We know that the equation of a line is given by
[tex]y-y_1=m(x-x_1)[/tex]To find it we need the slope m and a point that the line passes thorugh. In this case we have the point (8,10) but we don't know the slope. What we know is that the line we are looking for is parallel to the line
[tex]y=2x-5[/tex]We also know that for two lines to be parallel they have the same slope. Then, if we fin the slope of the line y=2x-5, we have the slope of the line we are looking for. To find the slope of the line y=2x-5 we note that it is written in the slope-intercept form
[tex]y=mx+b[/tex]From this we know that the slope is multiplying the x variable when it is written in that form. Hence m=2.
Then the line we are looking for has an slope of 2 and passes through the point (8,10). Pluggin the values in the equation of a line we have.
[tex]y-10=2(x-8)[/tex]Writting it in the slope intercept form we have
[tex]\begin{gathered} y-10=2(x-8) \\ y-10=2x-16 \\ y=2x-16+10 \\ y=2x-6 \end{gathered}[/tex]Then the line parallel to y=2x-5 and passes through the point (8,10) is
[tex]y=2x-6[/tex]Use the model to solve for x
PLS HELPPP
Answer:
I think x is -6
Step-by-step explanation:
Side 1:
3x+1
3x-10+1=(-29)
3x-6+1=(-17)
Side 2:
2x-5
2x-10-5=(-25)
2x-6-5=(-17)
Which expression is undefined? (9-9) A 2 -3) )B. O C. )D. 0
Answer:
Option B
Step-by-step explanation:
Undefined expression:
An undefined expression is a division by 0, or a fraction in which the denominator is 0.
In this question, the undefined expression is given by option B.
For each equation in the table, give the slope of the graph.
Solving the Question
Linear equations are typically organized like this: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept.
When the equation is like [tex]y=b[/tex], it means that it is a horizontal line and the slope is 0.
When the equation is like [tex]x=d[/tex], it is a vertical line and the slope is undefined.
AnswerFirst equation: 0
Second equation: undefined
Third equation: [tex]\dfrac{4}{5}[/tex]
What is the area of a rectangle with vertices
(-1, -4), (-1, 6), (3, 6), and (3, -4)?
* 16 square units
24 square units
O 36 square units
40 square units
The most appropriate choice for distance formula will be given by Area of rectangle is 40 sq units
What is distance formula?
Distance formula is used to find the distance between two points.
Let A and B be two points with coordinate [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] respectively
Distance between A and B = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
Here,
Let A = (-1 , -4), B = (-1, 6), C = (3, 6) and D = (3, -4)
Length of AB =
[tex]\sqrt{((-1)-(-1))^2 + (-4-6)^2}\\\sqrt{100}\\10 units[/tex]
Length of BC =
[tex]\sqrt{((-1)-3)^2 + (6-6)^2}\\\sqrt{16}\\4 units[/tex]
Length of rectangle = 10 units
Breadth of rectangle = 4 units
Area of rectangle = [tex]10 \times 4[/tex] = 40 sq units
Fourth option is correct
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a rectangle width is 3 1/2 inches and the lenght is 4 3/4 inches. What is the area of the rectangle?
The area of the rectangle with length [tex]4 \frac{3}{4}[/tex] inches and width [tex]3 \frac{1}{2}[/tex] inches will be;
⇒ [tex]16 \frac{5}{8}[/tex] inches²
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The length of the rectangle = [tex]4 \frac{3}{4}[/tex] inches
= 19 / 4 inches
The width of the rectangle = [tex]3 \frac{1}{2}[/tex] inches
= 7 / 2 inches.
Since, We know that;
The area of the rectangle = Length x Width
Substitute all the values , we get;
The area of the rectangle = Length x Width
The area of the rectangle = 19 / 4 x 7 / 2
= 133 / 8 inches²
= [tex]16 \frac{5}{8}[/tex] inches²
Therefore,
The area of the rectangle with length [tex]4 \frac{3}{4}[/tex] inches and width [tex]3 \frac{1}{2}[/tex] inches will be;
⇒ [tex]16 \frac{5}{8}[/tex] inches²
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For each expression build a rectangle using all of tiles,....
a.
[tex]\begin{gathered} y^2+xy+2x+2y \\ Factor_{\text{ }}as\colon \\ (y+2)(x+y) \end{gathered}[/tex]i) Sketch each rectangle:
ii) Find its dimensions
iii)
[tex]\begin{gathered} y^2+xy+2y+2x \\ \text{grouping terms:} \\ (y^2+xy)+(2y+2x)=y(y+x)+2(y+x)=(y+x)(2+y) \end{gathered}[/tex]A veterinarian is visited by many pets and their owners each day. Before the doctor attends to each pet, an assistant records information including the type, age, weight, and height of each pet. What are the individuals in the data set?
Since all the information in the study, such as the type, the age and the weight are related to the pet, individuals in each data-set are the pets.
Who are the individuals on a data-set or on a study?The individual of a data-set is the object which is being analyzed in the study, the object that has it's characteristics analyzed.
In the context of this problem, these following information are analyzed, at the register when the doctor attends each pet and registers the information.
Type of the pet.Age of the pet.Weight of the pet.Height of the pet.All these information belong to the pet that visits the veterinary, hence the individuals in each data-set are the pets.
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A tub of theater popcorn has 247.5 grams of popcorn, which is 275% larger than a regular bag of popcorn. How many grams of popcorn would be in a regular sized bag.
Let's begin by listing out the information given to us:
A tub has this: 247.5 grams of popcorn = 275%
regular-sized bag: x grams = 100%
We will solve using simple proportion
[tex]\begin{gathered} 247.5g=275 \\ xg=100 \\ \text{Cross Multiply, we have:} \\ 247.5\cdot100\cdot g=275\cdot x\cdot g \\ \text{Make x the subject of formula (divide by 275g)} \\ \frac{247.5\cdot100\cdot g}{275\cdot g}=\frac{275\cdot x\cdot g}{275\cdot g} \\ 0.9\cdot100=x\Rightarrow x=900 \\ x=900g \end{gathered}[/tex]Write the rate as fraction in simplest form 22 gallons of pest rifles for 8 acres of crops
Since the given rate is 22 gallons of pest for 8 acres of crops, then
We need to find how many acres per gallon
Then we will divide 22 acres by 8 gallons to find the rate
[tex]rate=\frac{22}{8}[/tex]Divide up and down by 2 to simplify
[tex]\begin{gathered} rate=\frac{\frac{22}{2}}{\frac{8}{2}} \\ \\ rate=\frac{11}{4} \end{gathered}[/tex]The answer is:
The rate is 11/4 gallon per acre (2 3/4)
The area of this figure 20 in. is square inches. 28 in. 30 in. 7 in. 25 in.
The shape can be broken into two separate rectangles of the forms below.
Bothe shapes give a rectangle, therefore the area of the shape is
Area of Shape = Area of rectangle A + Area of rectangle B
Since Area of rectangle = LENGTH X BREADTH, we then have below
[tex]\begin{gathered} \text{Area of shape = (28 x 7)}+(25\times30) \\ =196+750 \\ =946\text{ square inches} \end{gathered}[/tex]In conclusion, the answer is 946 square inches
Use a calculator to find the values of X. Round sides to the nearest 10th and angles to the nearest whole number. Use sin or COS as appropriate.
Given the information about the triangle, we can use the cosine function on angle x to get the following:
[tex]\begin{gathered} \cos x=\frac{\text{adjacent side}}{hypotenuse}=\frac{7}{16} \\ \Rightarrow\cos x=\frac{7}{16} \end{gathered}[/tex]solving for x, we get:
[tex]\begin{gathered} \cos x=\frac{7}{16} \\ \Rightarrow x=\cos ^{-1}(\frac{7}{16})=64.1 \\ x=61.1\degree \end{gathered}[/tex]therefore, the value of x is 61.1
Type the correct answer in the box. Consider functions f and g: f(x) = (x+1)^3g(x)= x^1/3 +1Evaluate the function composition. (fog)(–64) =
The composition
[tex](f\circ g)(x)[/tex]Means that you have to evaluate x in g(x) first, and then evaluate that result in f(x)
In other words:
[tex](f\circ g)(x)=f(g(x))[/tex]Let's use this for this question:
[tex]\begin{gathered} f(x)=(x+1)^3 \\ g(x)=\sqrt[3]{x}+1 \\ \\ (f\circ g)(-64)=f(g(-64)) \\ \rightarrow g(-64)=-3 \\ \rightarrow f(-3)=-8 \\ \\ \text{Thereby} \\ (f\circ g)(-64)=-8 \end{gathered}[/tex]Which answer choice below is a solution to this equation?7x + 5 – 2x = 2x – 7A. 2B. 0C. -4D. 8
SOLUTION:
Step 1:
In this question, we are given the following:
[tex]7x\text{ + 5 - 2 x = 2 x- 7}[/tex]Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} 7\text{ x - 5 - 2 x = 2 x - 7} \\ 5x\text{ - 5 = 2x - 7} \\ collecting\text{ like terms, we have that:} \\ 5\text{ x - 2x = - 7 - 5} \\ 3\text{ x = - 12} \\ Divide\text{ both sides by 3, we have that:} \\ x\text{ =}\frac{-12}{3} \\ x\text{ = - 4 \lparen OPTION C \rparen} \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]x\text{ = - 4 \lparen OPTION C\rparen}[/tex]
Find the surface area of a glazed donut with an outer diameter of 7 cm and an inner diameter of 3 cm. The donut is 2 cm tall
Solution:
If the outer diameter is 7, then the outer radius is b=7/2.
On the other hand, if the inner diameter is 3, then the inner radius is a= 3/2.
Now, the surface area of a torus (glazed donut) with inner radius a and outer radius b is given by
[tex]SA=\pi^2\mleft(b+a\mright)\mleft(b-a\mright)\text{ =}\pi^2(b^2-a^2)[/tex]Then, applying the data of the problem to the above equation, we can conclude that the surface area of the given glazed donut would be:
[tex]SA=\pi^2(b^2-a^2)=\pi^2((\frac{7}{2})^2-(\frac{3}{2})^2)=98.69[/tex]so that, the correct answer is:
[tex]SA=98.69\approx98.7[/tex]
Dr. Hughes instructs her students to solve the equation, 2x - 5y = -20, for y. What is the correct first step?Add +5y to both sides of the equation.O Add -2x to both sides of the equation.Add +2x to both sides of the equation.Divide each term in the equation by -5.
We have the following expression given:
2x -5y = -20
For this case the correct set in order to begin is add 5y in both sides
Add +5y to both sides of the equation.
If Allie’s parents are willing to spend $300 for a party, how many people can attend?
At least 20 people can attend the party
True or False? The end behaviors of each end of any quadratic function are always inthe same direction.
In general, given a quadratic function,
[tex]\begin{gathered} f(x)=ax^2+bx+c \\ a,b,c\rightarrow\text{ constants} \end{gathered}[/tex]The end behaviors of each end of the function are given by the limits of f(x) when x approaches +/-infinite.
Therefore,
[tex]\lim_{x\to\infty}f(x)=\lim_{x\to\infty}ax^2=a\lim_{x\to\infty}x^2=a*\infty[/tex]and
[tex]\lim_{x\to-\infty}f(x)=\lim_{x\to-\infty}ax^2=a\lim_{x\to-\infty}x^2=a*\infty[/tex]Thus, the two limits are the same and depend on the sign of a.
Hence, the answer is True, the statement is True.y = 2x divided by 6?
Answer: I'm not sure if you're trying to find x or y, but y = x/3 and x = 3y
Step-by-step explanation:
Find an equation of the line described. Write the equation in slope-intercept form.With slope of -2 through (0,4)the equation of the line is y=0
y = -2x + 4
Explanations:The equation of the line having a slope m, and passing through the point (x₁, y₁) is given as:
y - y₁ = m (x - x₁)
From the description given:
The line passes through the point (0, 4)
That is, x₁ = 0, y₁ = 4
The slope of the line, m = -2
Substitute x₁ = 0, y₁ = 4, and m = -2 into the equation y - y₁ = m (x - x₁)
y - 4 = -2 (x - 0)
y - 4 = -2(x)
y - 4 = -2x
y = -2x + 4
Dave and his friends went out to celebrate his birthday at Chill's in buda. their meal cost $86 and they left a 15% tip how much was the total bill including tip?
The meal cost is $86
its 15% is:
$86 x 0.15 = $12.9
then the tip was $12.9. Then, the total bill would be:
$86 + $12.9 = $98.9
that is the total bill was $98.9
It's in the photo, it's a bit to hard to type out.
Perpendicular lines have slopes that are negative reciprocals.
If two perpendicular lines have slopes m1 and m2, then we have the following equation:
[tex]m_1=-\frac{1}{m_2}[/tex]Then, we can analyze each pair.
a) In this case, both lines have the same slope (m = 1/5). They are parallel, not perpendicular.
b) In this case, the slopes are different. They are reciprocals (m1 = 1/m2), but they are not negative reciprocals, so they are not perpendicular.
c) In this case the slopes are the negative of each other (2/3 and -2/3), but they are not negative reciprocals. Then, they are not perpendicular.
d) In this case, the slopes are negative reciprocals:
[tex]-\frac{1}{m_2}=-\frac{1}{-\frac{3}{2}}=\frac{1}{\frac{3}{2}}=\frac{2}{3}=m_1[/tex]Then, this lines are perpendicular.
Answer: Option d.
When interest rates are low, some automobile dealers offer loans at 0% APR, as indicated in a 2016 advertisement by a prominent car dealership, offering zero percent financing or cash back deals on some models.Zero percent financing means the obvious thing—that no interest is being charged on the loan. So if we borrow $1,200 at 0% interest and pay it off over 12 months, our monthly payment will be $1,200/12 = $100.Suppose you are buying a new truck at a price of $26,000. You plan to finance your purchase with a loan you will repay over two years. The dealer offers two options: either dealer financing with 0% interest, or a $2,600 rebate on the purchase price. If you take the rebate, you will have to go to the local bank for a loan (of $23,400) at an APR of 6.5%.What would your monthly payment be if you took the rebate? (Round your answer to the nearest cent.)
HELP PLEASEEEEE!!!!!!
Answer: D=2/7 R=4/7
Step-by-step explanation: there are 7 parts and D is the 2nd part R is the 4th part.
A bag contains 5 red marbles and 3 blue marbles. A marble is selected at random and not replaced into the bag. Another marble is then selected from the bag. How would you describe these two events?
Marble Events
there are 5 + 3 = 8 marbles
If one marble is selected then there are now
8 - 1 = 7 marbles
Then answer is
The two events are Dependent
Event B is dependent on Event A
A gumball machine contains orange, yellow, and purple gum balls. The probability of getting an orange gumball is 3/4. The probability of getting a yellow gumball is 1/6. If there are 36 gumballs in the machine, how many are there of each color number of purple marbles _______ number of yellow marbles_____ number of orange marbles______
Given:
Probability of getting orange gumball is, p(o) = 3/4.
Probability of getting yellow gumball is, p(y) = 1/6.
The objective is to find the number of each colored gumballs.
Since, the sum of the events of probability is always 1.
Then, the probability of purple ball p(p) can be calculated as,
[tex]\begin{gathered} \frac{3}{4}+\frac{1}{6}+p(p)=1 \\ p(p)=1-\frac{3}{4}-\frac{1}{6} \\ p(p)=\frac{12-3(3)-1(2)}{12} \\ p(p)=\frac{1}{12} \end{gathered}[/tex]Since, it is given that the total number of gumball is N = 36.
Then, the number of orange ball can be calculated as,
[tex]\begin{gathered} p(o)=\frac{n(o)}{N} \\ \frac{3}{4}=\frac{n(o)}{36} \\ n(o)=36\cdot\frac{3}{4} \\ n(o)=27\text{ balls.} \end{gathered}[/tex]Similarly, the number of yellow ball can be calculated as,
[tex]\begin{gathered} p(y)=\frac{n(y)}{N} \\ \frac{1}{6}=\frac{n(y)}{36} \\ n(y)=\frac{36}{6} \\ n(y)=6 \end{gathered}[/tex]And the number of purple ball can be calculated as,
[tex]\begin{gathered} p(p)=\frac{n(p)_{}}{N} \\ \frac{1}{12}=\frac{n(p)}{36} \\ n(p)=\frac{36}{12} \\ n(p)=3 \end{gathered}[/tex]Hence, the number of orange ball is 27, number yellow ball is 6 and number of purple ball is 3.
By noon, the temperature in Nome had risen by 13 degrees. What was the temperature there at noon (Nome is -27 currently)
If there will be an increase of 13 degrees, the temperature will be -14 degrees.
What was the temperature there at noon?We know that by noon, the temperature had risen by 13 degrees, and currently the temperature is -27 degrees.
A "rise" in temperature means that the temperature increases, so the temperature at noon will be 13 degrees more than now, and now it is -27 degrees, so we will get:
-27° + 13° = -14°
The temperature at noon will be -14°.
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Parallelogram ABCD was transformed to form parallelogram A'B'C'D'.У.101864D2-10-8-616 8 10a245-6881-101Which rule describes the transformation that was used to form parallelogram A'B'C'D'?O (x + 10, y + 3)0 (-x, y-3)O (x - 10.y-3)(x + 10. y-3)
Explanation
Step 1
to find the transformation, count the units moved in each axis
for x, (red line)
for y( green line)
[tex]\begin{gathered} \text{for x}\Rightarrow horizontal\Rightarrow from\text{ 2 to -8=-8-(2)=-}10 \\ \text{for y }\Rightarrow vertical\text{ }\Rightarrow\text{from 5 to 2, =2-5=-3} \\ so,\text{ the transformation is} \\ (x-10,y-3) \end{gathered}[/tex]Line segment AB is on square ABCD. Segment EF on equilateral triangle EFG is 12 units longer than AB. Square ABCD and triangle EFG have equal perimeters. What is the length of AB?
The length of segment AB when the line segment AB is on square ABCD is 36 units.
What is the length of segment AB?From the task content, the length of the line segment AB which is a side of the square ABCD is to be determined.
In this case, since the perimeters of triangle EFG and square ABCD are equal as given;
Let the length of segment AB = x.
Therefore, EF = x + 12.
Therefore, the perimeter of the equilateral triangle = 3(x +12).
While the perimeter of square ABCD is; 4x.
Therefore, since the perimeters are equal, we equate them and this will be:
3(x + 12) = 4x
3x + 36 = 4x
36 = x.
Therefore, the length is 36 units.
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Clara and Toby are telemarketers.
Yesterday, Clara reached 4 people in 10 phone calls, while Toby reached 3 people in 8 phone calls.
If they continue at those rates, who will reach more people in 40 phone calls?
Use the drop-down menu to show your answer.
Question 1 1. Which of the following is NOT a true statement? 1 point 21 22 23 24 25 26 27 28 O A. Angle 1 and Angle 5 are corresponding angles. w B. Angle 2 and Angle 7 are alternate interior angles. C. Angle 5 and Angle 8 are vertical angles. D. Angle 3 and Angle 7 are corresponding angles. O I e Type here to searchwhats the answer
Note:
Corresponding agles are angles on corresponding (the same) side of the two lines intersected by the transversal
Alternate angles are angles on the opposite sides of the transversal