Marisol's annual salary as an engineer is $75,000. After receiving a
promotion, her new annual salary is $80,000. What percent increase in her
salary resulted from her promotion?
The percent increase in her salary resulted from her promotion is 6.67%.
The annual salary of Marisol as an engineer = $75000.
After, the promotion salary of Marisol as an engineer = $80000.
We have to find the increment in her salary after promotion in percentage.
Before finding the increment in percentage we find the total increment in dollar in her salary after promotion.
Total increment in dollar = Salary after Promotion − Salary before Promotion
Total increment in dollar = $80,000 − $75,000
Total increment in dollar = $5000
As we know that we can find the percentage by multiplying the required number by 100 because percentage is the ratio with 100.
So, the increment in salary after promotion in percentage.
% increment = (Total increment/Salary before) * 100
% increment [tex]= (\frac{5000}{75000})*100[/tex]
% increment = 0.0667 * 100
% increment = 6.67%
Now we see that percent increase in her salary resulted from her promotion is 6.67%.
To learn more about percentage link is here
https://brainly.com/question/14801224
#SPJ1
What is the area, in coordinate units, of the triangle in the figure below
The area of the triangle in the image is 10 square units, thus, option C is the correct one.
What is the area of the triangle?
For a triangle of height H and a base B, the area is given by:
A = H*B/2.
In the image we can see that the base of the triangle goes from (0, 0) to (5, 0), then the length of the base is 5 units.
While the height goes from (0, 0) to (0, 4), so the height is 4 units.
Then the area will be:
A = (4 units)*(5 units)/2 = (20 square units)/2 = 10 square units.
The area is 10 square units.
Learn more about area:
https://brainly.com/question/24487155
#SPJ1
x =7, -2, 0, 7
y= 10,0,10,3
Is this a function?
Answer: No, this is not a function.
Functions exist when there are a unique set of x-values and each can match with a y-value. There cannot be a repeating x-value because this creates a discontinuity in the graph. You can have as many repeating y-values as you’d like as long as they each have a unique x-value and are not duplicate plot points.
Since x = 7 repeats in the domain of x-values, this cannot be a function.
Find two integers whose sum is -7 and whose product is 12.
Answer: -3 and -4
Step-by-step explanation:
The sum of -3 + -4 = -7
The product of -3 x -4 = 12 (a negative times a negative equals a positive)
Kadeem and Quinn both drive 25 miles. Kadeem drives at a constant speed of 50 miles an hour. Quinn drives at a constant speed of 75 miles per hour. Who takes longer to drive 25 miles? How much longer?
Answer:
Kareem takes longer to drive the 25 miles. Kadeen takes 10 minutes longer than Quinn.
Step-by-step explanation:
The formula for time is distance over speed (distance/speed)
Kadeem
distance/speed = 25/50 = 1/2 hour = 30 minutes
Quinn
distance/speed = 25/75 = 1/3 hour = 20 minutes
Factorise the following:
a) x^2 + 10x + 16
b) x^2 + 7x + 12
c) x^2 + 13x + 12
Answer:
Step-by-step explanation:
a)
[tex]x^2+10x+16=\\x^2+2x+8x+16=\\x(x+2)+8(x+2)=\\(x+2)(x+8)[/tex]
b)
[tex]x^2+7x+12=\\x^2+3x+4x+12=\\x(x+3)+4(x+3)=\\(x+3)(x+4)\\[/tex]
c)
[tex]x^2+13x+12=\\x^2+x+12x+12=\\x(x+1)+12(x+1)=\\(x+1)(x+12)[/tex]
Answer:
[tex]\textsf{(a)} \quad (x+8)(x+2)[/tex]
[tex]\textsf{(b)} \quad (x+4)(x+3)[/tex]
[tex]\textsf{(c)} \quad (x+12)(x+1)[/tex]
Step-by-step explanation:
Factoring quadratics
To factor a quadratic in the form [tex]ax^2+bx+c[/tex] find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].Rewrite [tex]b[/tex] as the sum of these two numbers.Factor the first two terms and the last two terms separately.Factor out the common term.Part (a)[tex]\textsf{Given}: \quad x^2+10x+16[/tex]
Two numbers that multiply to 16 and sum to 10 are: 2 and 8.
[tex]\implies x^2+2x+8x+16[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x+2)+8(x+2)[/tex]
Factor out the common term (x + 2):
[tex]\implies (x+8)(x+2)[/tex]
Part (b)[tex]\textsf{Given}: \quad x^2+7x+12[/tex]
Two numbers that multiply to 12 and sum to 7 are: 3 and 4.
[tex]\implies x^2+3x+4x+12[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x+3)+4(x+3)[/tex]
Factor out the common term (x + 3):
[tex]\implies (x+4)(x+3)[/tex]
Part (c)[tex]\textsf{Given}: \quad x^2+13x+12[/tex]
Two numbers that multiply to 12 and sum to 13 are: 1 and 12.
[tex]\implies x^2+x+12x+12[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x+1)+12(x+1)[/tex]
Factor out the common term (x + 1):
[tex]\implies (x+12)(x+1)[/tex]
Choose the number line that correctly compares 24−−√ and 4.256.
The number line that correctly compares √24 and 4.256 is number line C.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.
This ultimately implies that, a number line can be used for the comparison of two or more numbers such as √24 and 4.256. Also, a number line typically decreases in numerical value towards the left and increases in numerical value towards the right.
Taking the square root of √24, we have:
√24 = 4.899
In this context, we can reasonably and logically deduce that 4.899 is greater than 4.256 (4.899 > 4.256) and would be placed at the right hand side of the number line and further from 4.899 as shown in number line C in the image attached below.
Read more on number line here: https://brainly.com/question/17325155
#SPJ1
What are the roots of the roots of the function f(x)=x^2+2x-1
The roots of the function f(x) = [tex]x^2+2x-1[/tex] are
x = [tex]-1+\sqrt{2}[/tex]
x = [tex]-1-\sqrt{2}[/tex]
The function is given f(x)= [tex]x^2+2x-1[/tex]
The roots of given function will be at f(x) = 0
Substitute the value in the equation
[tex]x^2+2x-1[/tex] =0
Here to find the roots of the function, we have to use the quadratic formula in the given function
Roots of the function = [tex]\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]
From the given function the values of
a = 1
b = 2
c = -1
Substitute the values in the quadratic formula and find the roots of the function
= [tex]\frac{-2+/-\sqrt{2^2-4(1)(-1)} }{2(1)}[/tex]
= [tex]\frac{-2+/-\sqrt{4+4} }{2}[/tex]
= [tex]\frac{-2+/-2\sqrt{2} }{2}[/tex]
The roots of the given functions are
x = [tex]-1+\sqrt{2}[/tex]
x = [tex]-1-\sqrt{2}[/tex]
Hence, the roots of the function f(x) = [tex]x^2+2x-1[/tex] are
x = [tex]-1+\sqrt{2}[/tex]
x = [tex]-1-\sqrt{2}[/tex]
Learn more about quadratic formula here
brainly.com/question/9300679
#SPJ1
Someone explain this to me please
Answer:
0.31
Step-by-step explanation:
√13.7/3.05^2 + 2.6
= 3.7/ 9.3 + 2.6
= 3.7/ 11.9
= 0.31
Function g is a transformation of function f.
-6 -5
4
g(x) =
لا
-2 -1
-1
f(x)
-2
-3
What is the equation of function g?
-5
-6
2
For f(x) = 2x + 3 and g(x) = -x^2 + 1, The composite function defined by (f o g)(x) is equal to (f o g)(x) = - 2 x^2 + 5
As per the question statement, We are given f(x) = 2x + 3 and g(x)=x^2+1
and we are supposed to find the composite function defined by (f o g)(x)
(f o g)(x) = f(g(x))
(f o g)(x) = 2 (g(x)) + 3
(f o g)(x) = 2( -x^2 + 1 ) + 3
(f o g)(x) = - 2 x^2 + 5
Hence, For f(x) = 2x + 3 and g(x) = -x^2 + 1, The composite function defined by (f o g)(x) is equal to (f o g)(x) = - 2 x^2 + 5
Composite Function: A function that is composed of further functions, each of which serves as the input to the next.To learn more about composite functions, click on the link given below:
https://brainly.com/question/20379727
#SPJ1
help needed asap!! will award brainiest
A rectangular sandbox has a width represented by the polynomial (x-1) and a length represented by (6x-5). What is the total area of the sandbox?
The total area of the sandbox is given by 6x^2-11x+5
Width of the sandbox = (x-1)
Length of the sandbox = (6x-5)
Rectangle area in geometry refers to the area that a rectangle occupies on a two-dimensional plane. A quadrilateral, a form of a two-dimensional object with four sides and four vertices, is what a rectangle is. The rectangle's four angles are all right angles or exactly 90 degrees. The rectangle's opposing sides are equal and parallel to one another.
The formula for the area of a rectangle:
Area of rectangle = Length*Width
Substituting the value in the formula we get:
Area of rectangle = (x-1)*(6x-5)
= 6x^2-5x-6x+5
= 6x^2-11x+5
Learn more about rectangles:
https://brainly.com/question/15019502
#SPJ1
The graph is a function. + O True O False
the provided graph is not a function .
s
The complement of an angle is half of it’s size. Find the angle
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:The \:\: angles \:\: are \:\: 60° \:\: and \:\:30° [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Sum of two complementary angles is 90°
Let's assume one of them to be x, the other one will be x/2 as one of the angles is complementary to other one.
[tex]\qquad \tt \rightarrow \: x + \dfrac{x}{2} = 90[/tex]
[tex]\qquad \tt \rightarrow \: \dfrac{2x + x}{2} = 90[/tex]
[tex]\qquad \tt \rightarrow \: 3x = 90 \times 2[/tex]
[tex]\qquad \tt \rightarrow \: x = 180 \div 3[/tex]
[tex]\qquad \tt \rightarrow \: x = 60 \degree[/tex]
and
[tex]\qquad \tt \rightarrow \: \dfrac{x}{2} = 60 \div 2 = 30 \degree[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
A line has a slope of 1/3 and includes the points (6,1) and (9,j). What is the value of j?
Answer:
j = 2
Step-by-step explanation:
Slope of a line is given by:
[tex]\medium \text{$\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$}[/tex]
where (x₁, y₁) and (x₂, y₂) are two points on the line
This is commonly referred to as rise/run
Given the two points (6, 1) corresponding to (x₁, y₁) and (9, j) corresponding to (x₂, y₂)
[tex]\text{Slope = }\dfrac{\ensuremath{j}-1}{9-6}=\dfrac{j-1}{3}[/tex]
But we are given the slope as 1/3
So we get
[tex]\dfrac{j-1}{3} = \dfrac{1}{3}[/tex]
Multiplying by 2 on both sides gives us:
j - 1 = 1
Adding 1 to both sides gives us
j - 1 + 1 = 1 + 1
j = 2
Anais bought
2 1/2 yards of ribbon. She had
feet 1
6 inches of ribbon left after trimming some curtains. How many inches of ribbon did Anais use to trim the curtains
The inches of ribbon that Anais use to trim the curtains is 12 inches.
How to illustrate the information?From the information, Anais bought 2 1/2 yards of ribbon and then he had 1 feet 6 inches of ribbon left after trimming some curtains.
It should be noted that 12 inches = 1 feet
Therefore, the inches that will be left will be:
= 2 1/2 - 1 6/12
= 2 1/2 - 1 1/2
= 1 feet
It should be noted that 1 feet = 12 inches.
Learn more about fractions on:
brainly.com/question/17220365
#SPJ1
Kevin is making potato casserole for a dinner party. He needs 2½ pounds of potatoes per guest. How many pounds of potatoes will he need for 6 guests? O 15 pounds 6.5 pounds O 25 pounds O 12.5 pounds - Previous
Answer:
15 pounds
Step-by-step explanation:
Kevin is making potato casserole for a dinner party. He needs 2½ pounds of potatoes per guest. How many pounds of potatoes will he need for 6 guests?
15 pounds
6.5 pounds
25 pounds
12.5 pounds
2.5lb × 6 guest = 15 pounds
Answer: 15 pounds of potatoes.
Step-by-step explanation:
Kevin will perform basic multiplication to find how many potatoes he needs for all of the guests. Since each person requires 2 1/2 pound of potatoes and there are a total of 6 guests, multiplying these two values will find the pounds of potatoes that are needed for all of the guests.
2 1/2 * 6 = 15 pounds of potatoes
Therefore, Kevin needs 15 pounds of potatoes to make potato casserole for everyone at the dinner party.
can someone help me with this please
Answer:
x=4
Step-by-step explanation:
15-9=6
10-6=4
Answer:
x = 6 cm
Step-by-step explanation:
The two shapes are similar. That means one figure is exactly a multiple of the other figure
We can see that the ration of the length of the bigger rectangle to the length of the smaller rectangle is 15/9 = 5/3
Therefore the ratio of the width of the bigger rectangle to the width of the smaller rectangle must also be 5/3
Given width of big rectangle = 10 and that of small rectangle is x
We get
10/x = 5/3
Multiply by x both sides:
x × 10/x = x × 5/3
10 = 5x/3
Multiply by 3 both sides
30 = 5x
5x = 30
Dividing by 5 both sides
5x/x = 30/5
x = 6 cm
Complete the following table of ordered pairs that are solutions of the equation
a. The complete table for the ordered pairs that are solutions to y = x³ - 4 is
x y
-1 -5
0 -4
1 -3
2 4
b. The graph of the equation is shown below
Determining Ordered pairsFrom the question, we are to complete the given table of ordered pairs that are solutions to the given equation.
The given equation is
y = x³ - 4
Now, we will determine the values of y for the given values of x
When x = -1
y = x³ - 4
y = (-1)³ - 4
y = -1 - 4
y = -5
(-1, -5)
When x = 0
y = x³ - 4
y = (0)³ - 4
y = 0 - 4
y = -4
(0, -4)
When x = 1
y = x³ - 4
y = (1)³ - 4
y = 1 - 4
y = -3
(1, -3)
When x = 2
y = x³ - 4
y = (2)³ - 4
y = 8 - 4
y = 4
(2, 4)
Thus,
The table is
x y
-1 -5
0 -4
1 -3
2 4
The graph is shown below
Learn more on Determining ordered pairs here: https://brainly.com/question/28502533
#SPJ1
Whats 6% of 583! Because its very confusing and if you can help that would be great
Answer:
34.98is the answer ............ .............
Answer: 34.98
Step-by-step explanation:
'Percent (%)' means 'out of one hundred':
6% = 6 'out of one hundred',
p% is read p 'percent',
6% = 6/100 = 6 ÷ 100
What does it mean to calculate the percentage of a number?
6% of 583 = ?
... is equivalent to multiplying them:
6% × 583 = ?
6% of 583 =
6% × 583 =
6/100 × 583 =
(6 ÷ 100) × 583 =
6 × 583 ÷ 100 =
3,498 ÷ 100 =
34.98
Write an equation for the line parallel to the given line that contains C.
5
C(1,7); y=x+4
The equation of the line parallel to the given line that contains C is obtained as y = x + 6.
What is termed as the parallel lines?Parallel lines are two or more lines which lie within the same plane but never intersect. They are equal in distance and have the same slope. Parallel lines have been straight lines which never meet, no matter how far they are extended. Numerous pairs of angles are formed when two parallel lines have been intersected by another line known as a transversal.For the given question;
The equation of the line is given as;
y = x + 4
The standard form of the equation of line in slope intercept form is;
y = m x + c
where, m is the slope and c is the y intercept.
On comparing;
m₁ = 1
Now, the other lien is parallel to the given line.
Thus, slopes of both lines will be equal.
m₁ = m₂ = 1
The passing points of the line are;
(x₁, y₁) = C(1, 7)
Now, the equation of lien will be;
y - y₁ = m₂(x - x₁)
Put the values;
y - 7 = 1(x - 1)
Simplifying.
y = x + 6
Thus, the equation of the line parallel to the given line that contains C is obtained as y = x + 6.
To know more about the parallel lines, here
https://brainly.com/question/12065995
#SPJ13
You want to drink an average of at least 64 fluid ounces of water each day of the week.
How many fluid ounces of water should you drink on Sunday to reach your goal?
Monday-64
Tuesday-76
Wednesday-66
Thursday-72
Friday-58
Saturday-56
Sunday-56 fluid ounces of water require to reach your goal.
What is a average means?Average: A value that ought to represent the sample is what is meant by the term "Average." The average is calculated by dividing the total number of values in a given set by the sum of all the values in that set. Additionally called the arithmetic mean.In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. If we want to calculate the average for a set of data, we add up all the values and divide this sum by the total number of values.To learn more about : Arithmetic mean.
Ref : https://brainly.com/question/1136789
#SPJ13
HELP QUICK!
A coordinate plane is shown below. Circle the letter of each true statement.
A. The y-coordinate for point A is 3.
B. Point D has the same x-coordinate as
point E.
C. The x-coordinate for point F is 7.
D. The ordered pair for point G is (8, 6).
E. Point H names the ordered pair (10, 9).
F. Point B is 8 units away from the origin.
G. Point C is 1 unit left and 2 units up from
point D.
In the coordinate plane shown we can say that the y-coordinate of point A is 3.
Let us now take the statement one by one and try to find out if they are true or false.
A. True. The y-coordinate for A is 3
B. False. Point D has x-coordinate of 5 and E has 6
C. True The x-coordinate for F is 7
D. True The ordered pair for point G is (8,6)
E. False. Point H names the ordered pair (9,10).
F. false point B is √34 units away from origin
G. True.
The coordinate plane is a two-dimensional surface created by combining two number lines. A single horizontal number line makes up the x-axis. The name of the vertical number line, which is the other number line, is the y-axis. The intersection of the two axes is the origin. The graphing of points, lines, and other objects can be done using the coordinate plane.
To learn more about coordinate plane visit:
https://brainly.com/question/28471473
#SPJ1
Each droplet that you sneeze is approximately 7 x 10-3 mm in diameter. If you wear an N95 mask, which filters virus particles as small as 8 x 10-5, will you sufficiently protect those around you? Explain your reasoning.
Answer:
Yes, 7 x [tex]10^{-3}[/tex] in standard form is 0.007mm
8 x [tex]10^{-5}[/tex] in standard form is 0.00008 mm. The mask will catch particles that are much smaller than 0.007 in diameter.
Step-by-step explanation:
f(x) = 2x² + 3x - 6
g(x) = -4x + 10
Find: g(f(x))
A drilling crew dug to a depth of 26 ½ feet during their first day of drilling. On the second day, the crew dug down 9½ feet more than on the first day. Describe the depth of the bottom of the hole after the second day.
The depth of the bottom of the hole after the second day is 36 feet using addition operation.
What is addition?In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the sum refers to the outcome of the operation.
Given the depth on the first day is 26 ½ feet.
Depth on the second day = 9½ feet more than on the first day i.e. 9½ feet + depth on the first day
This implies, depth on the second day = 9½ + 26 ½
= 36 feet
Therefore, the depth of the bottom of the hole after the second day is 36 feet.
To learn more about addition, visit:
https://brainly.com/question/25621604
#SPJ9
Write the equation of line perpendicular to y = 4 that passes through (5, 2)
one may note that y = 4 is a horizontal line, and a line perpendicular to a horizontal line will be a vertical one, Check the picture below.
let in the region where . explain why must have a global minimum at some point in (note that is unbounded---how does this influence your explanation?). then find the global minimum. minimu
the formula for a function of the form y= a е⁻ˣ +b x with global minimum at (1,10) is y= 5е¹ ⁻ ˣ +5 x
We can use first and second derivative tests to determine all coefficients of the function described in statement so that the point given is an absolute minimum. The expressions for such tests are introduced below:
First Derivative Test
-a .е⁻ˣ +b = 0 (1)
b=a .е⁻ˣ
Second Derivative Test
y''= a . .е⁻ˣ (2)
Where y'' >0
If we know that ( x,y) = 9 1,10) , then we have the following system:
10 = a е⁻¹ +b (3)
b= a е⁻¹ (4)
y'' = a е⁻¹ (5)
By (4) in (3):
10= 2aе⁻¹
a=10/2е⁻¹
a= 5е
By (5) we prove that y''>0, and we get the value of by (4):
b=5
Thus, the formula for a function of the form y= a е⁻ˣ +b x with global minimum at (1,10) is . y= 5е¹ ⁻ ˣ +5 x
learn more about of derivative here
https://brainly.com/question/25707915
#SPJ4
please help me quickly
Answer:
80 degrees
Step-by-step explanation:
If ATUV is translated to image ATUV, as shown below, by the rule
(x, y) → (x+8, y - 3), what are the coordinates of ATUV?
==========================================================
Explanation:
The given translation rule is (x, y) → (x+8, y - 3) which says "shift 8 units right and 3 units down".
The inverse transformation will undo each to get "8 units left and 3 units up"
So the inverse is (x, y) → (x-8, y + 3)
Use this inverse to determine the preimage of point T'(2,-6)
[tex](\text{x},\text{y})\to(\text{x}-8,\text{y}+3)\\\\(2,-6)\to(2-8,-6+3)\\\\(2,-6)\to(-6,-3)\\\\[/tex]
Therefore, preimage point T is located at (-6,-3) which points us to answer choice B
If we were to apply the rule of "shift 8 units right and 3 units down" to T(-6,-3), you should arrive at T'(2,-6)