In a parallelogram, two adjacent sides are 2.c – 7 and 3x – 6. If the perimeter of the parallelogram is 34, find x and the shorter side of the parallelogram X= Shorter Side =
Answers
Given the information on the problem, we have the following parallelogram:
since the perimeter is 34, we can write the following equation:
[tex]2(3x-6)+2(2x-7)=34[/tex]solving for x, we get:
[tex]\begin{gathered} 2(3x-6)+2(2x-7)=34 \\ \Rightarrow6x-12+4x-14=34 \\ \Rightarrow10x-26=34 \\ \Rightarrow10x=34+26=60 \\ \Rightarrow x=\frac{60}{10}=6 \\ x=6 \end{gathered}[/tex]now that we have that x = 6, we can find the measure of the sides:
[tex]\begin{gathered} x=6 \\ 3(6)-6=18-6=12 \\ 2(6)-7=12-7=5 \end{gathered}[/tex]therefore, x = 6 and the shorter side measures 5 units
Related Questions
In the parallelogram below, if < A = 34 °, what is the measure of < D?
Answers
Given,
The measure of angle A is 34 degree.
Required
The measure of angle D.
It is given that, ABCD is a parallelogram.
According to the property of parallelogram , the opposite sides of the parallelogram are equal and parallel.
The sum of adjacent interior angle between two parallel line is 180 degree.
So,
[tex]\begin{gathered} \angle A+\angle D=180^{\circ} \\ 34^{\circ}+\angle D=180^{\circ} \\ \angle D=146^{\circ} \end{gathered}[/tex]Hence, the measure of angle D is 146 degree.
If carpeting costs R75,50/m and an entrance hall has a length of 468,cm. Determine the cost of carpenting the hallway?
Answers
The cost of carpeting the hallway is Rs. 35,334.
The cost of carpeting is Rs. 7,550 per meter. We have an entrance hall. The length of the entrance hall is 468 cm. We need to find out the total cost of carpeting the hallway.
First of all, we will convert all the quantities to the same units. The length of the entrance hall is 468/100 = 4.68 meters.
The total cost of carpeting the hallway is the product of the length of the hallway and the cost of carpeting per unit length. Let the cost be represented by the variable "C".
C = Rs. 7,550*4.68
C = Rs. 35,334
Hence, the cost of carpeting the hallway is Rs. 35,334.
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Which strategy could you apply to find the distance between any two numbers on the number line? ©MPS
Answers
To find the distance between any two numbers on the number line you have to subtract the smallest to the greatest
Use the distributive property to expand the expression 3(-3a+4)
Answers
In this case, given 3(-3a+4), -4a+4 are all being multiplied because they are inside the parenthesis. 3 is multiplying-3a+4. So, let’s expand:
3(-3a+4)
3(-3a)+3(4)
-9a+12 is the simplified expression using the distributive property.
write each measure in radians and express the answer in terms of π4. 315 degrees 5. -450 degrees
Answers
The equivalent measure of (315) degrees in radians will be (7π/4) rads.
As per the question statement, we are provided with an angular measure of 315 in the units of degrees,
And we are required to convert the above mentioned angular measure into it's equivalent unit of radians.
To solve this question, first we need to know about the relation between the two units of angular measure, degrees and radians, which goes as,
[180° = (π) rads]
Now using the unitary method and the above conversion reference point, we get,
[180° = (π) rads]
Or, [1° = (π/180) rads],
And, [315° = {(π/180) * 315} rads]
Or, [315° = {π * (315/180)} rads]
Or, 315° = [π * {(5 * 7 * 3 * 3)/(3 * 3 * 4 * 5)} rads]
Or, [315° = {π * (7/4)} rads]
Or, [315° = (7π/4) rads]
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hello I'm confused on this question and need help thank you
Answers
Given the data:
36, 14, 18, 18, 34
Let's find the standard deviation of the sample distances.
To find the standard deviation, apply the formula:
[tex]S=\sum_{i\mathop{=}1}^n\sqrt{\frac{(x_i-x_{avg})^2}{n-1}}[/tex]Where:
n = 5
Let's first find the average/,mean:
[tex]\begin{gathered} avg=\frac{36+14+18+18+34}{5} \\ \\ avg=\frac{120}{5} \\ \\ avg=24 \end{gathered}[/tex]The mean of the sample is 24.
Now, to find the standard deviation, we have:
[tex]\begin{gathered} S=\sqrt{\frac{(36-24)^2+(14-24)^2+(18-24)^2+(18-24)^2+(34-24)^2}{5-1}} \\ \\ S=\sqrt{\frac{(12)^2+(-10)^2+(-6)^2+(-6)^2+(10)^2}{4}} \\ \\ S=\sqrt{\frac{144+100+36+36+100}{4}} \\ \\ S=\sqrt{\frac{416}{4}} \\ \\ S=\sqrt{104} \\ \\ S=10.20 \end{gathered}[/tex]Therefore, the standard deviation of the given sample distances is 10.20
ANSWER:
10.20
The line y-5= 9/7(x + 4) is graphed in the coordinate plane. Complete the sentences below describing this process. By inspecting the equation, the graph of the line has a slope of.............
Answers
We have a line with equation:
[tex]y-5=\frac{9}{7}(x+4)[/tex]The expression of the line is the slope-point form, that is:
[tex]y-y_0=m(x-x_0)[/tex]where (x0,y0) is a point of the line and m is the slope.
As in this case, m = 9/7, then the slope is 9/7.
By inspecting the equation, the graph of the line has a slope of 9/7.
We also know that (x0,y0) = (-4, 5), that belong to the line.
By inspecting the equation the graph of the line passes through the point (-4, 5).
To find the value of y(3) we replace x with the value 3:
[tex]\begin{gathered} y-5=\frac{9}{7}(3+4)=\frac{9}{7}\cdot7=9 \\ y-5=9 \\ y=9+5 \\ y=14 \end{gathered}[/tex]The value of y(3) is 14. The point is (3, 14).
What is the slope of the line segment?15129601 2 3 4 50-30-303
Answers
Ok, so:
To find the slope of the segment, we have to take two points:
Let's take: A(2,6) and B(1,3).
We calculate the slope as this:
m =( ( y2 - y1 ) / ( x2 - x1 )).
Where A( x1, y1) and B( x2, y2) are the points we took.
Then, m = (3 - 6) / (1-2), this is m = -3/-1, and that's equal to m=3
divide the question(4.8x10^9)/(2.0x10^3)
Answers
We operate as follows:
[tex]\frac{4.8\cdot10^9}{2.0\cdot10^3}=2400000[/tex][tex]=2.4\cdot10^6[/tex]Given that sine = 0.87, using sin²0 + cos²0 = 1,
find cose (in Quadrant I). Show all your work for
credit - answer given to three decimal
approximation.
Answers
Work Shown:
[tex]\sin^2(\theta)+\cos^2(\theta)=1\\\\\cos^2(\theta) = 1-\sin^2(\theta)\\\\\cos(\theta) = \sqrt{1-\sin^2(\theta)} \ \ \ \text{.... cosine is positive in Q1}\\\\\cos(\theta) = \sqrt{1-(0.87)^2}\\\\\cos(\theta) \approx 0.4930517\\\\\cos(\theta) \approx 0.493\\\\[/tex]
can you please help with the 2 column proofs. It is not a test/quiz
Answers
COnsider the figure,
Two triangles are said to be congruent if all their three sides and three angles are equal.
SInce angle K and N are both right angles, we have,
[tex]<\text{MKL}=<\text{MNL}[/tex]The side ML is the shared side, and hence equal for both the triangles.
SInce LM bisects angle KLN, we have,
[tex]<\text{KML}=<\text{NML}[/tex]Thus, from AAS theorem ( stands for Angle-angle-side), when two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.
Hence the triangles are congruent.
solve for x y and z.
Answers
let us find z
[tex]\begin{gathered} \cos 30=\frac{adjacent}{\text{hypotenuse}} \\ \cos 30=\frac{z}{24} \\ z=24\cos 30 \\ z=20.7846096908 \\ z=20.8 \end{gathered}[/tex]let us find x.
[tex]\begin{gathered} \sin 30=\frac{\text{opposite}}{\text{hypotenuse}} \\ \sin 30=\frac{\text{height}}{24} \\ height=24\sin 30 \\ \text{height}=12 \\ \\ \cos 45=\frac{adjacent}{\text{hypotenuse}} \\ \cos 45=\frac{12}{x} \\ x=\frac{12}{\cos 45} \\ x=\frac{12}{0.70710678118} \\ x=16.9705627485 \\ x=17.0 \end{gathered}[/tex]let us find y
[tex]\begin{gathered} \tan 45=\frac{opposite}{\text{adjacent}} \\ \tan 45=\frac{y}{12} \\ y=12\tan 45 \\ y=12.0 \end{gathered}[/tex]Alyssa spins a spinner with 10 sections of equal size. Each section is colored either blue, green, orange, or red. Alyssa spins the spinner 80 times
The results of the spins are shown.
Color
Number of Spins 16 8
Blue Green Orange Red
16
40
Move numbers to the table to show how many sections of each color are most likely on the spinner.
Color
Number of Sections
Blue Green Orange Red
2
3
4
5
6
Answers
Answer:
Answered below with assumption of numbers
Step-by-step explanation:
Using blue = 16 green = 8 orange = 16 red = 40
40/80 or 1/2 is red 1/2 * 10 = 5 sections
16 / 80 or 1/5 is blue or orange = 1/5 * 10 = 2 each
then the rest are green 8 out of 80 or 1/10 = 1
The sum of the measures of angle M and angle R is 90°. The measure of angle M is (5x + 10)". The measure of angle R is 55° What is the value of x? Record your answer. Be sure to use the correct place value. B I UE E х, х? KY
Answers
Given data:
The given angle M is ∠M=(5x+10)°.
The given angle R is ∠R=55°.
The expression for the sum of both the angles is,
[tex]\angle M+\angle R=90^{\circ}[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} (5x+10)^{\circ}+55^{\circ}=90^{\circ} \\ 5x=25^{\circ} \\ x=5^{\circ} \end{gathered}[/tex]Thus, the value of x is 5 degrees.
a sphere has a diameter of 3.5 inches what's the volume?
Answers
Solution
[tex]\begin{gathered} D\text{ = 3.5} \\ r\text{ = }\frac{D}{2}\text{ = }\frac{3.5}{2}\text{ = 1.75} \\ \text{Volume of a sphere = }\frac{4}{3}\times\pi\times r^2 \\ \text{ =}\frac{4}{3}\times\frac{22}{7}\times(1.75)^2^{} \\ \text{ =}\frac{26.95}{21}\text{ =12.83} \end{gathered}[/tex]Final Answer = 12.83
a offers three kinds of meat toppings and 17 * a vegetable topping and how many different ways could you select a meat topping or a vegetable topping
Answers
Since this restaurant offers three types of meat toppings and seventeen types of vegetable toppings we can use the fundamental counting principle to determine the number of possible outcomes. This is done below:
[tex]3\cdot(17)=51[/tex]We could select 51 possible combinations of meat and vegetable toppings.
how do you find a vertex in intercept form
Answers
Quadratic functions can be written in vertex form, or
[tex]y=a\mleft(x-h\mright)^2+k[/tex]This is especially useful because the vertex of the function is found at the point (h, k).
We can find this form by completing squares, for instance, let y be:
[tex]y=x^2+bx+c[/tex]we can see that this equation is equal to
[tex]y=x^2+2(\frac{b}{2})x+(\frac{b}{2})^2-(\frac{b}{2})^2+c[/tex]because
[tex]2(\frac{b}{2})=b[/tex]and
[tex](\frac{b}{2})^2-(\frac{b}{2})^2=0[/tex]However, in this form, we can see that the first 3 terms are a perfect square, that is
[tex]x^2+2(\frac{b}{2})x+(\frac{b}{2})^2=(x+\frac{b}{2})^2[/tex]hence,
[tex]\begin{gathered} y=x^2+bx+c \\ y=(x+\frac{b}{2})^2-(\frac{b}{2})^2+c \end{gathered}[/tex]If we define
[tex]\begin{gathered} -(\frac{b}{2})^2+c=k \\ \text{and} \\ h=\frac{b}{2} \end{gathered}[/tex]we have that
[tex]y=(x+h)^2+k[/tex]the constant a arise when you have a leading term different from 1 in x^2.
What transformations to the linear parent function, f(x) = x, give the functiong(x) = 3x - 1? Select all that apply.A. Horizontally stretch by a factor of 3.B. Shift left 1 unit.nC. Vertically stretch by a factor of 3.UD. Shift down 1 unit.SUBMIT
Answers
We are given a parent function f(x)= x and asked the transformation process that takes it to g(x)=3x-1
PART 1
If g(x) = 3f (x): For any given input, the output g(x) is three times the output of f(x), so the graph is stretched vertically by a factor of 3. If g(x) = f (3x): For any given output, the input of g is one-third the input of f(x), so the graph is shrunk horizontally by a factor of 3.
In this case, we can state that the function was first stretched by 3.
PART 2
To move a function up, you add outside the function: f (x) + b is f (x) moved up b units. Moving the function down works the same way; f (x) – b is f (x) moved down b units.
We can also say that the function was shifted downwards by 1
ANSWER: OPTION C AND D
sadie has ananction figure collection of 200 action figures. She keeps 90 percent of the action figures on her wall. how many action figures does she keep on her wall
Answers
we have the following:
[tex]\begin{gathered} n=200\cdot\frac{90}{100} \\ n=180 \end{gathered}[/tex]therefore, 180 action figures keep on her wall
Misty the cat loved to eat tuna. He wanted to make sure he had enough for the whole week. If misty ate 1\2can of tuna every day,how many cans would he need for a whole week
Answers
Answer:
3.5
Step-by-step explanation:
0.5 * 7 = 3.5
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2.Each year on the same day, Susan deposits $100 into a savings account that earns simple interest at a rate of 3%. She makes no withdrawals. How much interest has Susan’s account earned after 2 years?3.Each year on the same day, Susan deposits $175 into a savings account that earns simple interest at a rate of 3.5%. She makes no withdrawals. How much interest does Susan’s account earn after 5 years?
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
P = $100
r = 3% = 0.03
t = 2 years
Step 02:
Simple Interest = P * r * t
= 100 * 0.03 * 2
= 6
The answer is:
Susan earned $6 as simple interest after 2 years.
Identify the polynomial by selecting the most accurate name for the example: 3x² + 6x - 10
Answers
Notice that the degree of the polynomial
[tex]3x^2+6x-10[/tex]is 2. Then it is called a trinomial expression.
Find the value of the expression when x is 3.x² + 10x + 25
Answers
Given
Expression
[tex]x²+10x+25[/tex]Find
Value of the expression when x = 3
Explanation
Substitute x = 3 in the given expression.
we obtain ,
[tex]\begin{gathered} x²+10x+25 \\ (3)^2+10(3)+25 \\ 9+30+25 \\ 64 \end{gathered}[/tex]Final Answer
Therefore, the value of the expression when x = 3 is 64
Find the mean, median, and mode of the set of data.10, 11, 4, 7, 12, 11, 16, 6, 9, 15
Answers
Before we begin we will order the data set given
4, 6, 7, 9, 10, 11, 11, 12, 15, 16
Mean.
The mean of a data set is given by:
[tex]\operatorname{mean}=\frac{\sum ^{}_{}x_i}{n}[/tex]where the denominator means that we have to add the points on the data and then divide them result by the number of points in the data. In this case we have:
[tex]\begin{gathered} \operatorname{mean}=\frac{4+6+7+9+10+11+11+12+15+16}{10} \\ \operatorname{mean}=\frac{101}{10} \\ \operatorname{mean}=10.1 \end{gathered}[/tex]Hence the mean of the data set is 10.1
Median.
The median is the central value of the ordered data set. In this case we have an even number of values which means that the median is the average of the central values. The central values in this set are the the fifth and sixth term, that is, 10 and 11. The median is then:
[tex]\begin{gathered} \operatorname{median}=\frac{10+11}{2} \\ \operatorname{median}=\frac{21}{2} \\ \operatorname{median}=10.5 \end{gathered}[/tex]Mode
The mode is value that occur most frequently. In this case only the 11 repeats itsefl, hence the mode is 11.
Summing up we have:
Mean 10.1
Median 10.5
Mode 11
Sally has 71 peppermints. Bernard has p fewer peppermints than Sally. Write an expression that shows how many peppermints Bernard has.
Answers
an expression is:
y = 71 - p
Evaluate the expression x2 + 3x for x = −6
Answers
Answer:
30
Step-by-step explanation:
The value of the expression x² + 3x at x = - 6 will be 18.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ x² + 3x
The value of the expression at x = - 6 will be given as,
⇒ (-6)² + 3(-6)
⇒ 36 - 18
⇒ 18
The worth of the articulation x² + 3x at x = - 6 will be 18.
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Positive numbers are not closed under subtraction. Give an example below.
Answers
A set S is said to be closed under subtraction if:
[tex]\forall a,b\in S,\text{ a-b}\in S\text{ and b-a}\in S[/tex]Since the set given is that of positive numbers, we pick two different positive numbers, say 6 and 9.
[tex]\begin{gathered} \\ 9-6=3\in S \\ 6-9=-3\notin S \end{gathered}[/tex]Since -3 is not a positive number, we can then conclude that the set of positive numbers are
sin 0 = 1. Find tan 8.A.404141OB. 49O C. 40D.409e
Answers
Because sine is opposite side/ hypotenuse. tangent = opposite angle / adjacent, so we need to find the adjacent side using Pitagora's theorem
[tex]\begin{gathered} c^2=a^2+b^2 \\ 41^2=9^2+b^2 \\ 1681\text{ - }81=b^2 \\ \sqrt{1600}=b \\ 40=b \end{gathered}[/tex]And now we find tangent.
[tex]tan\theta=\frac{oppositeside}{adjacentside}=\frac{9}{40}[/tex]So, the correct option is C
A fast food restaurant sold 35 burgerswith cheese. If the ratio of burgers soldwith cheese compared to withoutcheese was 7:3, how many burgers didthey sell total?
Answers
Answer:
The total number of burgers sold is: 50
Problem Statement
The question tells us a restaurant sold 35 burgers with cheese and also that the ratio of burgers sold with cheese compared to burgers sold without cheese is 7:3.
We are asked to find the total amount of burgers sold; with and without the cheese.
SOLUTION
The question already told us that the ratio of burgers sold with cheese to those without cheese is 7:3. This means that for every 7 burgers with cheese sold, the restaurant also sold 3 burgers without any cheese.
This further implies that out of 10 burgers sold at a time, the restaurant must have sold 7 cheeseburgers and 3 burgers without cheese.
This means that we can say:
[tex]35\text{ burgers represent }\frac{7}{10}\text{ of burgers sold by the restaurant}[/tex]If this is the case, then we can also say that:
[tex]\frac{3}{10}\text{ of the total burgers sold is without cheese}[/tex]Thus, we can write an equation stating that "35 burgers plus 3/10 of the total burgers (B) must be equal to the total number of burgers (B)"
This is done below:
[tex]\begin{gathered} 35+\frac{3}{10}\times B=B \\ 35+\frac{3B}{10}=B \\ \text{Multiply both sides by 10} \\ 350+3B=10B \\ \text{Subctract 3B from both sides} \\ 350+3B-3B=10B-3B \\ 350=7B \\ \text{Divide both sides by 7} \\ \frac{350}{7}=\frac{7B}{7} \\ 50=B \\ \\ \therefore B=50 \end{gathered}[/tex]Final Answer
Thus, the total number of burgers sold is: 50
Israel y su amigo fueron al cine y compraron dos entradas de cine a 12.50 cada una también compraron dos bolsas de palomitas de maíz y dos bebidas cada bolsa de pantalones de maíz cuestan 2.25 gastaron un total de 33 en el teatro escribir resolver una ecuación para encontrar el costo de una bebida.Israel and his friend went to the movies and bought two movie tickets at 12.50 each they also bought two bags of popcorn and two drinks each bag of corn pants cost 2.25 spent a total of 33 in the theater write solve an equation to find the cost of a drink.
Answers
Let,
x = number of drinks/número de bebidas
y = number of popcorn/número de palomitas de maíz
z = number of tickets/número de entradas
A = price of drinks/precio de las bebidas
B = price of popcorn/precio de las palomitas de maíz
C = price of tickets/precio de las entradas
T = total cost/coste total
We get,
[tex]\text{ T = Ax + By + Cz}[/tex]But,
x, y, z = 2
B = 2.25
C = 12.50
T = 33.00
Conectemos los valores a la fórmula para poder determinar el precio de las bebidas.
[tex]\text{ T = Ax + By + Cz }\rightarrow\text{ 33 = A(2) + (2.25)(2) + (12.50)(2)}[/tex][tex]\text{33 = A(2) + (2.25)(2) + (12.50)(2) }\rightarrow\text{ 33 = 2A + 4.50 + 25.00}[/tex][tex]\text{ 33 = 2A + 29.5 }\rightarrow\text{ 2A = 33 -29.5 }\rightarrow\text{ 2A = 3.50}[/tex][tex]\text{ A = }\frac{3.50}{2}\text{ = 1.75}[/tex]Por tanto, el coste de las bebidas es 1.75.