The slope of a line can be calculated with the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]You know that the line passes through the following points:
[tex]\mleft(-31,26\mright);(4,36)[/tex]For this case, you can set up that:
[tex]\begin{gathered} y_2=36 \\ y_1=26 \\ x_2=4 \\ x_1=-31 \end{gathered}[/tex]Then, knowing the coordinates shown above, you can substitute them into the formula in order to find the slope of the line. This is:
[tex]\begin{gathered} m=\frac{36-26}{4-(-31)} \\ \\ m=\frac{10}{35} \\ \\ m=\frac{2}{7} \end{gathered}[/tex]The answer is:
[tex]m=\frac{2}{7}[/tex]heyy could you help me out I have been stuck in this problem for a long time I sent a pic of the problem by the way
Given two triangles ABC and DEF
They have the following:
1. AC = DF
2. 3. AB = DE
4.
so, if we take 1, 2 and 3
the triangles are congruent using SAS
And if we take 1 , 2 and 4
the triangle are congruent using ASA
So, the answer is the options: D and E
If Lydia invests $3000 in a certificate of deposit and d dollars in a stock, write an expression for the total amount she invested.
ANSWER:
[tex]\text{ total amount }=3000+d[/tex]STEP-BY-STEP EXPLANATION:
The total invested is equal to 3000 investment and the previous money in stock, therefore, the expression would be:
[tex]\text{ total amount }=3000+d[/tex]I need help with this I need to know what I’m doing wrong.. do I need to put a negative for (y+8^2) or a positive 8 so confused… help #4write in standard equation for a circle and identify center and radius
4) You have the following equation:
[tex]x^2+10x+y^2-16=0[/tex]In order to determine the radius and center of the circle, complete squares for x. You don't complete squares for y because there is no term with y in the given expression. It is only a y^2 term.
By adding 25 and subtracting 25 left side of the equation you obtain:
[tex]x^2+10x+25+y^2-16-25=0[/tex]The first three terms are a perfect square (x + 5)^2, then, by using this factor and by simplifying in the previous equation you can write:
[tex](x+5)^2+y^2-41=0[/tex]Finally, add 41 both sides:
[tex](x+5)^2+y^2=41[/tex]The previous equation is in standard form for a circle equation:
[tex](x-h)^2+(y-k)^2=r^2[/tex](h,k) is the center of the circle and r the radius. By comparin the previous equation with the expression you obtain you obtain:
center of the circle = (-5,0)
radius r = √41
Graph the equation-6x + 2y = 10 2. Compare and Contrast this graph to the graph from the previous problem. pleas be SPECIFIC:)
we have the equation
6x + 2y = 10
To graph the line we need at least two points
Find out the first point
For x=0
6(0)+2y=10
2y=10
y=5
The first point is (0,5)
Find out the second point
For x=3
6(3)+2y=10
2y=10-18
2y=-8
y=-4
the second point is (3,-4)
Plot the points and join them to graph the line
using a graphing tool
The function g(x) approaches positive infinity as x approaches positive infinity. The zeros of the function are -1,2 and 4. Which graph best represents g(x)?
Explanation
We are asked to select the correct option for which g(x) approaches positive infinity as x approaches positive infinity.
Also, the zeros of the function are -1,2 and 4.
The correct option will be
Calculate the area of the region enclosed by the x-axis and the curve y(x)=−x^2−3x+4.(show a figure and detailed answer please)
Given that the region is enclosed by the x-axis and this curve:
[tex]y=-x^2-3x+4[/tex]You can graph the function using a Graphic Tool:
Noice that the area region you must calculate is:
Notice that it goes from:
[tex]x=-4[/tex]To:
[tex]x=1[/tex]Therefore, you can set up that:
[tex]Area=\int_{-4}^1(x^2-3x+4)-(0)dx[/tex]In order to solve the Definite Integral, you need to:
- Apply these Integration Rules:
[tex]\int x^ndx=\frac{x^{n+1}}{n+1}+C[/tex][tex]\int kf(x)dx=k\int f(x)dx[/tex]Then, you get:
[tex]=(\frac{x^3}{3}-\frac{3x^2}{2}+4)|^1_{-4}[/tex]- Evaluate:
[tex]=(\frac{1^3}{3}-\frac{3(1)^2}{2}+4)-(\frac{(-4)^3}{3}-\frac{3(-4)^2}{2}+4)[/tex][tex]Area\approx64.17[/tex]Hence, the answer is:
[tex]Area\approx64.17[/tex]Situation:Holly wants to save money for anemergency. Holly invests $1,000 in anaccount that pays an interest rate of6.25%
Given data:
Amount of money invested, P = $1000
Interest rate, r = 0.0625
Total money in the account, A = 5500
Now, to find the years use simple interest rate formula that is
[tex]A=P(1+rt)[/tex]Therefore, t will become
[tex]t\text{ = (A/P}-1\text{)/r}[/tex]Putting the values we get,
[tex]t=(\frac{5500}{1000}-1)\text{ / 0.0625}[/tex][tex]\begin{gathered} t=(5.5-1)\text{ / 0.0625} \\ t=\frac{4.5}{0.0625} \\ t=72 \end{gathered}[/tex]Thus, it will take 72 years for the account to reach 5500.
The weekly revenue for a product is given by R(x)=307.8x−0.045x2, and the weekly cost is C(x)=10,000+153.9x−0.09x2+0.00003x3, where x is the number of units produced and sold.(a) How many units will give the maximum profit?(b) What is the maximum possible profit?
Answer:
The number of units that will give the maximum profit is;
[tex]1900\text{ units}[/tex]The maximum possible profit is;
[tex]\text{ \$}239,090[/tex]Explanation:
Given that the weekly revenue for a product is given by ;
[tex]R(x)=307.8x-0.045x^2[/tex]and the weekly cost is ;
[tex]C(x)=10,000+153.9x-0.09x^2+0.00003x^3[/tex]Recall that
Profit = Revenue - Cost
[tex]P(x)=R(x)-C(x)[/tex][tex]\begin{gathered} P(x)=307.8x-0.045x^2-(10,000+153.9x-0.09x^2+0.00003x^3) \\ P(x)=307.8x-0.045x^2-10,000-153.9x+0.09x^2-0.00003x^3 \\ P(x)=153.9x+0.045x^2-0.00003x^3-10,000 \end{gathered}[/tex]Using graph to derive the maximum point on the function;
Therefore, the maximum point is at the point;
[tex](1900,239090)[/tex]So;
The number of units that will give the maximum profit is;
[tex]1900\text{ units}[/tex]The maximum possible profit is;
[tex]\text{ \$}239,090[/tex]Find mZCEF if mZCEF= 2x + 30,mZDEC = x + 102, and mZDEF = 132°DEFA) 30°C) 410B) 29°D) 320
1) Gathering the data
m∠CEF=2x +30
m∠DEC=x+102
m∠DEF=132
2) From the picture we infer that
m∠DEF = m∠CEF+m∠DEC
132 = m∠CEF +x +102
132-x-102=m∠CEF
m∠CEF=30
marisol has 4/12 cups of flour. A biscuit recipe she wants try requries 3/4 cup of flour for a single batch of biscuits. How many batch s of biscuits can Marisol make
The number of biscuit batches that Marisol can make from the given task content is; 4 / 9 batches.
What is the number of biscuit batches that can be made from the 4/12 cups of flour?It follows from the task content that the number of batches of biscuit that can be made from the given 4/12 batches of biscuit be determined.
By proportion, since it is given that the one biscuit recipe requires 3/4 cups of flour, it consequently can be inferred that;
In 4/12 cups of flour, the number of batches she can make is;
= 4/12 ÷ 3/4
= 4/12 × 4/3
= 16 / 36
= 4 / 9 batches of biscuits.
Ultimately, the number of batches of biscuits she can make is; 4 / 9 batches of biscuits.
Read more on fraction division;
https://brainly.com/question/1622425
#SPJ1
A sample has a mean of M = 90 and a standard devia-tion of s 20.=a. Find the z-score for each of the following X values.X = 95X = 80X = 98X = 88X = 105X = 76
Answer:
[tex]\begin{gathered} X=95,z=0.25 \\ X=80,z=-0.5 \\ X=98,z=0.4 \\ X=88,z=-0.1 \\ X=105,z=0.75 \\ X=76,z=-0.7 \end{gathered}[/tex]Explanation:
Given a sample with the following:
• Mean,M = 90
,• Standard deviation, s = 20
To find the z-score for each of the given X values, we use the formula below:
[tex]\begin{equation*} z-score=\frac{X-\mu}{\sigma}\text{ where }\begin{cases}{X=Raw\;Score} \\ {\mu=mean} \\ {\sigma=Standard\;Deviation}\end{cases} \end{equation*}[/tex]The z-scores are calculated below:
[tex]\begin{gathered} \text{When X=95, }z=\frac{95-90}{20}=\frac{5}{20}=0.25 \\ \text{When X=80, }z=\frac{80-90}{20}=\frac{-10}{20}=-0.5 \\ \text{When X=98, }z=\frac{98-90}{20}=\frac{8}{20}=0.4 \end{gathered}[/tex][tex]\begin{gathered} \text{When X=88,}z=\frac{88-90}{20}=\frac{-2}{20}=-0.1 \\ \text{When X=105, }z=\frac{105-90}{20}=\frac{15}{20}=0.75 \\ \text{When X=76, }z=\frac{76-90}{20}=\frac{-14}{20}=-0.7 \end{gathered}[/tex]If cosθ=3√2cosθ=32 then which of the following could be true?tan=−3√tangent is equal to negative square root of 3cscθ=12cosecant theta is equal to 1 halfsecθ=−2secant theta is equal to negative 2sinθ=2√2sine theta is equal to the fraction with numerator square root of 2 and denominator 2
Given that
[tex]\cos\theta=\frac{\sqrt{3}}{2}[/tex]we can determinate the sine of this angle using the following identity
[tex]\sin^2\theta+\cos^2\theta=1[/tex]If we substitute the value of the cosine on this identity, we're going to have:
[tex]\begin{gathered} \sin^2\theta+(\frac{\sqrt{3}}{2})^2=1 \\ \sin^2\theta+\frac{3}{4}=1 \\ \sin^2\theta=\frac{1}{4} \\ \sin\theta=\pm\frac{1}{2} \end{gathered}[/tex]The definitions of secant, tangent, and cosecant in terms of the sine and cosine are given by:
[tex]\begin{gathered} \tan\theta=\frac{\sin\theta}{\cos\theta} \\ \sec\theta=\frac{1}{\cos\theta} \\ \csc\theta=\frac{1}{\sin\theta} \end{gathered}[/tex]Using the known values for the sine and cosine functions on those definitions, we have:
[tex]\begin{gathered} \tan\theta=\frac{\pm\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\pm\frac{1}{\sqrt{3}}=\pm\frac{\sqrt{3}}{3}\ne-\sqrt{3} \\ \\ \csc\theta=\frac{1}{\pm\frac{1}{2}}=\pm2\ne\frac{1}{2} \\ \\ \sec\theta=\frac{1}{\frac{\sqrt{3}}{2}}=\frac{2}{\sqrt{3}}=\frac{2\sqrt{3}}{3}\ne-2 \\ \\ \sin\theta=\pm\frac{1}{2}\ne\frac{\sqrt{2}}{2} \end{gathered}[/tex]All options are false.
What expression represents the sum of ages of Hugo and his two siblings?
The correct option is D
The sum of their ages is 3x + 8
Explanation:Given that Hugo's age = x
Jasmine's age = x + 3
Manny's age = (x + 3) + 2 = x + 5
The sum of their ages is:
x + (x + 3) + (x + 5)
= x + x + x + 3 + 5
= 3x + 8
When multiplying or dividingpolynomials using the Tabular Method, write the number of terms for the polynomial ax^2+bx+c
Explanation
Answer
The number of terms for the polynomial is 3
2. Consider the linear expression.
3.2a - 1 - 4 1/3a + 7 - a
(a) What are the like terms in the expression?
(b) Simplify the linear expression.
Please type ALL the steps down.
a. The like terms are: 3.2a, -4⅓a, and -a; and -1 and 7.
b. The linear expression is simplified as: -2.1a + 6.
How to Simplify a Linear Expression?To simplify a linear expression, the like terms in the expression are combined together. Like terms in a linear expression are terms that have the same variables or variables with the same powers. Constant terms are also like terms. These like terms are combined together to simplify any given expression.
a. Given the linear expression, 3.2a - 1 - 4⅓a + 7 - a, the following are the like terms that exist in the expression:
3.2a, -4⅓a, and -a are like terms because they have the same variable.
-1 and 7 are like terms, because they are constants.
b. To simplify the linear expression, 3.2a - 1 - 4⅓a + 7 - a, combine the like terms together:
3.2a - 4⅓a - a - 1 + 7
3.2a - 4.3a - a - 1 + 7
-2.1a + 6
Learn more about like terms on:
https://brainly.com/question/15894738
#SPJ1
Michael says that 5 = 5 Is his answer correct? Explain. (1 O A. 00:00 Yes. Both expressions are equal to 625 СВ. 00:00 Yes Both expressions are equal to O C. 00:00 No. The first expression is equal to and the second expression is equal to 625 00:00 No. The first expression is equal to 625 and the second expression is equal to
Michael says that
[tex]5\cdot(\frac{1}{5^3})=5(5^3)[/tex]We are asked whether he is correct or not?
Let us simplify the equa
I need the answers please show work so I don’t fail
Solution
- The way to solve the question is that we should substitute the values of x and y given into the formula given to us.
- The formula given to us is:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ where, \\ (x_1,y_1)\text{ are the points given to us} \\ m\text{ is the slope} \end{gathered}[/tex]- Thus, we can solve the question as follows:
Question 1:
[tex]\begin{gathered} m=5 \\ x_1=3,y_1=6 \\ \\ \text{ Thus, the equation is:} \\ y-6=5(x-3) \end{gathered}[/tex]Question 2:
[tex]\begin{gathered} m=\frac{2}{7} \\ x_1=-5,y_1=4 \\ \\ \text{ Thus, the equation is:} \\ y-4=\frac{2}{7}(x-(-6)) \\ \\ y-4=\frac{2}{7}(x+6) \end{gathered}[/tex]Question 3:
[tex]\begin{gathered} m=-\frac{3}{2} \\ x_1=-7,y_1=-10 \\ \\ \text{ Thus, the equation is:} \\ y-(-10)=-\frac{3}{2}(x-(-7)) \\ \\ y+10=-\frac{3}{2}(x+7) \end{gathered}[/tex]Final Answer
Question 1:
[tex]y-6=5(x-3)[/tex]Question 2:
[tex]y-4=\frac{2}{7}(x+6)[/tex]Question 3:
[tex]y+10=-\frac{3}{2}(x+7)[/tex]Myra has a remote control toy boat.she runs the toy boat on a lake at a constant speed. The graph of a function representing the toy boats distance, y , in feet , from the shore of the lake after X seconds includes the points (1,8) and (1.5, 10.1)
Given
the constant speed.
the points 1 (1,8)
Point 2 (1.5, 10.1)
Procedure
y=mx+b
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ m=\frac{8-10.1}{1-1.5} \\ m=\frac{-2.1}{-0.5}=4.2 \end{gathered}[/tex][tex]\begin{gathered} y=mx+b \\ 8=4.2(1)+b \\ 8-4.2=b \\ 3.8=b \end{gathered}[/tex]the equation is: y=4.2x+3.8
The statements that are true are:
B. The rate of the change of the function is 4.2
D. The toy boat's speed on the lake is 4.2 feet per second
E. the toy boat is originally 3.8 feet from the shore of the lake
given two numbers 9 * 10 to the 8 power, and 30,000,000, which one is larger and by how much. 3 times larger or 30 times larger
The first number is 9 * 10^8
The second number = 30,000,000 = 3 * 10^7
so, the larger number is 9 * 10^8 because the power of 10 is the larger than the other number
To find how much is larger, divide 9 * 10^8 by 3 * 10^7
so,
so, it is 30 times larger
If 2/3rd of a trail is 3/4ths of a mile, how long is the whole trail?
Answer:
1 1/2 or 1.5 miles
Step-by-step explanation:
we can multiply 3/4 by 2/3 to see how many miles is in each third of a trail
3/4*2/3=6/12
1/2 of a mile per third of the trail so now we multiply by 3 to get whole trail
1/2 x/3/1=3/2
3/2= 1 1/2
Hopes this helps please mark brainliest
#5There are 357 students at Rydell MiddleSchool. The students were asked to choosetheir favorite class. Of the 21 students inHomeroom A, 8 students chose CSI as theirfavorite. Based on these results, how manyof the students in Rydell Middle Schoolwould you expect to choose CSI as theirfavorite class?
We could write the following proportion and then solve for x:
Therefore, we could expect that 136 students chose CSI as their favorite class in Rydell Middle School.
Figure 2 is the image of Figure 1. What is the scale factor?
Answer
Scale factor = (2/5)
Explanation
The scale factor shows the extent to which the original image has been dilated (enlarged or reduced). It is given mathematically as
[tex]\text{Scale factor = }\frac{Length\text{ of a side of the image}}{Length\text{ of the corresponding side of the original figure}}[/tex]From the image attached we can see that
Length of a side of the image = 4 dots
Length of the corresponding side of the original image = 10 dots
Scale factor = (4/10) = (2/5)
Hope this Helps!!!
(B) How many participants selected an image that is associated with being indeclsive
Answer:
8
Explanation:
The images that are associated with the trait 'indecisive' are 3 and 5.
• The frequency of the image 3 = 5
,• The frequency of the image 5 = 3
Add the two:
[tex]5+3=8[/tex]Therefore, the number of participants that selected an image that is associated with being indecisive is 8.
I need help on this problem getting the answers do you know what they are ??????????
• 16.
Common difeference:
Is the difference between consecutive numbers in an arithematic sequence
18 -20 = -2
16-18 = -2
14-16 = -2
Common difference = -2
• 17.
Explicit rule: Use the arithematic sequence formula
an = a1 +(n-1 ) d
Where:
a1 = first term = 20
d= common difference = -2
Replacing:
an = 20 + (n-1)-2
• 18.
Replace n by 11
an = 20 + (11-1 ) -2
an = 20 + (10)-2
an= 20 - 20
an = 0
Amount to be paid = 0 (zero)
The current, I, in an electrical conductor varies inversely as the resistance,R, of the conductor. The current is 5 amperes when the resistance is 882ohms. What is the current when the resistance is 428 ohms? Round youranswer to two decimal places if necessary.
ANSWER:
10.30 A
SOLUTION
I=k/R this is base on the definition of I is inversely proportional to R
we need to find the constant k
5=k/882
k=4410
substitute k and R value to get I
I=4410/428
I=10.30
y = 2x – 2 y = -x + 7
Given the system of equations:
[tex]\begin{gathered} y=2x-2 \\ y=-x+7 \end{gathered}[/tex]We will find the solution of the system by the graph
To draw each line, we need to know 2 points
So, we will substitute with 2 values of x and calculate the corresponding value of y
For the first equation: y = 2x - 2
[tex]\begin{gathered} x=0\rightarrow y=2\cdot0-2=-2 \\ x=2\rightarrow y\rightarrow=2\cdot2-2=2 \end{gathered}[/tex]So, the line passes through the points ( 0, -2 ) and ( 2, 2)
For the second line: y = -x + 7
[tex]\begin{gathered} x=0\rightarrow y=0+7=7 \\ x=2\rightarrow y=-2+7=5 \end{gathered}[/tex]so, the line passes through the points ( 0, 7) and ( 2, 5)
The graph of the system will be as shown in the following figure:
As shown in the figure:
Equation 1 is the blue line
Equation 2 is the red line
The point of intersection = ( 3, 4)
So, the answer is the solution of the system = ( 3, 4 )
Where in the xy-plane are the points with x < 0 and y is greater than or equal to 0?*O Quadrant IO Quadrant IIO Quadrant IIIO Quadrant IV
Answer:
Quadrant II
Explanation:
In the xy-plane:
• The value of x is less than 0 in Quadrant II and Quadrant III.
,• The value of y is greater than or equal to 0 in Quadrant I and Quadrant II.
Therefore, the quadrant with points x < 0 and y≥0 is Quadrant II.
A polynomial has one root that equals 2 + i. Name one other root of thispolynomial.
In a polynomial, if it has an imaginary root, then it also has the conjugate of that root. In this case, since 2 + i, is a root then 2 - i, is also a root.
I'll just send you the picture. there's too much to type
ANSWER
[tex]\text{ \$278.75}[/tex]EXPLANATION
We have that Sammi has $125.75 in her account and deposits (adds) $25.50 every month for 6 months.
To find how much is there after 6 months, first, find out how much she added to the account and then add that to the initial amount that was there.
After 6 months she deposited:
[tex]\begin{gathered} 6\cdot25.50 \\ \text{ \$153} \end{gathered}[/tex]Now, add that to the initial amount there:
[tex]\begin{gathered} 125.75+153 \\ \text{ \$278.75} \end{gathered}[/tex]That is the amount in the account at the end of 6 months.
How to find the distance of a circle given points (-2.1,1.5) and (0.8771,0)
Given:
There are given the two points of the circle:
[tex](-2.1,1.5)\text{ and (0.8771,0)}[/tex]