No solutions
Explanation
[tex]\begin{gathered} y=x+6\text{ Eq(1)} \\ y=x+2\text{ Eq(2)} \end{gathered}[/tex]
Step 1
replace Eq(1) in Eq (2)
[tex]\begin{gathered} y=x+2\text{ Eq(2)} \\ x+6=x+2 \\ \end{gathered}[/tex]Step 2
subtract x in both sides
[tex]\begin{gathered} x+6=x+2 \\ x+6-x=x+2-x \\ 6=2 \end{gathered}[/tex]6=2 is false, it means there is not solution for both equations,
a) Consider an arithmetic series 4+2+0+(-2)+.....i) What is the first term? And find the common difference d.ii) Find the sum of the first 10 terms S(10).b) Solve [tex] {2}^{x - 3} = 7[/tex]
Answer:
Explanation:
Here, we want to work with an arithmetic series
a) First term
The first term (a) of the arithmetic is the first number on the left
From the question, we can see that this is 4
Hence, 4 is the first term
To find the common difference, we have this as the difference between twwo subsequent terms, going from left to right
We have this as:
[tex]2-4\text{ = 0-2 = -2-0 = -2}[/tex]The common difference d is -2
ii) We want to calculate the sum of the first 10 terms
The formula for this is:
[tex]S(n)\text{ = }\frac{n}{2}(2a\text{ + (n-1)d)}[/tex]Where S(n) is the sum of n terms
n is the number of terms which is 10
a is the first term of the series which is 4
d is the common difference which is -2
Substituting these values, we have it that:
[tex]\begin{gathered} S(10)\text{ = }\frac{10}{2}(2(4)\text{ + (10-1)-2)} \\ \\ S(10)\text{ = 5(8+ (9)(-2))} \\ S(10)\text{ = 5(8-18)} \\ S(10)\text{ = 5(-10)} \\ S(10)\text{ = -50} \end{gathered}[/tex]Use the rectangle at the right to answer the following questions. a. Find the area of the entire rectangle. Show your work. b. Calculate the perimeter of the figure. Show your work.
Length of the entire rectangle = 12 + 5 = 17
Width of the entire rectangle = 6+4 = 10
Part a
Area of rectangle = Length x width
Area of the entire rectangle = 17 x 10 = 170 square units
Part b
Perimeter of rectangle = 2( length + width )
Perimeter of the entire rectangle = 2(17 + 10 )
=2 (27) = 54
Perimeter of the entire rectangle = 54 units
Length of the entire rectangle = 12 + 5 = 17
Width of the entire rectangle = 6+4 = 10
Part a
Area of rectangle = Length x width
Area of the entire rectangle = 17 x 10 = 170 square units
Part b
Perimeter of rectangle = 2( length + width )
Perimeter of the entire rectangle = 2(17 + 10 )
=2 (27) = 54
Perimeter of the entire rectangle = 54 units
evaluate the function found in the previous step at x= 1
Given:
[tex]y+\sqrt[]{x}=-3x+(x-6)^2[/tex]To evaluate the function at x=1, we simplify the given relation first:
[tex]\begin{gathered} y+\sqrt[]{x}=-3x+(x-6)^2 \\ Rearrange \\ y=-\sqrt[]{x}-3x+(x-6)^2 \end{gathered}[/tex]We let:
y=f(x)
[tex]f(x)=-\sqrt[]{x}-3x+(x-6)^2[/tex]We plug in x=1 into the above function:
[tex]\begin{gathered} f(x)=-\sqrt[]{x}-3x+(x-6)^2 \\ f(1)=-\sqrt[]{1}-3(1)+(1-6)^2 \\ \text{Simplify} \\ f(1)=-1-3_{}+25 \\ f(1)=21 \end{gathered}[/tex]Therefore,
[tex]f(1)=21[/tex]what is the x intercepts or zeros for y = x^2 - 6x + 5
Solution:
Given;
[tex]y=x^2-6x+5[/tex]The x-intercepts are the points where y=0.
Thus;
[tex]x^2-6x+5=0[/tex]Thus;
[tex]\begin{gathered} x^2-x-5x+5=0 \\ \\ x(x-1)-5(x-1)=0 \\ \\ x-1=0,x-5=0 \\ \\ x=1,x=5 \end{gathered}[/tex]ANSWER:
[tex]x=1,x=5[/tex]Steven read a total of 8 books over 4 months. After belonging to the book club for 7 months,how many books will Steven have read in all?
If he reads 8 books over 4 months it means that he reads 2 books per month. So, if we multiply this ratio by the 7 months we would find that he reads 14 books over 7 months.
The answer is 14 books.
Find the length of the missing side. Round answers to the nearest tenth if necessary. * S sva Your answer
Question:
Solution:
Notice that the angle between the sides of the square is 90 degrees:
Therefore, the angle of the vertex of the triangle measures 45 degrees:
thus, we obtain the following right triangle:
Now, apply the following trigonometric identity:
[tex]\cos \text{ (45) = }\frac{s}{5\sqrt[]{2}}[/tex]solving for s, we get:
[tex]s\text{ = cos(45) . 5 }\sqrt[]{2}\text{ = 5}[/tex]then, we can conclude that the correct answer is:
[tex]s\text{ = 5}[/tex]$11,335 is invested, part at 9% and the rest at 6%. If the interest earned from the amount invested at 9% exceeds the interest earned from the amount invested at 6% by $865.35, how much is invested at each rate?
The amount that was invested at 9% is $10303 , and at 6% is $1032 .
In the question ,
it is given that
total amount invested is $11335 .
let the amount invested at 9% be "x" .
so , the interest earned from 9% part is 0.09x
and let the amount invested at 6% be "y" .
the interest earned from 6% part is 0.06y
So , the equation is x + y = 11335 .
x = 11335 - y
Also given that interest earned from 9% amount exceeds the interest earned from 6% by $865.35 .
So , according to the question
0.09x = 0.06y + 865.35
On substituting x = 11335 - y in the above equation , we get
0.09(11335 - y) = 0.06y + 865.35
1020.15 - 0.09y = 0.06y + 865.35
0.09y + 0.06y = 1020.15 - 865.35
0.15y = 154.8
y = 154.8/0.15
y = 1032
and x = 11335 - 1032
x = 10303
Therefore , The amount that was invested at 9% is $10303 , and at 6% is $1032 .
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ASAP
Deena works at a customer service call center. She fields an average of 7 calls per hour. Employees are encouraged to field more than 280 calls per week. Deena has already fielded 112 calls this week.
How many more hours, x, does Deena need to work this week to reach the weekly goal of fielded calls if she continutes to field an average of 7 calls per hour? Select the inequality that includes the fewest number of hours Deena can work this week and still reach the weekly goal.
A.
x > 24
B.
x > 40
C.
x > 3
D.
x > 31
he two-way frequency table given shows the results from a survey of students who attend the afterschool program.
Takes Art Class Doesn't Take Art Class Total
Plays a Sport 45 120
Doesn't Play a Sport 45
Total 225
Does the data show an association between taking an art class and playing a sport?
There is a strong, positive association.
There is a strong, negative association.
There is a weak, positive association.
There is a weak, negative association.
The association between the variables art class and playing a sport is classified as follows:
There is a strong, negative association.
What is the association between the two variables?The association between variables can be classified either as positive or as negative, as follows:
Positive: both variables behave similarly, either both increases or both decreasing.Negative: the variables behave in an inversely manner, with one increasing and the other decreasing, or vice-versa.In the context of this problem, it is found that of the students that take art class, the majority do not play a sport, while among those who do not take art class, the majority play a sport, hence there is a strong and negative association between the two variables.
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yki10.87-2110-9--2-6-10Which system of equations is best represented by this graph?А3x – y = 240 +9y = 36B3. - y = 64x + 9y = 42- 3y = -18
System 2x2
Find slopes of k1 and k2
k1 slope = (10--2)/(4-0) = 12/4 = 3
k2 slope= (-9 -9)/ (8-0) = 8/-18 = -4/9
Now find k1, and k2 interceptions with y
k1 , interception= -2
k2 ,interception = 4
Then now, form the 2 equations
y = 3x - 2
and
y = (-4/9)x + 4
Now rewrite equations
3x - y = 2
and
9y + 4x = 36
Then now looking at options ,we find that
ANSWER IS
OPTION A)
3x - y = 2
what must be a factor if the polynomial function f(x) graphed ib the coordinate plane below ?
Solution
The question gives us a graph that crosses the x-axis at 3 points: x = 1, x = 2, and x = -3. We are asked to find which of the factors on the graph is in the options given.
- Whenever a graph crosses the x-axis at a point "a", it implies that x = a is a root of the graph and as a result, (x - a) must be a factor of the graph.
- We can apply this to the question and derive the factors of the graph as follows:
[tex]\begin{gathered} \text{ When }x=-3\colon \\ x=-3 \\ \text{Add 3 to both sides} \\ x+3=0 \\ \\ \text{Thus, }(x+3)\text{ is a factor of the graph.} \\ \\ \\ \text{When }x=1\colon \\ x=1 \\ \text{Subtract 1 from both sides} \\ x-1=0 \\ \\ \text{Thus, }(x-1)\text{ is a factor of the graph} \\ \\ \\ \text{When }x=2\colon \\ x=2 \\ \text{Subtract 2 from both sides} \\ x-2=0 \\ \\ \text{Thus, (}x-2)\text{ is a factor of the graph.} \\ \\ \\ \text{Thus, we can conclude that the 3 factors of the graph are:} \\ (x+3),(x+1),\text{ and }(x-2) \end{gathered}[/tex]- Going through the options, we can see that only (x - 1) is present in the options.
- Thus, (x - 1) is the answer
Final Answer
(x - 1) is the answer (OPTION B)
Parallel to x = -4 and passing through the point (-3,-5)find the equation of the line
A line of the form x = a, where "a" is a number is a VERTICAL LINE. The graph of the line x = - 4 is shown below:
The line that is parallel to this will also be a vertical line of the form x = a.
The line parallel passes through (-3, -5). So, this will have equation
x = - 3
Answer[tex]x=-3[/tex]
Find area and perimeter of the shape identify the shape
Part A
The dimensions of the shape shown are given as
length, l = 12 in
breadth (b) = width, w = 4 in
The area of the shape is given as;
[tex]\begin{gathered} A=l\times b \\ A=12\times4 \\ A=48in^2 \end{gathered}[/tex]Therefore, the area of the shape is 48 square inches.
Part B
The perimeter of a shape is the sum of all the outer sides enclosing the shape
From the above shape, we add all four sides together
[tex]\begin{gathered} P=12+12+4+4 \\ P=32in \end{gathered}[/tex]Consequently, we can get the perimeter using formula method as well
[tex]\begin{gathered} P=2(l+b) \\ P=2(12+4) \\ P=2(16) \\ P=2\times16 \\ P=32in \end{gathered}[/tex]Therefore, the perimeter of the shape is 32 inches.
Part C
From the dimension given in the question, since the shape has a length and width, and the length and width are not equal, then the shape is a rectangle.
The shape, therefore, is a rectangle.
A line passes through the points (7,9) and (10,1). What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
Answer:
[tex](y - 9) = (-8/3)\, (x - 7)[/tex].
Step-by-step explanation:
If a line in a cartesian plane has slope [tex]m[/tex], and the point [tex](x_{0},\, y_{0})[/tex] is on this line, then the point-slope equation of this line will be [tex](y - y_{0}) = m\, (x - x_{0})[/tex].
The slope of a line measures the rate of change in [tex]y[/tex]-coordinates relative to the change in the [tex]x[/tex]-coordinates. If a line goes through two points [tex](x_{0},\, y_{0})[/tex] and [tex](x_{1},\, y_{1})[/tex], the slope of that line will be:
[tex]\begin{aligned}m &= \frac{y_{1} - y_{0}}{x_{1} - x_{0}}\end{aligned}[/tex].
In this question, the two points on this line are [tex](7,\, 9)[/tex] and [tex](10,\, 1)[/tex], such that [tex]x_{0} = 7[/tex], [tex]y_{0} = 9[/tex], [tex]x_{1} = 10[/tex], and [tex]y_{1} = 1[/tex]. Substitute these values into the equation to find the slope of this line:
[tex]\begin{aligned}m &= \frac{y_{1} - y_{0}}{x_{1} - x_{0}} \\ &= \frac{1 - 9}{10 - 7} \\ &= \left(-\frac{8}{3}\right)\end{aligned}[/tex].
With the point [tex](7,\, 9)[/tex] as the specific point [tex](x_{0},\, y_{0})[/tex] (such that [tex]x_{0} = 7[/tex] and [tex]y_{0} = 1[/tex]) as well as a slope of [tex]m = (-8 / 3)[/tex], the point-slope equation of this line will be:
[tex]y - y_{0} = m\, (x - x_{0})[/tex].
[tex]\displaystyle y - 9 = \left(-\frac{8}{3}\right)\, (x - 7)[/tex].
Examine this lable of points, which are all on a certain line. 8 What is the slope of this line? Enter your answer as a number, like this 42 Or, if the slope is undefined. enter a lowercase letter "u. like this. u
The formula for determining slope, m is expressed as
slope, m = (y2 - y1)/(x2 - x1)
y1 represents initial value of y
y2 represents final value of y
x1 represents initial value of x
x2 represents final value of x
From the table,
y2 = - 8
y1 = 0
x2 = - 1
x1 = - 5
Slope, m = (0 - - 8)/(- 1 - - 5)
Slope, m = (0 + 8)/(- 1 + 5)
Slope, m = 8/4
Slope = 2
Express $20.35 as an equation of working h hours, when I equals income
Let
I ------> income in dollars
h -----> number of hours
$20.35 is the hourly pay
so
the linear equation that represent this situation is
I=20.35*hDetermine the value of each limit for the function below.f(x)=x/(x-2)^2(a) lim f(x). (b) lim f(x)x---2^-. x---2^+
We will have the following:
a)
[tex]\lim _{x\rightarrow2^-}\frac{x}{(x-2)^2}=\infty[/tex]b)
[tex]\lim _{x\rightarrow2^+}\frac{x}{(x-2)^2}=\infty[/tex]would this be (0, -1) since if b is greater than 1 but it is also -2
The y-intercept is the point where the graph cuts the y-axis. The y-axis is the line x = 0, therefore, to find the y-coordinate of this point we just need to evaluate x = 0 in our function.
[tex]\begin{gathered} y(x)=b^x-2 \\ y(0)=b^0-2 \end{gathered}[/tex]Any nonzero real number raised to the power of zero is one, therefore
[tex]y(0)=b^0-2=1-2=-1[/tex]The y-intercept is (0, -1).
1/2+1/9Please help me
If the fraction whose denominator are equal then they will add up
In the given fraction 1/2 +1/9, the denominator of both the fraction 1/2 & 1/9 is not same
so, to make the base same we take the LCM of the 2 & 9
[tex]\begin{gathered} \text{LCM of 2 \& 9 is 18} \\ Si,\text{ the fraction will be :} \\ \frac{1}{2}+\frac{1}{9}=\frac{9+2}{18} \\ \frac{1}{2}+\frac{1}{9}=\frac{11}{18} \end{gathered}[/tex]Answer : 11/18
Create a table of values for the function graphed below using the plotted points. Remember, table of values are written with the -values in order from least to greatest (read the graph from left to right).
To create the table of values, we need to find the coordinates of the given points.
The coordinatesare given by (x,y), where x ican be found by drawing an imaginary vertical line passing through the point, and the x-value is the value of the x-axis where the line intercepts the x-axis.
The y-coordinate is given by the point of interception on the y-axis of a horizontal line passing through the point, so, for the fir tpoint the coordinates are:
[tex]\begin{gathered} (-2,5) \\ x-value\rightarrow-2 \\ y-value\rightarrow5 \end{gathered}[/tex]If we apply the same procedure to the next points, we can find the following coordinates:
[tex]\begin{gathered} (-1,4) \\ (0,3) \\ (1,2) \\ (2,1) \end{gathered}[/tex]Thus, th table of values will be:
x y
-2 5
-1 4
0 3
1 2
2 1
a) Twice the difference of a number c and forty.b) Four times the sum of a number f and fifty.
a) We have a number X that is twice the difference of a number c and 40.
We can write this as:
[tex]X=2(c-40)[/tex]b) Four times the sum of a number f and fifty.
Then, X is:
[tex]X=4(f+50)[/tex]A long distance runner runs 2⁵ miles one week and 2⁷ miles the next week. How many times farther did he run in the second week than the first week?
Answer:
he ran 96 miles farther in the second week.
Explanation:
Given that A long distance runner runs 2⁵ miles one week;
[tex]2^5miles=2\times2\times2\times2\times2=32miles[/tex]And 2⁷ miles the next week;
[tex]2^7miles=2\times2\times2\times2\times2\times2\times2=128\text{ miles}[/tex]The amount of miles farther he run in the second week than the first week is;
[tex]\begin{gathered} 128-32 \\ =96\text{ miles} \end{gathered}[/tex]Therefore, he ran 96 miles farther in the second week.
The number of algae in a tub in a labratory increases by 10% each hour. The initial population, i.e. the population at t = 0, is 500 algae.(a) Determine a function f(t), which describes the number of algae at a given time t, t in hours.(b) What is the population at t = 2 hours?(c) What is the population at t = 4 hours?
a) Let's say initial population is po and p = p(t) is the function that describes that population at time t. If it increases 10% each hour then we can write:
t = 0
p = po
t = 1
p = po + 0.1 . po
p = (1.1)¹ . po
t = 2
p = 1.1 . (1.1 . po)
p = (1.1)² . po
t = 3
p = (1.1)³ . po
and so on
So it has an exponential growth and we can write the function as follows:
p(t) = po . (1.1)^t
p(t) = 500 . (1.1)^t
Answer: p(t) = 500 . (1.1)^t
b)
We want the population for t = 2 hours, then:
p(t) = 500 . (1.1)^t
p(2) = 500 . (1.1)^2
p(2) = 500 . (1.21)
p(2) = 605
Answer: the population at t = 2 hours is 605 algae.
c)
Let's plug t = 4 in our function again:
p(t) = 500 . (1.1)^t
p(4) = 500 . (1.1)^4
p(4) = 500 . (1.1)² . (1.1)²
p(4) = 500 . (1.21) . (1.21)
p(4) = 500 . (1.21)²
p(4) = 732.05
Answer: the population at t = 4 hours is 732 algae.
What is the slope of the line shown below?(2,2), (-1,-4) A. 2 B-6. C.6. D-2
Solution
The slope is given by
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ \Rightarrow m=\frac{-4-2}{-1-1}=\frac{-6}{-2}=3 \end{gathered}[/tex]Hence, the slope is 3
In the figure below, BAC~QPR. Use this information and the diagram below to name the corresponding parts of the similar triangles
a.
∠A is the right angle of the triangle ABC, so the corresponding angle is ∠P, which is the right angle of the triangle PQR.
b.
BC is the hypotenuse of the triangle ABC, so the corresponding side is QR, which is the hypotenuse of the triangle PQR.
c.
∠C is the smaller angle of the triangle ABC, so the corresponding angle is ∠R.
d.
∠Q is the bigger angle of the triangle PQR, so the corresponding angle is ∠B.
e.
PQ is the smaller leg of the triangle PQR, so the corresponding side is AB.
Find the slope of the line that contains the two points.ROUND YOUR ANSWER TO TWO DECIMAL PLACES.
The slope of a line is given by the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x1,y1) and (x2,y2) are the coordinates of the given points. Replace the given values and solve for m:
[tex]m=\frac{8-(-4)}{-6-0}=\frac{8+4}{-6}=\frac{12}{-6}=-2[/tex]The slope of the line that contains the two given points is -2.
Write the equation as an exponential equationlog_9(2x – 7) = 2x – 3
8. (03.07 MO)Solve x2 - 10x = -21. O x = 7 and x = 3O x = -7 and x = 3O x = -7 andx = -3O x = 7 and x = -3
Given:
Quadratic equation
[tex]x^2-10x+21=0[/tex]To find:
Values of x satisfying given equation.
Explanation:
Roots of equation of type
[tex]ax^2-bx+c=0[/tex]roots will be (x-a)(x-b) and x = a,b.
Solution:
We will factorize equation as:
[tex]\begin{gathered} x^2-10x+21=0 \\ x^2-7x-3x+21=0 \\ (x-3)(x-7)=0 \\ x=3,\text{ 7} \end{gathered}[/tex]Hence, 3 and 7 are values of x.
What is the slope of the line passing through the points (−1, 7) and (4, −1)? −5/62−8/5−2
Given the points:
(−1, 7) and (4, −1)
The slope of the line passing through the points is given by:
[tex]slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-7}{4-(-1)}=\frac{-8}{5}[/tex]So, the answer will be Slope = -8/5
A is the incenter of Triangle FHG Find the length of AT. Explain your thinking.
we have that
The incenter is the center of the triangle's incircle, the largest circle that will fit
AR=AT=AS -----> radius of the inscribed circle in the triangle
therefore
AT=3 units
