented as follows:
f(x) = 2^x.
The transformation that the function f(x) undergoes is defined as follows:
Reflection over the y-axis.
The rule that defines a function g(x) after a reflection of f(x) over the y-axis is given as follows:
g(x) = f(-x).
Hence the function g(x) is defined as follows:
g(x) = f(-x) = 2^(-x) = (1/2)^x.
As the negative exponent means that the base is inverted.
Then the graph of the exponential function has these following features:
Decreasing, as the base has an absolute value less than 1.Crosses the y-axis at y = 1, as when x = 0, y = (1/2)^0 = 1.Hence the last graph is the correct option.
More can be learned about reflections at https://brainly.com/question/28980122
#SPJ1
Only quadratic functions can be transformed. true or false
Answers
It is false, that only quadratic functions can be transformed.
Given that,
To justify the statement, "Only quadratic functions can be transformed."
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
It is not necessary that only quadratic functions can be transformed, all the functions can be transformed regardless of their nature such as linear functions, polynomial functions etc.
Thus, It is false, that only quadratic functions can be transformed.
learn more about function here:
brainly.com/question/21145944
#SPJ1
Multiply the two polynomials (3a² + 5a - 2)(5a² - 3a + 4)
Answers
SOLUTION
The polynomials expression given are
[tex]\mleft(3a^2+5a-2\mright)\mleft(5a^2-3a+4\mright)[/tex]Expand the expression by distributing the parentheses
[tex]3a^2\cdot\: 5a^2+3a^2\mleft(-3a\mright)+3a^2\cdot\: 4+5a\cdot\: 5a^2+5a\mleft(-3a\mright)+5a\cdot\: 4-2\cdot\: 5a^2-2\mleft(-3a\mright)-2\cdot\: 4[/tex]Simplify
[tex]\begin{gathered} 15a^4-9a^3+12a^2+25a^3-15a^2+20a-10a^2+6a-8 \\ \text{Rearranging and simplify} \\ 15a^4-9a^3+25a^3+12a^2-15a^2-10a^2+20a+6a-8 \\ 15a^4+16a^3-13a^2+26a-8 \end{gathered}[/tex]Hence, the answer is
[tex]15a^4+16a^3-13a^2+26a-8[/tex]Connor was given a box of assorted chocolates for his birthday. Each night, Connortreated himself to some chocolates. There were originally 18 chocolates in the boxand after 3 nights, there were 9 chocolates remaining in the box. Write an equationfor C, in terms of t, representing the number of chocolates remaining in the box tdays after Connor's birthday.
Answers
The equation for C in terms of t is C = 18 – 3t.
Algebra is the area of mathematics that aids in expressing issues or circumstances into mathematical expressions.
Given that Connor was given a box of assorted chocolates for his birthday
The box originally contained 18 chocolates.
There were still 9 chocolates in the box after three nights.
Now we have to find the equation for C in terms of t
18 – 9 = 9
After 3 nights
9 / 3 = 3
18 = chocolates at the beginning.
C = 18 – 3t
Therefore the equation for C in terms of t is C = 18 – 3t.
To learn more about algebra visit
https://brainly.com/question/21196212
#SPJ9
5. 2. A rectangular print is 36 inches long and 24 inches wide. It will be placed inside a rectangular frame that is 2 inches wide on all sides. What is the area when the print is inside the frame A. 864 in. B. 960 in? C. 980 in. D. 1,120 in.
Answers
Since the frame has 2 inches wide on all sides, the frame measures:
Then, the area of the frame is
[tex]\begin{gathered} A=\text{basexheight} \\ A=40\times28 \end{gathered}[/tex]which gives
[tex]A=1120in^2[/tex]then, the answer is 1120 inches squared, which corresponds to option D.
Light intensity (I) is proportional (a) to the inverse square of distance (d) of a subject from a lightsource. The relationship in intensities for subjects at different distances from the same source canbe likewise seen as a ratio or proportional relationship.I x 1 1A proportional relationship can be mathematically expressed as follows for light intensity (I) inlumens when a subject is at the light source.=Lumens at origin or sourceSo, if a light intensity (I) is 569 lumens at the source, what is the light intensity (I) at 9 distancefrom the source,?Round the value to the nearest tenth if necessary. You do not need to include a label for lumens.Only the number, rounded to the tenth, will be necessary.
Answers
ANSWER
The light intensity is 7.0
STEP-BY-STEP EXPLANATION:
What to find? The value of the proportionality constant.
Given parameters
• Light intensity = 569 lumens
,• Distance = 9
According to the question, Light intensity (I) is proportional to the inverse square of the distance.
This can be expressed mathematically as
Let the intensity of light be represented as I
Let the distance be represented as d
[tex]I\text{ }\propto\text{ }\frac{1}{d^2}[/tex]The next thing is to introduce a constant k
[tex]\begin{gathered} I\text{ = }\frac{K\cdot\text{ 1}}{d^2} \\ I\text{ = }\frac{K}{d^2} \end{gathered}[/tex]Recall that,
I = 569 lumens
d = 9
The next thing is to substitute the parameters into the above formula
[tex]\begin{gathered} \frac{Lumens\text{ at current distance}}{\text{Lumens at origin or source}}\text{ = }\frac{1}{d^2} \\ \frac{\text{Lumens at current distance}}{\text{5}69}\text{ = }\frac{1}{(9)^2} \\ \frac{\text{Lumens at current distance}}{\text{5}69}\text{ = }\frac{1}{81} \\ \text{Cross multiply} \\ 569\cdot\text{ }1\text{ = Lumens at current distance }\cdot\text{ 81} \\ \text{Divide both sides by 81} \\ \frac{569}{81}\text{ = }\frac{Lumens\text{ at current distance }\cdot\text{ 81}}{81} \\ \text{Lumens at current distance = 7.0} \end{gathered}[/tex]How many people did Trevor survey?
74
92
107
137
Answers
Answer:
92 I think because in my class I heard my friend tell me
There are 1.5 litres of water in a bottle.
There are 250 millilitres of water in another bottle.
Work out the total amount of water in the two bottles
Answers
Answer:
1.75 liters
Step-by-step explanation:
250 mililters is a quarter of 1 litre
In 1991, minimum wage was $4.25 per hour; in 1997, minimum wage increased in $5.15 per hour. Find the rate of change in the minimum wage per year from 1991 to 1997.
Answers
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
[tex]\begin{array}{|cc|ll} \cline{1-2} \stackrel{x}{year}&\stackrel{y}{wage}\\ \cline{1-2} 1991&4.25\\ 1997&5.15\\ \cline{1-2} \end{array} \hspace{5em} (\stackrel{x_1}{1991}~,~\stackrel{y_1}{4.25})\qquad (\stackrel{x_2}{1997}~,~\stackrel{y_2}{5.15}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5.15}-\stackrel{y1}{4.25}}}{\underset{run} {\underset{x_2}{1997}-\underset{x_1}{1991}}} \implies \cfrac{0.90}{6}\implies \cfrac{0.15}{1}\implies 0.15~\frac{\$}{year}[/tex]
The graphs of 3x + 9y = 15 and y = mx - 4
are parallel lines. What is the value of m?
Answers
The graph of equations [3x + 9y = 15] and [y = mx - 4] are not parallel and the value of m is 13/3.
What are graphs?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.Although 'graph' and 'chart' are sometimes used interchangeably, they are two separate types of images. Charts are tables, graphs, or images that concisely and clearly organize enormous volumes of data. Charts are used by people to forecast the future and evaluate existing facts. However, graphs emphasize the basic data and display changes over time.So, the graph of the equations:
3x + 9y = 15y = mx - 4The value of m:
y = mx - 4: Equation is in the form of the slope.Now,
y = mx - 49 = 3m - 4Now, solve for m as follows:
9 = 3m - 43m = 9+43m = 13m = 13/3Now, plot the graph as follows:
(Refer to the graph attached below)It is clearly visible that the lines of both equations are not parallel.
Therefore, the graph of equations [3x + 9y = 15] and [y = mx - 4] are not parallel and the value of m is 13/3.
Know more about graphs here:
https://brainly.com/question/28953186
#SPJ1
Given f(x)=3x^3 - 4x^2 + 2x - 1 and g(x) = x - 4, state the quotient and remainder of f(x)/g(x), in the form q(x) + r(x)/g(x)
Answers
Dividing f(x) = 3x³ - 4x² + 2x - 1 by g(x) = x - 4 will yield a quotient of q(x) = 3x² - 8x + 34 and a remainder of 135, that is (3x² - 8x + 34) + 135/(x - 4).
Calculating for the quotient and remainderApplying the long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder.
We shall divide the dividend f(x) = 3x³ - 4x² + 2x - 1 by the divisor g(x) = x - 4 as follows;
3x³ divided by x equals 3x²
x - 4 multiplied by 3x² equals 3x³ - 12x²
subtract 3x³ - 12x² from 3x³ - 4x² + 2x - 1 will result to 8x² + 2x - 1.
8x² divided by x equals 8x
x - 4 multiplied by 8x² equals 8x² - 32x
subtract 8x² - 32x from 8x² + 2x - 1 will result to 34x - 1.
34x divided by x equals 34
x - 4 multiplied by 34 equals 34x - 136
subtract 34x - 136 from 34x - 1. will result to a remainder of 135.
Therefore by the long division method, f(x) = 3x³ - 4x² + 2x - 1 divided by g(x) = x - 4 gives a quotient q(x) = 3x² - 8x + 34 with a remainder of 135.
Learn more about long division method here: https://brainly.com/question/25289437
#SPJ1
Compare: 4.3 x 10^6 O 12 x 10^5A.>B.
Answers
To check the bigger or smaller number, we can adjust the numbers such that they both have the same exponential power.
The first number can be written as shown below:
[tex]4.3\times10^6=4.3\times10\times10^5=43\times10^5[/tex]Now, both numbers have the same exponent. Therefore, we can compare the numbers 43 and 12.1.
Observation of the numbers on the number line shows that:
[tex]43>12.1[/tex]Therefore, we have that:
[tex]43\times10^5>12.1\times10^5[/tex]The correct option is OPTION A.
help meeeeeeeeee pleasee
Answers
Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]
i need help figuring out how to know which one goes where
Answers
Simplify each of the expressions
[tex]undefined[/tex]For a certain casino slot machine, the odds in favor of a win are given as 67 to 33. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive. The probability is ___
Answers
Data:
• Odds in favor of a win are given as 67 to 33.
Procedure
• We have to find the total sample (,T,), which can be calculated as follows:
[tex]T=67+33=100[/tex]Then, to calculate the probability, we have to divide the odds in favor of a win by T.
[tex]\frac{67}{100}=0.67[/tex]Answer: 0.67
ANSWER MY QUESTIONS PLEASE .........? A paddleboat can move at a speed of 14 kilometers per hour in still water. The boat is paddled 10 kilometers downstream in a river in the same time it takes to go 5 kilometers upstream. What is the speed of the river? Round your answer to the nearest tenth. AND A woman drives an SUV that gets 13 miles per gallon (mpg). Her husband drives a hybrid that gets 60 mpg. Every week, they travel the same number of miles. They want to improve their combined mpg. They have two options on how they can improve it.
Option 1: They can tune the SUV and increase its mileage by 1 mpg and keep the hybrid as it is.
Option 2: They can buy a new hybrid that gets 85 mpg and keep the SUV as it is.
Compute and state the combined mpg for each option. Round your answers to the nearest tenth. Then tell which option will give a better combined mpg.
Answers
Answer:
Step-by-step explanation:
the suv question the first option would make the suv go from 13 mpg to 14 mpg and add 14 to 60 to get 74 and divided by 2 to get 37 is their average mpg
Options two would make the hybrid 85 mpg and the suv still 13 add them together to get 98 and divide them by 2 to get 49
Option 2 will give more mileage
paddle boat question
10/14+x=5/14-x
Cross multiply
10(14-x)=5(14+x)
140-10x=70+5x
70=15x
70/15=x
X=4.7 is the speed of the current
Please don’t quote me on this paddle boat one XD
Hopes this helps
Clay has $50 on his bus pass and it’s $3.00 each time he rides. He will be able to ride the bus twice a day for 11 days? True or false?
Answers
Given that each bus ride is $3, and that assuming the takes the ride twice a day,
[tex]\begin{gathered} \text{Amount spent a day on bus ride = 2 }\times\text{ \$3} \\ =\text{ \$6} \end{gathered}[/tex]If he takes the ride in the same manner for 11 days,
[tex]\begin{gathered} \text{Amount spent in 11 days = 11 }\times\text{ \$6} \\ =\text{ \$ 66} \end{gathered}[/tex]Thus, he needs $66 to ride the bus twice for 11 days.
Since Clay has $50, he will not be able to ride the bus twice for 11 days.
Hence, the correct answer is False
What happens if the rate of change is not constant in a function?
Answers
Answer:
time will be a straight line, and you can find the rate of change by calculating the slope of the line. If the rate of change is not constant, a graph of the measured quantity vs. time will be curved instead of straight
Step-by-step explanation:
Answer:
When the rate of change is constant, the graph results in a straight line. When the rate of change is not constant, the graph will include a curved line.
Step-by-step explanation:
When using an equivalent fraction to find a percent why do you write 100 as the denominator?
Answers
We do so beacuse it is easy to convert a fraction to a percent when the denominator is 100.
What is equivalent fraction?Equivalent fractions are the fractions that have different numerators and denominators but are equal to the same value.
What is denominator?Denominator is the part of a fraction that is below the line and that functions as the divisor of the numerator.
What is percentage?A percentage or percent is a fraction that always has the denominator as 100.
When using an equivalent fraction to find a percent we write 100 as denominator.
If a fraction does not have a denominator of 100, you can convert it to an equivalent fraction with a denominator of 100, and then write the equivalent fraction as a percent.
We do so because it is easy to convert a fraction to a percent when the denominator is 100.
To know more about equivalent fractions, visit
https://brainly.com/question/1797146
#SPJ1
Find the slope (-19,12) (-9,1)
Answers
Answer:
m= -11/10
Step-by-step explanation:
Refer to formula m= y2-y1
x2-x1
1-12 = -11 (negative bc 1 comes first but is less than 12.)
Think of it as -12+1 it would be -11 going towards 0.
-9--19 = 10
Let ZD be an acute angle such that cos D = 0.64. Use a calculator to approximate the measure of ZD to the nearest tenthof a degree.m/D
Answers
Given:
[tex]\cos D=0.64[/tex]D is an acute angle
Find-:
The value of D
Explanation-:
The angle D is:
[tex]\begin{gathered} \cos D=0.64 \\ \\ D=\cos^{-1}(0.64) \\ \\ D=50.208 \end{gathered}[/tex]The value of the nearest tenth is 50.2
Clare has $102.38 in her savings account. At the ATM, she deposits 3 checks she received for her birthday. Each check was written for $15.00. Then, she withdraws $20 in cash. What is Clare's new account balance?
Answers
Answer:
127.38
Step-by-step explanation:
Answer:
127.38
Step-by-step explanation:
15 x 3 = 45
(102.38 + 45) - 20 = 127.38
To insure a house valued at £3000 costs £2.25. Find the value of a house which costs £3.37 1/2 to insure.
Answers
Using the cross-multiplication method, we know that the house which costs £3.37 has a value of £4,493.33.
What is a cross-multiply method?One might cross-multiply an equation between two fractions or rational expressions in mathematics, more specifically in elementary arithmetic and elementary algebra, to make the equation simpler or to find the value of a variable.When using the cross-multiplication approach, the denominator of the first term is multiplied by the numerator of the second term and vice versa.So, the value of the house costs £3.37:
House that costs £2.25 is valued at £3000.Now, use the cross-multiplication method as follows:
2.25/3000 = 3.37/x2.25x = 3000 × 3.372.25x = 10,110x = 10,110/2.25x = 4,493.33Therefore, using the cross-multiplication method, we know that the house which costs £3.37 has a value of £4,493.33.
Know more about a cross-multiply method here:
https://brainly.com/question/28839233
#SPJ1
Correct question:
To ensure a house valued at £3000 costs £2.25. Find the value of a house that costs £3.37.
solve 6/7 dividid 36/56 and put the answer in simplest form. A. 6/8 B. 8/6 C. 4/3 2/8
Answers
The correct answer is C. (4/3)
Fraction calculation steps:
6/7 ÷ 36/56 = 6/7 × 56/36 = (6×56)/(7×36) = 336/252
(336÷84)/(252÷84) = 4/3
Learn more about fraction here: brainly.com/question/78672
#SPJ1
Shannon invests money in a bank account which gathers
compound interest each year.
After 5 years there is $673.40 in the account.
After 8 years there is $737.99 in the account.
Work out the annual interest rate of the bank account.
Give your answer as a percentage to 1 d.p.
Answers
By using the concept of compound interest, rate of interest is 3.1 %
What is compound interest?
If the interest on a certain principal at a certain rate over a certain time increase exponentially rather than linearly, the interest earned is called Compound interest.
If the principal is P, rate is r and time is t, then amount is
[tex]A = P(1 + \frac{r}{100})^n[/tex]
Let the principal be $P and the rate be r% per annum
After 5 years there is $673.40 in the account.
[tex]673.40 = P(1 + \frac{r}{100})^5\\[/tex]............. (1)
After 8 years there is $737.99 in the account.
[tex]737.99 = P(1 + \frac{r}{100})^8[/tex] ................. (2)
Dividing (2) by (1),
[tex](1 +\frac{r}{100})^3 = 1.096\\\\1 + \frac{r}{100} = (1.096)^{\frac{1}{3}}\\\\1 + \frac{r}{100} = 1.031\\\\\frac{r}{100} = 1.031 -1\\\\\frac{r}{100} =0.031\\\\r = 0.031 \times 100\\[/tex]
r = 3.1 %
Rate is 3.1 %
To learn more about compound interest, refer to the link-
https://brainly.com/question/24274034
#SPJ13
6
Simplify the expression: (1318) + 24 ÷ 6
Answers
help meeeeeeeeeeeeeeeeeeee pleaseee rnnnn rn!!!!
Answers
The length of shorter feet is 2.5 ft and the length of longer feet is 6.5 ft.
By Pythagorean theorem,
[tex]( Hypotenuse)^{2} = (Base)^{2}+ (Perpendicular)^{2}[/tex]
Let base = x
perpendicular = x+4
Hypotenuse = 7
Putting the value in equation,
[tex]7^{2} = x^{2} +(x+4)^{2}[/tex]
[tex]49 = x^{2} +x^{2}+8x+16[/tex]
[tex]2x^{2} +8x+16-49=0[/tex]
[tex]2x^{2} +8x-33=0[/tex]
[tex]x = \frac{-8 + \sqrt{64 - 4(2)(-33)} }{2*2}[/tex] or [tex]\frac{-8 - \sqrt{64 - 4(2)(-33)} }{2*2}[/tex]
[tex]x=\frac{-8 + \sqrt{64 +264} }{4}[/tex] or [tex]\frac{-8 - \sqrt{64 +264} }{4}[/tex]
[tex]x = \frac{-8 + \sqrt{384} }{4}[/tex] or [tex]\frac{-8 - \sqrt{384} }{4}[/tex]
[tex]x = \frac{-8+18.1}{4}[/tex] or [tex]\frac{-8-18.1}{4}[/tex]
[tex]x = \frac{10.1}{4}[/tex] or [tex]\frac{-26.1}{4}[/tex]
[tex]x = 2.5[/tex] or [tex]-6.5[/tex]
As, length can't be negative, we will take x = 2.5
Therefore, x+ 4 = 2.5 + 4
= 6.5
Hence, the length of shorter feet is 2.5 ft and the length of longer feet is 6.5 ft.
Learn more about length on:
https://brainly.com/question/8552546
#SPJ1
Reflect the given coordinate points across the line y= x
Answers
Given the points:
[tex]\begin{gathered} B\colon(-3,-1) \\ C\colon(-3,3) \\ D\colon(0,3) \end{gathered}[/tex]We need to reflect the points over the line y = x
The rule of reflection is as follows:
[tex](x,y)\rightarrow(y,x)[/tex]So, the points after reflection will be:
[tex]\begin{gathered} B^{\prime}\colon(-1,-3) \\ C^{\prime}\colon(3,-3) \\ D^{\prime}\colon(3,0) \end{gathered}[/tex]Suppose you are the manager of a firm. The accounting department has provided cost estimates, and the sales department sales estimates, on a new product. Analyze the data they give you, determine what it will take to break even, and decide whether to go ahead with production of the new product The product has a production cost function C(x)=560x + 17,080 and a revenue function R(x) = 700xThe break-even quantity is ______units.
Answers
Consider that the break-even quantity is the one corresponding to which the profit is zero i.e. the production cost becomes equal to the revenue earned.
Equate the functions and solve for the break-even quantity as follows,
[tex]\begin{gathered} C(x)=R(x) \\ 560x+17,080=700x \\ 700x-560x=17,080 \\ 140x=17,080 \\ x=122 \end{gathered}[/tex]Thus, the break-even quantity is 122 units.