SOLUTION
Step 1 :
In this question, we have that Figure 1 and Figure 2 are similar.
The point that corresponds to point U is Point E.
A man starts his job with a certain monthlysalary and earns a fixed increment every year. If his salary was$7500 after 4 years of service and $9000 after 10 years ofservice, what was his starting salary and what is the annualincrement? Do you consider it a fair increment according to ourpresent cost of life and infletion?
Let starting salary = x
Increment every year = y
Therefore:
Salary after 4 years of service = x+4y
Salary after 10 years of service = x+10y
We have the equations:
[tex]\begin{gathered} x+4y=7500 \\ x+10y=9000 \end{gathered}[/tex]Substracting equation 1 from equation 2, we get:
[tex]x+10y-(x+4y)=9000-7500[/tex]Simplify:
[tex]\begin{gathered} x+10y-x-4y=1500 \\ 6y=1500 \\ Solve\text{ for y} \\ \frac{6y}{6}=\frac{1500}{6} \\ y=250 \end{gathered}[/tex]Next, substitute y = 250 in the equation 1:
[tex]x+4(250)=7500[/tex]And solve for x:
[tex]\begin{gathered} x+1000=7500 \\ x+1000-1000=7500-1000 \\ x=6500 \end{gathered}[/tex]Answer:
Starting salary = $6500
Annual increment = $250
the scale of a map say that 4 cm represents 5km what distance on the map in cm represents an actual distance of 10 km
We can do as follow s
centimeters km
4 5
x 10
which is the same as saying that 4 centimeters are 5km, so x centimeters are 10 km. We want to find the value of x. To do so, we use the fact that this is a proportion, so it must happen that
[tex]\frac{4}{5}\text{ = }\frac{x}{10}[/tex]So if we multiply on both sides by 10, we get
[tex]x\text{ = }\frac{4_{}\cdot10}{5}\text{ = }\frac{40}{5}=8[/tex]So 8 cm represent 10 km.
Complete the table for y = 2x + 2 and graph the resulting line.
Answer
The table is
x | y
-2 | -2
0 | 2
2 | 6
4 | 10
6 | 14
The graph is then
Explanation
In the absence of the table, I will use a couple of values for x to obtain corresponding values of y.
Then, these points will be marked on the graph and the line connecting the points is drawn.
y = 2x + 2
when x = -2
y = 2x + 2
y = 2(-2) + 2
y = -4 + 2
y = -2
The point will then be (-2, -2)
when x = 0
y = 2x + 2
y = 2(0) + 2
y = 0 + 2
y = 2
The point will then be (0, 2)
when x = 2
y = 2x + 2
y = 2(2) + 2
y = 4 + 2
y = 6
The point will then be (2, 6)
when x = 4
y = 2x + 2
y = 2(4) + 2
y = 8 + 2
y = 10
The point will then be (4, 10)
when x = 6
y = 2x + 2
y = 2(6) + 2
y = 12 + 2
y = 14
The point will then be (6, 14)
The full table and graph will then be presented under 'Answer'.
Hope this Helps!!!
1. d decreased by three
We need to write the expression:
d decreased by three
So. the new value will be less than the old value by 3
The word decreased mean the negative sign
So, the expression will be:
[tex]d-3[/tex]
11. A map is drawn so that 2 inches represents 700 miles. If the distance betweentwo cities is 3850 miles, how far apart are they on the map?a. 5.5 inchesb. 11 inchesc. 22 inchesd. 6 inchese. 12 inches
Given:
• 2 inches represents 700 miles on the map.
,• Actual distance between two cities = 3850 miles
Let's find the distance on the map.
Let's first find how many miles 1 inch represent.
We have:
[tex]\frac{700}{2}=350\text{ miles}[/tex]This means on the map, 1 inch represent 350 miles.
Now, to find the distance between the two cities on the map, we have:
[tex]\frac{3850}{350}=11\text{ inches}[/tex]Therefore, the distance between the two cities on the map is 11 inches.
ANSWER:
b. 11 inches
Given the function g(x) = x2 – 2, find the range when the domain is {-2, -1, 1, 3} A. {-1, 2, 7} B. {-6, -3, 3, 11} C. {-7, -2, -1, 1} D. {-11, -3,3, 6}
The domain of the function is the values of x
Domain = {-2, -1, 1, 3}
We will substitute x by these values to find g(x)
g(x) is the range of the function
x = -2
[tex]g(-2)=(-2)^2-2=4-2=2[/tex]x = -1
[tex]g(-1)=(-1)^2-2=1-2=-1[/tex]x = 1
[tex]g(1)=(1)^2-2=1-2=-1[/tex]x = 3
[tex]g(3)=(3)^2-2=9-2=7[/tex]The range of the function is the values of g(x)
Range = {-1, 2, 7}
The answer is A
can someone please help me find the answer to the following?
Answer:
1077.19 ft
Explanation:
Using the depression angle, we get that one of the angles of the formed triangle is also 18° because they are alternate interior angles, so we get:
Now, we can relate the distance x, the angle of 18°, and the height of the tower using the trigonometric function tangent, so:
[tex]\begin{gathered} \tan 18=\frac{Opposite}{Adjacent} \\ \tan 18=\frac{350}{x} \end{gathered}[/tex]Now, solving for x, we get:
[tex]\begin{gathered} x\cdot\tan 18=x\cdot\frac{350}{x} \\ x\cdot\tan 18=350 \\ \frac{x\cdot\tan18}{\tan18}=\frac{350}{\tan 18} \\ x=\frac{350}{\tan 18} \end{gathered}[/tex]Using the calculator, we get that tan(18) = 0.325, so x is equal to:
[tex]x=\frac{350}{0.325}=1077.19\text{ }ft[/tex]Therefore, the forest ranger is at 1077.19 ft from the fire.
The following chart below represents the bedtimes of 100 students at Waller Junior High in a recent survey Number of Students Bedtime 8:00 PM 22 8.30 PM 17 9:00 PM 36 9:30 PM 25 If all 750 students at WJH were surveyed, what is the best prediction of the number of students who would have a bedtime of 9:00 PM in
Answer
The predicted number of students with bedtime of 9:00 PM
= 270 students
Explanation
For surveying and sampling, the fraction of a particular case in the sample is generalized for the entire population to predict that case for the population.
So, if we want the number of students who would have a bedtime of 9:00 PM, we first find the percentage of students with bedtime of 9:00 PM in the sample.
Number of students with bedtime of 9:00 PM in the survey = 36
Total number of students in the survey = 22 + 17 + 36 + 25 = 100
Percentage of students with bedtime of 9:00 PM in the survey = (36/100) = 0.36
So, in the population of 750 students,
The predicted number of students with bedtime of 9:00 PM = (0.36) (750) = 270 students
Hope this Helps!!!
Which of the qqq-values satisfy the following inequality?6−3q≤16−3q≤16, minus, 3, q, is less than or equal to, 1Choose all answers that apply:Choose all answers that apply:(Choice A)Aq=0q=0q, equals, 0(Choice B)Bq=1q=1q, equals, 1(Choice C)Cq=2q=2q, equals, 2
Given -
6 - 3q ≤ 1
To Find -
The q-values that satisfy inequality =??w
Step-by-Step Explanation - ion
We will check for each of the given values;
A) q = 0
Putting q = 0, we get:
6 - 3(0) ≤ 1
6 ≤ 1
But, Six is greaterr than onee
So, this is the incorrect option.
B) q = 1
Putting q = 1, we get:
6 - 3(1) ≤ 1
3 ≤ 1
But, three is greater than one
So, this is the incorrect option.
C) q = 2
Putting q = 2, we get:
6 - 3(2) ≤ 1
0 ≤ 1
zero is less than one.
So, this is the correct option.
Final Answer -
Option (C) q = 2
which of the following is equivalent to the expression below? In(e^7)
Answer: C. 7
Explanation
When the exponent of a natural logarithm has an exponent, we can do the following:
[tex]\ln(e^7)=7\ln(e)[/tex]Additionally, we are given a natural logarithm, and the base for the natural logarithm is the mathematical constant e. When the argument of the logarithm is equal to the base, then it is equal to 1:
[tex]7\ln(e)=7\cdot1[/tex][tex]=7[/tex]Use the drawing tools to form the correct answers on the graph Consider function f(x)= ( 1 2 )^ x ,x<=0\\ 2^ x ,&x>0 Complete the table of values for function and then plot the ordered pairs on the graph. - 2 -1 1 2 f(x)
See explanation and graph below
Explanation:For x less than or equal to zero, we would apply the function f(x) = (1/2)^x
For x greater than zero, we would apply the function f(x) = 2^x
when x = - 2 (less than 0)
This falls in the 1st function
[tex]\begin{gathered} f(-2)\text{ = (}\frac{1}{2})^{-2} \\ f(-2)=\frac{1}{(\frac{1}{2})^2}\text{ = 1}\times\frac{4}{1} \\ f(-2)=2^2\text{ = 4} \end{gathered}[/tex]when x = -1 (less than 0)
This falls in the 1st function
[tex]\begin{gathered} f(-1)\text{ = (}\frac{1}{2})^{-1} \\ f(-1)\text{ = }\frac{1}{(\frac{1}{2})^1}\text{ = 2} \end{gathered}[/tex]when x = 0 (equal to 0)
This falls in the 1st function
[tex]\begin{gathered} f(0)\text{ = (}\frac{1}{2})^0 \\ f(0)\text{ = 1} \end{gathered}[/tex]when x = 1 (greater than 0)
This falls in the 2nd function
[tex]\begin{gathered} f(1)=2^1 \\ f(1)\text{ = 2} \end{gathered}[/tex]when x = 2 (greater than 0)
THis falls in the 2nd function
[tex]\begin{gathered} f(2)\text{ = }2^2 \\ f(2)\text{ = 4} \end{gathered}[/tex]Plotting the graph:
The end with the shaded dot reresent the function with equal to sign attached to the inequality [f(x) = (1/2)^x].
The end with the open dot represent the function without the equal to sign [f(x) = 2^x)
- x - 8 = -4x - 23 Solve for x
x=-5
Explanation
[tex]-x-8=-4x-23[/tex]Step 1
solve for x means we have to find the value for x that makes the equality true, to do that we need to isolate x
then
to isolate x we can apply the addition property of equality,it states that If two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal.
hence
Add 4x in both sides
[tex]\begin{gathered} -x-8=-4x-23 \\ -x-8+4x=-4x-23+4x \\ 3x-8=-23 \end{gathered}[/tex]Now, add 8 in both sides
[tex]\begin{gathered} 3x-8=-23 \\ 3x-8+8=-23+8 \\ 3x=-15 \end{gathered}[/tex]Step 2
now, we have a multiplication ( 3 multiplied by x), to isolate x we can apply the multiplication property,it says when you divide or multiply both sides of an equation by the same quantity, you still have equality
hence
divide both sides by 3
[tex]\begin{gathered} 3x=-15 \\ \frac{3x}{3}=\frac{-15}{3} \\ x=-5 \end{gathered}[/tex]therefore, the answer is
x=-5
I hope this helps you
the measure of an interior angle of an equilateral triangle is given as 3n-6. solve for the value of nA. 22B. 60C.6D. 2
Use the pair of functions to find f(g(x)) and g(f(x)) . Simplify your answers. f(x)=x−−√+4 , g(x)=x2+1
We have a case of composite functions, we must evaluate or replace one function as x value of the other one. In other words and doing the calculations
[tex]\begin{gathered} f(g(x))=f(x^2+1)=\sqrt{x^2+1}+4 \\ g(f(x))=(\sqrt{x})^2+8\sqrt{x}+16+1=x+8\sqrt{x}+17 \end{gathered}[/tex]Thus, the answer to the exercise is
f(g(x))=√(x^2+1) +4
g(f(x))=x+8√x+17
1. ABC Bank offers a certificate of deposit (CD), where you deposit money and are required to leaveit in the account for a set amount of time. You will be penalized if you withdraw your money fromit early. Suppose you want to deposit $6,000 in a 5-year CD where interest is accrued daily (1 year= 365 days).(a) How much money will you have in the account after 5 years if the APR is 2.12%? Round yourfinal answer to 2 decimals.(b) What is the annual percentage yield (APY) on this account? Round your final answer to 2decimals.
To calculate the ampount of money in the account after 5 years, we will use the formula:
[tex]A=p(1+\frac{r}{n})^{nt}[/tex]where A is the final amount
P is the initial amount or principal
r is the rate
n is the number of times the interest is applied
t is the time in years
From the question,
P = $6000 r = 2.12/100 = 0.0212 t= 5 n=365
substitute the values ibto the formula and evaluate
[tex]A=6000(1+\frac{0.0212}{365})^{365\times5}_{}[/tex][tex]A=6000(1+\frac{0.0212}{365})^{1825}[/tex][tex]A=6670.91[/tex]The amount is $6670.91
b)
To find the annual percentage yield (APY) on this account, we will use the formula:
[tex]APY=(1+\frac{r}{n})^n-1[/tex]Find the length of the leg x. enter the exact value, not a decimal approximation x1210x=
We can solve for the value of x using pythagorean theorem
[tex]c^2=a^2+b^2[/tex]where c is the hypotenuse ( in this case is 15) and a, b are the other legs of the triangle ( in this case is 8 and x).
Let's substitute the given values to the formula
[tex]\begin{gathered} c^2=a^2+b^2 \\ 15^2=8^2+x^2 \\ 225=64+x^2 \\ x^2=225-64 \\ x^2=161 \\ x=12.69 \end{gathered}[/tex]Now please follow this solution to solve for x in:
Identify the underlined place and 27.3856. Then round the number to that place.
Based on the positiion of the underlined decimal places, the underlined number is in the hundredths place.
Rounding it off, next to 8 in the hundredths place is 5 in the thousandths place.
If the number is 5 or greater, we add 1 to the previous decimal place therefore it is rounded to 27.39
What is the solution to -1-7? + 4 5 6 9 10 2 -10-9-8-7 6-5- 4 -3
Solution
To find the best expression, we need to first approximate the values before dividing it
[tex]\begin{gathered} 6\frac{3}{4}=6.75 \\ \\ We\text{ approximate to get} \\ 6.75\cong7 \end{gathered}[/tex]Similarly
[tex]\begin{gathered} 1\frac{2}{3}=1.6666666666667 \\ \\ we\text{ approximate to get} \\ \\ 1.6666667\cong2 \end{gathered}[/tex]Therefore, the answer is
[tex]7\div2[/tex]1.Given the graph, find the following:A: Identify the slope of the lineB.Identify the y-intercept of the lineC.Identify the x-intercept of the lineD. Write the equation of the line in slope-intercept form (y = mx+b)
A.
The slope of a line is the rate of change of the dependent variable (y) with respect to the independent variable (x).
Notice that for each increase of 3 units in the variable x, the variable y decreases 2 units. Then, the change in y is -2 when the change in x is 3. Then, the rate of change is:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{-2}{3}[/tex]B.
The y-intercept of a line is the value of y in which the line crosses the Y-axis. In this case, the line crosses the Y-axis at y=4. Then, the y intercept is:
[tex]4[/tex]C.
Similarly, the x-intercept is the value of x in which the line crosses the X-axis. In this case, we can see that the x-intercept is:
[tex]6[/tex]D.
Since the slope m is equal to -2/3 and the y-intercept b is equal to 4, then the equation of the line is:
[tex]y=-\frac{2}{3}x+4[/tex]7. Solve 3(x-4)=-5 for x.
Explantion:
3(x-4) = -5
Expand the bracket:
3x -12 = -5
Collect like
1. According to the story of Pythagoras's discoveries and your own exploration during the lesson,
when does the relationship a² + b² = c² hold true?
The given relationship using the Pythagorean theorem holds true for a right-angled triangle.
We are given a mathematical relationship using the Pythagorean theorem. The Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relationship between the three sides of a right triangle in Euclidean geometry. The equation is given below.
a² + b² = c²
We need to describe the situation when this relationship holds true. The variables "a", "b", and "c" represent the sides of a triangle. The Pythagorean theorem is applicable to a right-angled triangle. It states that the sum of the squares of the base and the perpendicular is equal to the square of the hypotenuse.
Here a, b, and c denote the lengths of the base, the perpendicular, and the hypotenuse of the triangle, respectively.
To learn more about triangles, visit :
https://brainly.com/question/2773823
#SPJ1
can you please help me
The relation between arcs AB and CD and angle x is:
[tex]m\angle x=\frac{1}{2}(m\hat{AB}+m\hat{CD})[/tex]Substituting with data, we get:
[tex]\begin{gathered} m\angle x=\frac{1}{2}(110+160) \\ m\angle x=\frac{1}{2}\cdot270 \\ m\angle x=135\text{ \degree} \end{gathered}[/tex]2. Given the degree and zero of a polynomial function, identify the missing zero and then find the standard form of the polynomial
Degree: 2; zero: -7 + 2i
The missing zero is:
+
i
The expanded polynomial is:
The expanded quadratic equation with real coefficients is y = x² + 14 · x + 45.
How to determine the least polynomial that contains a given root
In this problem we need to determine the expanded quadratic equation with real coefficients such that one of its roots is - 7 + i 2. According with the quadratic formula, quadratic equations can have two conjugated complex roots, that is:
r₁ = α + β, r₂ = α - β
Then, the complete set of roots of the quadratic equation are r₁ = - 7 + i 2 and r₂ = - 7 - i 2. Then, the factor form of the polynomial is:
y = (x + 7 - i 2) · (x + 7 + i 2)
y = x · (x + 7 + i 2) + (7 - i 2) · (x + 7 + i 2)
y = x² + 7 · x + i 2 · x + (7 - i 2) · x + 7 · (7 - i 2) + i 2 · (7 - i 2)
y = x² + 7 · x + i 2 · x + 7 · x - i 2 · x + 49 - i 14 + i 14 - i² 4
y = x² + 14 · x + 45
To learn more on quadratic equations: https://brainly.com/question/1863222
#SPJ1
Please help!! slope-intercept form!!
Answer: y=1x+4
Step-by-step explanation: the b (y-intercept) is 4 and when you go up 1/1 (1) it crosses the lines
how do i solve for scale factor from smaller to larger?
Answer:
1) k = 3
2) k = 2
Explanation:
To find the scale factor from the smaller to the larger figure, we need to divide the length of the larger figure by the length of the smaller figure.
The figures are similar, so we will use corresponding sides. Then:
[tex]\begin{gathered} k=\frac{\text{ larger length}}{\text{ smaller length}} \\ \text{ For the first figure:} \\ k=\frac{21}{7}=3 \\ \text{For the second figure:} \\ k=\frac{8}{4}=2 \end{gathered}[/tex]Therefore, the answers are:
1) k = 3
2) k = 2
write a ratio that is equivalent to 12:36 using the collums for 2 and 6
The given ratio is 12:36, which can be expressed as a fraction 12/36. An equivalent expression to this one can be obtained by simplifying
[tex]\frac{12}{36}=\frac{6}{18}[/tex]Therefore, the answer is 6/18.Which of the following is the closet approximation to 3√20?A) 3B) 5C) 2D) 4
The given expression is:
[tex]\sqrt[3]{20}[/tex]This can also be written as:
[tex]20^{(\frac{1}{3})}[/tex]The result = 2.71
Since 7 is greater than 5, it will become 0 and add 1 to 2 to become 3
Therefore, the closest approximation is 3
Perform the operation. Write your answer in scientific notation. 7.86×10^9________3×10^4
Answer:
2.62 * 10^ 5
Explanation:
To perform the operation given we rewrite it as
[tex]\frac{7.86}{3}\times\frac{10^9}{10^4}^{}[/tex]Now,
[tex]\frac{7.86}{3}=2.62[/tex]and
[tex]\frac{10^9}{10^4}^{}=10^{9-4}=10^5[/tex]therefore,
[tex]\frac{7.86}{3}\times\frac{10^9}{10^4}^{}=2.62\times10^5[/tex]which is our answer!
what is 10+5 rounded to the nearest thousand
the given expression is,
10 + 5 = 15
now we will round off it to the nearest
Hi i need help with unit rate fractions and ill show an example i need to have this figured out by thurday for a test and i have no clue so pls help
To find the rate in teaspoons per cup we divide the number of teaspoons by the cups:
[tex]\frac{4}{\frac{2}{3}}=\frac{12}{2}=6[/tex]Therefore, the unit rate is 6 teaspoons per cup.