The linear equation that passes through (15, 40) and (41, 61) is:
y = (21/26)*x + 725/26
How to get the linear equation?A general line is written as:
y = m*x + c
Where m is the slope and c is the intercept of the y-axis.
If the linear equation passes through two points (x₁, y₁) and (x₂, y₂), then the slope can be written as:
slope = (y₂ - y₁)/(x₂ - x₁)
In this case the line passes through (15, 40) and (41, 61), then the slope is:
m = (61 - 40)/(41 - 15) = 21/26
Then the line is:
y = (21/26)*x + c
To find the value of c we can replace the values of one of the poitns, if we use the first one we will get:
40 = (21/26)*15 + c
40 = 315/26 + c
40 - 315/26
725/26 = c
The linear equation is.
y = (21/26)*x + 725/26
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Graph each pair of inequalities and indicate the solution set of the system with Cross hatching or shading. The cross hatching or shading, if extended would cover a set of three letters.
Given:
[tex]\begin{gathered} y4 \end{gathered}[/tex]To graph each pair of inequalities and indicate the solution set with cross hatching or shading
Solution
Determine the x and y intrcept of each of the given ineqiualities
[tex]\begin{gathered} y4 \\ 3x+2y=4 \\ y-intercept,make,x=0 \\ 3(0)+2y=4 \\ 2y=4 \\ y=\frac{4}{2}=2 \\ Coordinateof\text{ the y-intercept}:(0,2) \\ x-intercept,make,y=0 \\ 3x+2(0)=4 \\ 3x=4 \\ x=\frac{4}{3} \\ Coordinate\text{ of the x-intercept}:(\frac{4}{3},0) \end{gathered}[/tex]Plot the graph as shown below
It can be observed that the solution set is unbounded, as shown by the cross hatching
I keep overthinking and confusing myself can you help me please
We are asked to prove that triangles △PQR and △TSR are congruent.
Let us write the statements and reasons to prove that the given triangles are congruent.
[tex]\begin{gathered} 1.\: Statement\colon\: \bar{PQ}\cong\bar{TS} \\ 1.Reason\colon Given \end{gathered}[/tex]We are given that R is the midpoint of QS and PT
This means that QR ≅ SR and also PR ≅ TR by the property of "Definition of midpoint"
[tex]\begin{gathered} 2.\: Statement\colon\: \bar{QR}\cong\bar{SR} \\ 2.\: Reason\colon\: \text{Definition of midpoint} \end{gathered}[/tex][tex]\begin{gathered} 3.\: Statement\colon\: \bar{PR}\cong\bar{TR} \\ 3.\: Reason\colon\: \text{Definition of midpoint} \end{gathered}[/tex]So, now we have 3 equal sides in both triangles
Therefore, by the property of "Side-Side-Side" (SSS) the given triangles are congruent.
[tex]\begin{gathered} 4.\: Statement\colon\: \triangle PQR\cong\triangle TSR \\ 4.\: Reason\colon\: \text{Side}-\text{Side}-\text{Side theorem of triangle congruence } \end{gathered}[/tex]here is my question:simplify 10p4
The value of 10P4 is 5040
Permutations and combinations are defined as the various ways in which objects from a set may be selected, generally without replacement, to form subsets.
Given 10P4
we have to evaluate the value of 10P4
10P4 is in the form of npr
Formula for npr = n!/(n-r)!
Here n =10 and r=4
Now substitute the values in the formula
(10! )/(10-4)!
= (10! )/6!
=(10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)/(6 x 5 x 4 x 3 x 2 x1)
= 10 x 9 x 8 x 7
= 5040
Therefore the value of 10P4 is 5040
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Answer:
The value of 10P4 is 5040
Permutations and combinations are defined as the various ways in which objects from a set may be selected, generally without replacement, to form subsets.
Given 10P4
we have to evaluate the value of 10P4
10P4 is in the form of npr
Formula for npr = n!/(n-r)!
Here n =10 and r=4
Now substitute the values in the formula
(10! )/(10-4)!
= (10! )/6!
=(10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)/(6 x 5 x 4 x 3 x 2 x1)
= 10 x 9 x 8 x 7= 5040
Step-by-step explanation:
Matilda covers the interior faces of a kitchen drawer with shelf paper. The height of the drawer is 3/4 its width and the depth front to back is 7/4 its width. if the exact amount of shelf paper needed is 846 square inches what is the depth of the drawer? help me I need help
To know the depth of the drawer you need to know that the shelf paper is the area of the interior faces of the drawer, then:
A = 846sq in
the area is equal to:
[tex]A=A_b+A_l[/tex]Where:
Ab is the area of the base of the drawer
Al is the area of the laterals of the drawer
The Area of the base is:
[tex]A_b=\frac{7}{4}x\cdot x=\frac{7}{4}x^2[/tex]And the area of the laterals is the sum of the area of every lateral:
[tex]A_l=2\lbrack(\frac{3}{4}x)\cdot(\frac{7}{4}x)\rbrack+2\lbrack(\frac{3}{4}x)\cdot(x)\rbrack[/tex][tex]A_l=\frac{21}{8}x^2+\frac{3}{2}x^2=\frac{33}{8}x^2[/tex]Then:
[tex]846=\frac{7}{4}x^2+\frac{33}{8}x^2[/tex][tex]846=\frac{188}{32}x^2=\frac{47}{8}x^2=5.87x^2[/tex]The we clear the x:
[tex]\frac{846}{5.87}=x^2[/tex][tex]\sqrt[]{144.12}=x[/tex][tex]x=12.004in[/tex]The depth of the drawer is x= 12,004 inchesif 1/4 of the class is girls and one half of the girls in the class are wearing dresses what fraction of the class are girls with dresses one eighth 1/6 1/5 1/4
Given that one-fourth of the class are girls;
[tex]f(G)=\frac{1}{4}[/tex]And one half of the girls in the class are wearing dresses;
[tex]f(D)=\frac{1}{2}[/tex]The fraction of the class that are girls with dresses is;
[tex]\begin{gathered} f(G\cap D)=\frac{1}{4}\times\frac{1}{2} \\ f(G\cap D)=\frac{1}{8} \end{gathered}[/tex]Therefore, the fraction of the
find dy/
dx
Find where y = csc^-1(1/9x+5)
Answer:
csc(9x)
Step-by-step explanation:
put each improper fraction into a mixed number 50/9
Divide the numerator by the denominator:
50 divided by 9 = 5 with a reminder of 5
Write the whole number (5) , and use the remainder as a numerator and 9 as the numerator:
5 5/9
If ABCDE is reflected over the x-axis and then translated 3units left, what are the new coordinates B?E..ADO A. (1, -2)O B. (7,-2)C. (4, -2)D. (-7,2)CBX
Recall that the rule of transformation for a point (x,y) reflected over the x-axis is:
[tex](x,y)\rightarrow(x,-y),[/tex]and the rule of transformation for a point translataled n units to the left is:
[tex](x,y)\rightarrow(x-n,y).[/tex]Therefore, point B(4,2) reflected over the x-axis:
[tex](4,2)\rightarrow(4,-2),[/tex]and then translated 3 units to the left has as image the following point:
[tex](4,-2)\rightarrow(4-3,-2)=(1,-2).[/tex]Answer:[tex]\begin{equation*} (1,-2). \end{equation*}[/tex]For which equation would x = 12 NOT be a solution?Options:X\1=12x\4=2x\3=4x\2=6
Given:
[tex]x=12[/tex]is given.
Required:
Which option is not appropriate.
Explanation:
Now we check all the option for this
[tex]\begin{gathered} \frac{x}{1}=12 \\ x=12 \end{gathered}[/tex]which is appropriate
[tex]\begin{gathered} \frac{x}{4}=2 \\ x=8 \end{gathered}[/tex]which is not appropriate
[tex]\begin{gathered} \frac{x}{3}=4 \\ x=12 \end{gathered}[/tex]which is appropriate
[tex]\begin{gathered} \frac{x}{2}=6 \\ x=12 \end{gathered}[/tex]which is appropriate
Final answer:
What is the slope of y= -4
Hello!
We have the equation of the line y = -4.
Let's put this equation in a cartesian plane:
Notice that this equation will be always constant. So, as we just have a straight line with no inclination, the slope is 0.
V = πr (R²-r²)
make r the subject of the formula
The subject of the formula is [tex]\pi r = {r(R^{2}- r^{2})}[/tex]
Given,
V = πr (R²-r²)
then to find r in terms of the other values divide both the sides by the multiplier of r.
r is multiplied by πr²
Now divide both sides by V
[tex]\frac{V}{\pi r } = \frac{\pi r(R^{2}- r^{2})}{\pi r}[/tex]
[tex]\frac{V}{\pi r } = {(R^{2}- r^{2})}[/tex]
[tex]{\pi r } = \frac{{(R^{2}- r^{2})}}{V} \\\\\pi r^{2} = {r(R^{2}- r^{2})}[/tex]
Hence the answer is the subject of the formula is [tex]\pi r = {r(R^{2}- r^{2})}[/tex]
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What is eight times the square root of two square root of two
Given expression is
[tex]8\sqrt[]{2\sqrt[]{2}}[/tex]Now, solving it as:
[tex]8\sqrt[]{2\sqrt[]{2}}=8\cdot2^{\frac{3}{4}}[/tex]So,
[tex]8\cdot2^{\frac{3}{4}}[/tex]is the required solution.
how to solve 2(q+4)=16how to solve 7j+2=12+5jhow to solve 12z=60-3z
Answer:
Given that to solve
a) 2(q+4)=16
we get,
[tex]\begin{gathered} 2\mleft(q+4\mright)=16 \\ 2q+8=16 \end{gathered}[/tex][tex]2q=16-8[/tex][tex]2q=8[/tex]Dividing 2 on both sides we get,
[tex]q=4[/tex]Answer is: q=4
b)7j+2=12+5j
we get,
[tex]7j+2=12+5j[/tex][tex]7j-5j=12-2[/tex][tex]2j=10[/tex]Dividing 2 on both sides, we get
[tex]j=10[/tex]c) 12z=60-3z
we get,
[tex]12z=60-3z[/tex][tex]12z+3z=60[/tex][tex]15z=60[/tex]Dividing 15 on both sides we get,
[tex]z=4[/tex]
a researcher wants to determine the number of televisions in a household.he conducts a survey of 40 random select house and I obtains data in accompying tabe. what is the relative frequency distribution of the data
The relative frequency (RF) can be calculated as follows:
[tex]RF=\frac{F}{\sum ^{}_{}F}[/tex]where RF is the relative frequency, F is the value of the frequency, and ∑F represents the sum of all frequencies.
Using a spreadsheet, we can get the following table:
Based on this table, we can see that ∑F = 40. Thus, we have to divide each frequency by 40 to get the relative frequency. As an example, using the first, second, and third row:
[tex]RF_1=\frac{1}{40}=0.025[/tex][tex]RF_2=\frac{15}{40}=0.375[/tex][tex]RF_3=\frac{13}{40}=0.325[/tex]Answer:
Which expression has a quotient of about 7? F 7:2 G 23 : 7 H 36 : 5 J 13:6 Type here to search O | a 3
The question simply means when you divide two numbers, the one that will result to 7
Hence;
36 ÷ 5 = 7.2
H is the correct option
All points from which of the following patterns would be contained on the given graph?321-6-5-4-3 -2 -1 0123 4 5 6-1-2-3OA. -1.-3.-5.-7....OB. -3, -7, -11, -15....OC. -2,-5.-8.-11.....OD. 3,5,7.9....Ht
To determine which pattern could represent points on the graph, we notice that the following points are on the graph:
[tex](1,-1),(2,-3),(3,-5).[/tex]We can infer that the point
[tex](4,-7)[/tex]is also on the line.
Therefore, the pattern that could be contained in the graph is:
[tex]-1,-3,-5,-7...[/tex]Answer: Option A.
A Snap Cube PrismA rectangular prism is 3 units high, 2 units wide, and 5 units long. What is its surfacearea in square units? Explain or show your reasoning (work).
62 u² (square units)
1) A rectangular prism is made up of 6 rectangles. So we can write them out:
2 rectangles (3 x 2)
2 rectangles ( 5 x 2)
2 rectangles ( 5 x 3)
2) Therefore the Total Surface Area of that prism can be found by applying the formula for the area of each rectangle times 2. Like this:
[tex]\begin{gathered} \text{TSA}=\text{ 2(3}\times2\text{ +5}\times2+5\times3) \\ \text{TSA}=\text{ 2(6 +10+15)} \\ \text{TSA}=\text{ 2(31)} \\ \text{TSA}=62 \end{gathered}[/tex]3) Hence the answer is 62 u² (square units)
Can you solve this ? Solve the x And get Angle 1 :And Angle 2 :Question 17
SOLUTION
Solve for the value of x using supplementary angles
If the sum of two angles is 180 degrees then they are said to be supplementary angles, which form a linear angle together.
[tex]\begin{gathered} <1=4x-5 \\ <2=x \end{gathered}[/tex]To solve using the supplementary angle rule
Add the two angles together
[tex]\begin{gathered} <1+<2=180^0 \\ 4x-5+x=180 \\ collect\text{ like terms} \\ 4x+x=180+5 \\ 5x=185 \end{gathered}[/tex]Divide both side by 5
[tex]\begin{gathered} 5x=185 \\ \frac{5x}{5}=\frac{185}{5} \\ x=37 \end{gathered}[/tex]Hence the value of x = 37 degree
The measure of Angle 1 = <1 = 4x-5 = 4(37) - 5 = 143 degree
The measure of Angle 2 = <2 = x = 37 degree
Sindy surveyed a group of students. The table represents the hours, h, they spent studying and their scores, s.What does the slope of the trend line equation s = 32.4h + 302.6 represent? For an increase of 1 h in study time the test score will increase by approximately 302.6.For an increase of 302.6 h in study time the test score will increase by approximately 1.For an increase of 32.4 h in study time the test score will increase by approximately 1.For an increase of 1 h in study time the test score will increase by approximately 32.4.
The slope of the trend line is 32.4, and it represents the change of s per 1 hour.
Then, as the slope is 32.4 it represents: For an increase of 1 h in study time the test score will increase by approximately 32.4
Can I please get some help with this equation? Evaluate and simplify log of csc(5pi/6) multiplied by csc(pi/4). Explain your work.
1) Considering that the 1st property of Logarithms tells us:
[tex]\log _ab\text{ =c}\Leftrightarrow a^c=b[/tex]2) Let's evaluate that:
[tex]\begin{gathered} \log _{\csc (\frac{5\pi}{6})}(\frac{\csc \pi}{4})=x\Rightarrow\csc (\frac{5\pi}{6})^x=\csc (\frac{\pi}{4}) \\ \\ \csc (\frac{5\pi}{6})^x=\csc (\frac{\pi}{4}) \\ \log \csc (\frac{5\pi}{6})^x=\log \csc (\frac{\pi}{4}) \\ \text{x}\log \csc (\frac{5\pi}{6})^{}=\log (\sqrt[]{2}) \\ x\log (2)=\text{ log(}\sqrt[]{2}) \\ x=\frac{\log\sqrt[]{2}}{\log\text{ 2}} \\ x=\frac{1}{2} \end{gathered}[/tex]• Notice that we've descended that exponent x, to become a factor (3rd line).
,• Then divided both log with a common base, in this case, base 10.
3) Hence that equation yields 1/2 as its result.
A=1/2(a+b)h solve for h can you please explain as well?
h = 2A/(a+b)
Explanation:
A=1/2(a+b)h
To solve for h, we will make h the subject of formula
The first thing we will do is bring the 1/2 to the other side of the equation:
[tex]\begin{gathered} A\text{ = }\frac{(a+b)h}{2}\text{ cross multiply} \\ 2A\text{ = (a+b)h} \end{gathered}[/tex]To make h stand alone, we would divide both sides by the values in the bracket:
[tex]\begin{gathered} \frac{2A}{(a+b)}\text{ = }\frac{(a+b)h}{(a+b)} \\ h\text{ = }\frac{2A}{a\text{ + b}} \end{gathered}[/tex]Therefore, h = 2A/(a+b)
An experiment consists of spinning the spinner shown. All outcomes are equally likely. Find P(<7). Express your answer as a fraction in simplest forn
There are 8 total outcomes. Now, we need to find where P(<7).
This means the outcomes where the number is less than 7.
There are 6 numbers under the 7 = 1,2,3,4,5,6
The probability is given by the next formula:
[tex]P=\frac{\text{Number of favorable outcomes}}{\text{Total of possible outcomes}}[/tex]Where:
Number of favorable outcomes = 6
Total of possible outcomes = 8
Replacing these values:
[tex]P=\frac{6}{8}[/tex]Simplify the expression, divide both numbers by 2:
[tex]P=\frac{3}{4}[/tex]The correct answer is the second one.
At the end of the first half of a basketball game, UCONN and SCSU were tied. During the second half UCONN scored 48 points and SCSU scored twice as many points as they had in the first half. What was the final score of UCONN won by 2 points?
Okay, here we have this:
Let's take the endpoints of UCONN as x and those of SCSU as y. So:
x=y+2
And:
So the UCONN points of the first half are: x/3. And since they were tied SCSU had the same points at the first half.
And those UCONN points of the second half are 2x/3, and the SCSU points at the end were then x/3+48.
So, we obtain that:
y=x/3+48
x=(x/3+48)+2
x=x/3+50
x-x/3=50
2x/3=50
2x=150
x=75
And, replacing in y:
y=75/3+48=25+48=73
Finally we obtain that the final score was: UCONN 75: SCSU 73
Question 5 Cameron put his dog Buddy in a kennel while he went on a long business trip. The equation y = 15x + 25 shows the total charge y that Cameron will pay to put Buddy in a kennel for x days. Which statement is true? The kennel charges $15 for the first day and $25 per day after the first day. The kennel charges an initial fee of $25 and $15 per day. The kennel charges $25 per day with an initial fee of $15. The kennel charges $25 for the first day and $15 per day after the first day. SUBMI
The true statement regarding the expression is that D. The kennel charges $25 for the first day and $15 per day after the first day.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this case, Cameron put his dog Buddy in a kennel while he went on a long business trip and the equation y = 15x + 25 shows the total charge y that Cameron will pay to put Buddy in a kennel for x days.
Therefore, option D illustrate this.
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Put the steps in order to find the distance between these
Answer:
See attachedStep-by-step explanation:
The distance between the points is found using the given coordinates and the distance formula.
The distance formula is based on right triangle and Pythagorean theorem and is the calculation of the hypotenuse provided the legs are known.
So the right order of operations is attached for you below.
You have found most of it, just small correction is needed.
Answer:
1., 2., 4., 5., 6., 3., 7.
Step-by-step explanation:
1. Draw a right triangle by dropping a vertical side and a horizontal side. (See attachment).
2. Determine the vertical side (2 units) and horizontal side (6 units) lengths by counting on the grid (be careful of the scale), or using the vertical coordinated (3 to 1) and horizontal coordinate (-2 to 4).
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
Therefore:
a = 2b = 64. Use the Pythagorean Theorem for right triangles to determine the diagonal length:
[tex]\implies \sf 2^2+6^2=c^2[/tex]
[tex]\sf 5.\quad 4 + 36 = c^2[/tex]
[tex]\sf 6. \quad 40 = c^2[/tex]
[tex]\sf 3.\quad \sqrt{40}=\sqrt{c^2}[/tex]
7. √40 is between √36 and √49, so between 6 and 7 - closer to 6, so about 6.3 units.
Given that f(x) = 9x2 - 180 = 0, find x. A) x = +2 V5 B) x = +3 v5 C) x = +5 V2 D) x=+5 v3
Given data:
The given function is f(x)=9x^2-180=0
The given expression can be written as,
[tex]\begin{gathered} 9x^2-180=0 \\ 9(x^2-20)=0 \\ (x^2-20)=0 \\ x=\pm2\sqrt[]{5} \end{gathered}[/tex]Thus, option (A) is correct.
III m 40 ft 65 ft What is the area of this trapezoid? square feet
remember that the area of a trapezoid can be expressed as
[tex]\begin{gathered} A=\frac{(B+b)\cdot h}{2} \\ \end{gathered}[/tex]Replace in the formula taking into account that B is the greater base, b is the smallest base and h is the height of the trapezoid.
[tex]\begin{gathered} A=\frac{(95+65)\cdot40}{2} \\ A=\frac{160}{2}\cdot40 \\ A=80\cdot40 \\ A=3200 \end{gathered}[/tex]The area of the trapezoid is 3,200 sqft.
An animal shelter has 12 cats and 9 dogs. If 1 cat and 1 dog adopted, would the ratio of cats to dog remain the same? Explain.
At the beggining the ratio of cats to dogs is
[tex]\frac{12}{9}=\frac{4}{3}[/tex]because ratio indicates a fraction (12 cats divided by 9 dogs)
After the adoption there were 11 cats and 8 dogs, then the ratio is
[tex]\frac{11}{8}[/tex]Since
[tex]\frac{4}{3}\ne\frac{11}{8}[/tex]Answer: the ratio of cats to dog does not remain the sameIf points P and Q lie in the interior of ∠ABC, then overline{PQ} lies in the interior of ∠ABC.True or false?
PQ is just the line segment that connects the points P and Q, so if both point are in the interior of and angle, the line segment connecting them has to be also in the interior of this angle, so true.
I need help question
as x approaches 8, x approaches 8
it's just 8