The equation of a line is y + 8 = 16/11 (x + 2).
Here we have to find the equation of a line which are passing through points (-2, -8) and (9, 8).
Slope of a line = [tex]\frac{y_{2} - y_{1} }{x_{2}- x_{1} }[/tex]
([tex]x_{1} , y_{1}[/tex]) = (-2, -8)
([tex]x_{2} , y_{2}[/tex]) = ( 9, 8)
The slope(m) = [tex]\frac{8-(-8)}{9-(-2)}[/tex]
= 16/ 11
The equation of a straight line is:
y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex])
The point ([tex]x_{1} , y_{1}[/tex]) = ( -2, -8)
y - (-8) = 16/11( x -(-2))
y + 8 = 16/11(x + 2)
Therefore the equation of a line is y + 8= 16/11( x +2).
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1.Arsenic-74 is used to locate brain tumors. It has a half-life of 17.5 days. 90 mg wereused in a procedure. Write an equation that can be used to determine how much ofthe isotope is left after x number of half-lives.2. how much would be left after 70 days ?
2) 5.625 mg will be left
Explanation:1) Half-life = 17.5 days
initial amount of Arsenic-74 = 90 mg
To get the equation, we will use the equation of half-life:
[tex]\begin{gathered} N_t\text{ = N}_0(\frac{1}{2})^{\frac{t}{t_{\frac{1}{2}}}} \\ where\text{ N}_t\text{ = amount remaining} \\ N_0\text{ = initial amount} \\ t_{\frac{1}{2}\text{ }}\text{ = half-life} \end{gathered}[/tex][tex]N_t\text{ = 90\lparen}\frac{1}{2})^{\frac{t}{17.5}}[/tex]2) we need to find the remaining amount of Arsenic-74 after 70 days
t = 70
[tex]\begin{gathered} N_t=\text{ 90\lparen}\frac{1}{2})^{\frac{70}{17.5}} \\ N_t\text{ = 5.625 mg} \end{gathered}[/tex]So after 70 days, 5.625 mg will be left
Find -x + 10 subtracted from 0.A. 0B. -x + 10C. x - 10
GIVEN:
We are given the following expression;
[tex]-x+10[/tex]Required;
To find the value of this expression subtracted from 0.
Step-by-step solution;
To subtract the expression from zero, we re-write as follows;
[tex]\begin{gathered} 0-(-x+10) \\ \end{gathered}[/tex]Note at this point that a negative times a negative results in a positive.
That is,
[tex]\begin{gathered} -\times(-)=+ \\ \\ Also; \\ \\ -\times(+)=- \end{gathered}[/tex]Therefore, we simplify as follows;
[tex]\begin{gathered} 0-(-x+10) \\ \\ =0+x-10 \\ \\ =x-10 \end{gathered}[/tex]Therefore, the correct answer is option C
ANSWER:
[tex]C:x-10[/tex]What is the gcf of 12 and 86?
factors of 12: 1, 2, 3, 4, 6, 12
factors of 86: 1, 2, 43, 86
Then, the greatest common factor (gcf) is 2
Below are the times (in days) it takes for a sample of 5 customers from Tony's computer store to pay their invoices.
In this problem, we have the following data sample:
[tex]32,37,24,22,20.[/tex]We must compute the standard deviation of this data sample.
1) First, we compute the mean value which is given by the following formula:
[tex]\bar{x}=\frac{\sum^n_{i\mathop=1}x_i}{n}=\frac{32+37+24+22+20}{5}=\frac{135}{5}=27.[/tex]2) Now, we compute the standard deviation using the following formula:
[tex]\sigma=\sqrt[]{\frac{\sum^n_{i\mathop{=}1}(x_i-\bar{x})^2}{n-1}}=\sqrt[]{\frac{208}{5-1}}\cong7.21.[/tex]Answer
The standard deviation is 7.21.
Solve 3p + 9q = 18 for q
Answer:
[tex]q=2-\frac{1}{3}p[/tex]Explanation:
Given the equation;
[tex]3p+9q=18[/tex]We want to make q the subject of formula;
firstly, let's subtract 3p from both sides;
[tex]\begin{gathered} 3p-3p+9q=18-3p \\ 9q=18-3p \end{gathered}[/tex]Then let us divide both sides by the coefficient of q;
[tex]\begin{gathered} \frac{9q}{9}=\frac{18-3p}{9} \\ q=2-\frac{1}{3}p \end{gathered}[/tex]Therefore, making q the subject of formula;
[tex]q=2-\frac{1}{3}p[/tex]For triangle ABC, ∡c=90°. Draw and label a diagram for this triangle, then find the measures of the remaining angles and sides. Explain how you found each measure.
Given:-
[tex]\Delta ABC,\angle C=90[/tex]To find:-
Draw and label a diagram for this triangle, then find the measures of the remaining angles and sides. Explain how you found each measure.
At first construct an right angled triangle at c. so we get,
So now we need to use a protractor and measure the angle A and angle B.
Question 35?Find the indicated function and state its domain in interval notation?
Question 35.
Given:
[tex]\begin{gathered} f(x)=x-5 \\ \\ g(x)=\sqrt[]{x+3} \\ \\ \text{Let's solve for }\frac{f(x)}{g(x)} \end{gathered}[/tex]To solve the function operation, let's divide both functions.
Hence, we have:
[tex]\frac{f(x)}{g(x)}=\frac{x-5}{\sqrt[]{x+3}}[/tex]Now, let's find the domain of the function f(x)/g(x).
Domain is the set of all possible x-values that makes the function true.
Hence, to find the domain, set the expression in the radicand equal to zero.
We have:
x + 3 = 0
Subtract 3 fromboth sides:
x + 3 - 3 = 0 - 3
x = - 3
Therefore, the domain in interval notation is:
(-3, ∞).
ANSWER:
[tex]\begin{gathered} \frac{h(x)}{g(x)}=\frac{x-5}{\sqrt[]{x+3}} \\ \\ \text{Domain:}(-3,\infty) \end{gathered}[/tex]
Josiah can jog 5/6 mile in 15 min find his average speed in miles per hour
Answer:
3 1/3 miles per hourStep-by-step explanation:
Given speed:
5/6 mile per 15 minConvert this to mph as follows:
5/6 mile per 15*1/60 h, since 1 min = 1/60 h5/6 mile per 1/4 h, simplify5/6 : 1/4 mile per 1/4 : 1/4 h, divide both sides by 1/45/6 *4 mile per 1 h, multiply10/3 mile per hour, 3 1/3 miles per hour, convert to mixed fractionAnswer:
10/3 miles per hour
Step-by-step explanation:
Given that,
→ 5/6 mile in 15 min
→ 15 min × 4 = 1 hour
Average speed in miles per hour,
→ 5/6 × 4
→ 20/6
→ 10/3 miles per hour
Hence, required answer is 10/3.
What is the slope of a line parallel to the line whose equation is 3x-18y=-3783x−18y=−378. Fully simplify your answer.
ANSWER
Slope is 1/6
STEP-BY-STEP EXPLANATION
What to find? The slope of the line parallel to a given equation
Given equation
[tex]3x\text{ - 18y = -378}[/tex]The slope-intercept form of an equation is given below as
[tex]y\text{ = mx + b}[/tex]Where m is the slope of the line
y is the intercept of the y - axis
The next thing is to rewrite the above equation in the format of the slope-intercept equation
[tex]\begin{gathered} 3x\text{ - 18y = -378} \\ \text{ Isolate -18y by substracting 3x from both sides} \\ 3x\text{ - 3x - 18y = -378 - 3x} \\ -\text{ 18y = -3x - 378} \\ \text{Divide through by -18} \\ \frac{-18y}{-18\text{ }}\text{ = }\frac{-3x}{-18}\text{ - }\frac{378}{-18} \\ y\text{ = }\frac{1}{6}x\text{ + 21} \\ y\text{ = }\frac{1}{6}x\text{ + 21} \\ \text{ Since y = mx + b} \\ m\text{ = slope} \\ \text{Hence,m = }\frac{1}{6} \end{gathered}[/tex]For lines that are parallel to each other, the slope remains the same
[tex]m1\text{ = m2}[/tex]Therefore, the slope of the line parallel whose equation is y = 3x - 18y = -378 is 1/6
out of 1,000 plants, some were given a new fertilizer and the rest were given no fertilizer. Some of the plants lived and some of them died, as shown in the table above
which of the following statements is supported by the data?
A.fertilized plants died at a higher rate than unfertilized rate than unfertilozed plants did
B.fertilized plants qnd unfertilized plants died at the same rate
C. fertilized plants died at a lower rate than unfertilized plants died
D.None of the above statements can be supported by the data
The correct statement that supports the given data is; B: fertilized plants and unfertilized plants died at the same rate
How to find the death rate?Death rate is defined as the total number of deaths during a given time interval.
Now, we are given the following;
Total Number of Plants = 1000 plants
Total number of fertilized plants that lived = 200
Total number of fertilized plants that Died = 50
Total number of unfertilized plants that lived = 600
Total number of unfertilized plants that died = 150
Now, from the above it means that;
Death rate of fertilized plants = 50/250 = 0.2
Death rate of unfertilized plants = 150/750 = 0.2
Survival rate of fertilized plants = 200/250 = 0.8
Survival rate of unfertilized plants = 600/750 = 0.8
The death rates in both cases are equal
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the shorter leg of a right triangle is 7 m shorter than the longer leg. the hypotenuse is 7 m longer than the longer leg. find the side lengths of the triangle. length of the shorter leg:length of the longer leg:length of the hypotenuse:
Answer:
Explanation:
Let the length of the longer leg = x m
The shorter leg of a right triangle is 7m shorter than the longer leg. therefore:
Length of the shorter leg = (x-7) m
The hypotenuse is 7m longer than the longer leg.
Length of the hypotenuse = (x+7) m
We solve for x using Pythagoras Theorem.
[tex]\text{Hypotenuse}^2=\text{Opposite}^2+\text{Adjacent}^2^{}[/tex]This gives us:
[tex]\begin{gathered} (x+7)^2=x^2+(x-7)^2 \\ (x+7)(x+7)=x^2+(x-7)(x-7) \\ x^2+14x+49=x^2+x^2-14x+49 \\ 2x^2-x^2-14x-14x-49+49=0 \\ x^2-28x=0 \\ x(x-28)=0 \\ x-28=0\text{ or x=0} \\ x=28\text{ meters} \end{gathered}[/tex]Therefore:
• Length of the shorter leg: 28-7 = 21 meters
,• Length of the longer leg: 28 meters
,• Length of the hypotenuse: 28+7 = 35 meters
In the Alaskan temperature data set, what is the outlier, if any?5, 12, 14, 19, 19, 21, 25, 29, 33
ANSWER
5
EXPLANATION
We want to find the outlier in the data set given.
An outlier is a data point whose value is abnormal or incoherent with other values in the same data set.
That means that it's value does not tally with the other values in measure.
Therefore, the outlier from the data set is 5.
An inlet pipe on a swimming pool can be used to fill the pool in 20 hours. The drain pipe can be used to empty the pool in 45 hours. If the pool is 1/3 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?
We have the next given information:
- inlet pipe fill rate = 1/20 = 1job/hour
-The drain pipe empty rate = 1/45 job/hour
- The pool is 1/3 filled, then we need to fill 2/3.
If both are open, we have the next combined rate:
Combined rate =1/20 - 1/45 = 25/(20*45) = 25/900=1/36 = 1job/hour
Now,we need yo use the next equation:
rate * time = work done
Set x for time.
Replacing:
1/36 * x = 2/3
Multiply both sides by 36:
[tex]\begin{gathered} \frac{1}{36}*x=\frac{2}{3} \\ 36\left(\frac{1}{36}\right?x=36\ast\frac{2}{3} \\ x=24 \end{gathered}[/tex]Hence, it will take 24 hours to fill the pool
Can someone please help me?
I’ll give brainliest
Answer:
161/8
Step-by-step explanation:
all the work is in the pic below sorry if I am wrong
have a nice day:)
Answer:
20 [tex]\frac{1}{8}[/tex]
Step-by-step explanation:
multiply 5 [tex]\frac{3}{4}[/tex] × 3 [tex]\frac{1}{2}[/tex] ( change to improper fractions )
= [tex]\frac{23}{4}[/tex] × [tex]\frac{7}{2}[/tex]
= [tex]\frac{23(7)}{4(2)}[/tex]
= [tex]\frac{161}{8}[/tex]
= 20 [tex]\frac{1}{8}[/tex]
Calculate the simple interest earned. Round to the nearest cent.P = $4200, r = 7%, t = 1 year
The simple interest formula is defined as
[tex]\begin{gathered} I=Prt \\ \text{where} \\ P\text{ is the principal amount} \\ r\text{ is the rate converted to decimal} \\ t\text{ is time in years} \end{gathered}[/tex]Given
P = $4,200
r = 7% → 0.07 (converted to decimal)
t = 1 year
Substitute the following values and we get
[tex]\begin{gathered} I=(4200)(0.07)(1) \\ I=294 \end{gathered}[/tex]Therefore, the simple interest earned is $294.
a.Convert 7/9 to a percent and decimal.b.Write these numbers from least to greatest: 6/8, 7/8, 7/9
a. To convert the number 7/9 to a decimal we need to solve the division:
[tex]\frac{7}{9}=0.778[/tex]Thus, 7/9 as a decimal number is 0.778.
To convert it to a percent, multiply the decimal form by 100%:
[tex]0.778\cdot100=77.8\text{ \%}[/tex]b. To write the numbers from least to greatest we need to convert these fractions to the same denominator, we can do it by multiplying the fractions 6/8 and 7/8 by 9/9 and the fraction 7/9 by 8/8, as follows:
[tex]\begin{gathered} \frac{6}{8}\cdot\frac{9}{9}=\frac{54}{72} \\ \frac{7}{8}\cdot\frac{9}{9}=\frac{63}{72} \\ \frac{7}{9}\cdot\frac{8}{8}=\frac{56}{72} \end{gathered}[/tex]Thus, in order from least to greatest it is: 54/72 , 56/72 , 63/72.
This order corresponds to:
6/8 , 7/9 , 7/8
ANSWER PLEASE. FIRST ANSWER WILL BE BRAILIEST!!! DUE TODAY PLEASE HELP!!! WORTH 25 points!!!
The measure of angle C is given as follows:
<C = 80º.
Measure of angle CSegments AD and BE are parallel, hence the angles A and B are congruent, that is, they have the same measure:
<A = <B.
Angle ABE is of 50º, hence the measures of the congruent angles A and B are given as follows:
<A = <B = 50º.
The sum of the measures of the internal angles of a triangle is of 180º, hence the following relation from triangle ABC is established.
<A + <B + <C = 180º.
The measures of angles A and B were already found, hence we can solve for the measure of angle C with the above equation as follows:
<A + <B + <C = 180º.
50 + 50 + <C = 180
<C = 180 - 100
<C = 80º.
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ABC is congruent to DEF.
what is the length of AB and what is angle EDF?
Answer:
10 In the diagram below, DE divides AB and AC proportionally, m∠C = 26°, m∠A = 82°, and DF bisects ∠BDE. The measure of angle DFB is. 1) 36°. 2) 54°. 3) 72°.
Step-by-step explanation:
In the formula C = pmn, p stands for___
A. price per item
B. period
C. promotion
D. percent
a square box is being cut apart and has a measurement system below. What is the surface area of the box?
ANSWER
73.5 in²
EXPLANATION
To find the surface area, we have to find the area of one face - one of the squares of the diagram - and then multiply that by 6 - because cubes have 6 faces.
The area of one face is:
[tex]A_{\text{face}}=3.5^2in^2=12.25in^2[/tex]The surface area of the box is:
[tex]\begin{gathered} S_{}=6A_{\text{face}} \\ S=6\cdot12.25in^2^{} \\ S=73.5in^2 \end{gathered}[/tex]Solve the system by elimination. x+y=2x-y=6
ANSWER:
x = 4 and y = -2
STEP-BY-STEP EXPLANATION:
We have the following system of equations:
[tex]\begin{gathered} x+y=2 \\ x-y=6 \end{gathered}[/tex]To use the elimination system, we only have to add both equations, like this:
[tex]\begin{gathered} x+y+x-y=2+6 \\ 2x=8 \\ x=\frac{8}{2} \\ x=4 \\ \\ \text{ now, for y:} \\ x+y=2 \\ 4+y=2 \\ y=2-4 \\ y=-2 \end{gathered}[/tex]The value of x is 4 and the value of y is -2
Write the inequality that represents the sentence, "Four less than a number is greater than 49.Choose the correct answer below. A. X+4>49 -B. X-4249C. X-4> 49D. X+4> 49
Let x be the number
Thus, 4 less than a number means
[tex]x-4[/tex]4 less than a number means is greater than 49 means
[tex]x-4>49[/tex]The answer is x-4>49, option C.
Need help with question 2 related to literal C of question 1
For the given parabola:
Vertices, foci and asymptotes:
Vertices: (-2, 0) and (2, 0)
Foci: (-5.385, 0) and (5.385, 0)
Asymptotes: y = -(5/2)x and y = (5/2)x
Fundamental rectangle and conjugate axis endpoints:
Endpoints: 5 and -5
Simplify (c3d2)4.
cd24
c12d8
c7d12
c7d6
By algebra properties, the simplified form of (c³ · d²)⁴ is equal to c¹² · d⁸. (Correct choice: B)
How to simplify an algebraic expression
In this problem we find the power of the product of two powers whose variables are c and d and which must be simplified by using algebra properties. The complete procedure is shown below:
(c³ · d²)⁴ Given(c³)⁴ · (d²)⁴ Power of a productc¹² · d⁸ Power of a power / Definition of multiplication / ResultThe simplified form of the algebraic expression is c¹² · d⁸.
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Hans is a software salesman. His base salary is $1700, and he makes an additional $70 for every copy of History is Fun he sells. Let P represent his total pay (in dollars), and let N represent the number of copies of History is Fun he sells. Write an equation relating P to N. Then use this equation to find his total pay if he sells 26 coples of History Is Fun.
the equation is:
[tex]P=1700+70N[/tex]so if he sells 26 copies we get that:
[tex]P=1700+26\cdot70=3520[/tex]Please need help fast!
Answer:
Slope is [tex]-\frac{7}{2}[/tex] and the y-intercept is (0,-2)
Step-by-step explanation:
First, turn the equation into slope-intercept form.
Slope intercept form is [tex]y=mx+b[/tex]. Where m is the slope and b is the y-intercept
The equation would be [tex]y=\frac{4-7x}{-2}[/tex]. Which is equal to [tex]y=\frac{-7}{2} x-2[/tex].
This means that the slope would be [tex]-\frac{7}{2}[/tex] and the y-intercept is (0,-2)
A. Solve for y.
y = ______
B. Find the measure of angles A, C and D showing all work.
∠A = _______, ∠C = ________, ∠D = ________
A and B are Vertical Angles and are thus congruent.
A = B
3y - 24 = 51
3y - 24 + 24 = 51 + 24
3y = 75
3y/3 = 75/3
y = 25
We can solve for A, but we already know A = B and B = 51, so A = 51.
C and D are also Vertical Angles. Since these angles go all the way around, they add up to 360.
51 + 51 + C + D = 360
C = D
C = x
D = x
D + C = 2x
102 + 2x = 360
102 - 102 + 2x = 360 - 102
2x = 258
2x/2 = 258/2
x = 129
C = 129
D = 129
what is 288 divided by 16
Answer:
18
Step-by-step explanation:
16x18=288
The solution is, Yes, because the last digit is 8, which is divisible by 4.
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
288 divisible by 16
i.e. 288/16 = 18
so, it is divisible.
now, we know that,
because the last digit is 8, which is divisible by 4.
Hence, The solution is, Yes, because the last digit is 8, which is divisible by 4.
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Identify if the statement is consistent or inconsistent. If the system is consistent, identify wether the equations are dependent or independent.
The solution of the system is: (9, -6)
If a system has at least one solution, it is said to be consistent.
If a consistent system has exactly one solution, it is independent.
Then, the system is consistent and the equations are independent.
How many feet are represented by a 4-in. line if it is drawn to ascale of 1/2 in. = 1 ft?
When working with scales, we can find the measures by using the rule of three.
From the scale, we know that 1/2 in corresponds to 1 ft, so, the rule of three is:
1/2 in --- 1ft
4 in --- x
Where "x" is the size of the line in feet repreented by the 4 in line in the drawing.
So, we cross multiply to get the equation:
[tex]\begin{gathered} \frac{1}{2}x=4\cdot1 \\ x=2\cdot4 \\ x=8 \end{gathered}[/tex]Thus, this lines represents a size of 8 ft.
