Answer:
$445.20
Step-by-step explanation:
First, find his pay after the 5% raise:
400(1.05)
= 420
Find his pay after the 6% raise:
420(1.06)
= 445.2
So, his weekly pay is now $445.20
solve the equation 4+2|3x+4|=-4
“Absolute Value Equations and Inequalities”
the solutions are what?
please give an explanation if possible!
Answer:
Value of given expression x is -4
Step-by-step explanation:
Given equation in question;
4 + 2|3x + 4| = -4
Find:
Value of given expression
Computation:
4 + 2|3x + 4| = -4
Using BODMAS rule;
⇒ 4 + 2|3x + 4| = -4
⇒ 2|3x + 4| = - 4 - 4
⇒ 2|3x + 4| = - 8
⇒ |3x + 4| = - 8 / 2
⇒ |3x + 4| = - 4
⇒ 3x + 4 = - 8
⇒ 3x = -8 - 4
⇒ 3x = -12
⇒ x = -12 / 3
⇒ x = -4
Value of given expression x is -4
The lengths of the sides of a triangle are 3, 4, 5. Can the triangle be a right triangle?
Answer:
Yes it can
Step-by-step explanation:
To check wether it's a right angle triangle we need to apply the Pythagoras theorem
h^2= a^2 +b^2
Hypotenuse is always the longest side so
5^2 = 3^2 + 4^2
This is correct, so the triangle is a right angle triangle
Answer from Gauthmath
On a coordinate plane, triangles R S T and L M N are shown. Triangle R S T has points (5, 5), (2, 1), and (1, 3). Triangle L M N has points (0, negative 1), (2, negative 4), and (negative 2, negative 3). How does the area of triangle RST compare to the area of triangle LMN
Answer:
LMN has a larger area
Step-by-step explanation:
Given
RST
[tex]R =(5,5)[/tex]
[tex]S= (2,1)[/tex]
[tex]T = (1,3)[/tex]
LMN
[tex]L = (0,-1)[/tex]
[tex]M= (2,-4)[/tex]
[tex]N= (-2,-3)[/tex]
Required
Compare both areas
The area of triangle is:
[tex]Area = \frac{1}{2}|x_1y_2 - x_2y_1 + x_2y_3 - x_3y_2 + x_3y_1 - x_1y_3|[/tex]
For RST, we have:
[tex]Area = \frac{1}{2}|5*1 - 2*5 + 2*3 - 1*1 + 1*5 - 5*3|[/tex]
[tex]Area = \frac{1}{2}|-10|[/tex]
Remove absolute signs
[tex]Area = \frac{1}{2}*10[/tex]
[tex]Area = 10[/tex]
For LMN, we have:
[tex]Area = \frac{1}{2}|x_1y_2 - x_2y_1 + x_2y_3 - x_3y_2 + x_3y_1 - x_1y_3|[/tex]
[tex]Area = \frac{1}{2}|0*-4-2*-1+2*-3--2*-4--2*-1-0*-3|[/tex]
[tex]Area = \frac{1}{2}|-14|[/tex]
Remove absolute signs
[tex]Area = \frac{1}{2}*14[/tex]
[tex]Area = 7[/tex]
By comparing both areas, we can conclude that LMN has a larger area
Discount Comics is running a special: 20 comics for $5.00. Seth purchases 30 comics for $7.50. What is the sale price per comic? Need help!!
Answer:
$0.25
Step-by-step explanation:
Let's represent the comics by assigning it the letter C.
20C = $5.00
C = $5.00/20
= $0.25
We can confirm this by using the example where he uses 30 comics.
30C = $7.50
C = $7.50/30
= $0.25.
Therefore each comic costs $0.25
Which of the following statements is false ?
Answer:
The bases of an isosceles trapezoid are congruent is false.
Step-by-step explanation:
Let's analyse each option.
In a Rhombus, the diagonals are perpendicular at the point of intersection and bisect each other is true.
In isosceles trapezoid, the sides are congruent but not the bases. So, this incorrect!
The rectangle is an Equi-angular because all the angles are equal. So, this is true.
The base angles are congruent in isosceles trapezoid. So, this is true too.
which statements are true about function h?
Answer:
statement 1 is the true answer
The correct statements about function h(x) are:
1) As x approaches ∞, h(x) approaches ∞
2) The y-intercept is (0, 5)
3) The domain of a function h(x) is [tex](-\infty, \infty)[/tex]
4) As x approaches -∞, h(x) approaches -∞
What is function?"It defines a relation between input and output values.""In function, for each input there is exactly one output."What is exponential function?"A function of the form [tex]f(x)=a^x[/tex], where “x” is a variable and “a” is a constant."
What is domain?"It is a set of all possible input values for which a function is well defined."
What is range?"It is a set of all possible output values."
What is intercept?"It is a point at which the graph of the function intersects the X-axis or Y-axis."
For given question,
A function [tex]f(x)=x^{\frac{1}{3} }[/tex] is transformed to function [tex]h(x)=(2x)^{\frac{1}{3} }+5[/tex]
The domain of function h(x) is all real values.
To find the y-intercept, substitute x = 0
[tex]\Rightarrow h(0)=(2\times 0)^{\frac{1}{3} }+5\\\\ \Rightarrow h(0)=5[/tex]
So, the y-intercept of function h(x) is (0, 5)
To find the x-intercept, substitute y = 0 i.e., h(x) = 0
[tex]\Rightarrow 0=(2x)^{\frac{1}{3} }+5\\\\\Rightarrow (2x)^{\frac{1}{3} }=-5\\\\\Rightarrow 2x=-125\\\\\Rightarrow x=-62.5[/tex]
This means, the x-intercept of h(x) is (-62.5, 0)
From the graph of the function h(x), we can observe that as x approaches -∞ then h(x) approaches -∞ and as x approaches ∞ then h(x) approaches ∞
Therefore, the correct statements about function h(x) are:
1) As x approaches ∞, h(x) approaches ∞
2) The y-intercept is (0, 5)
3) The domain of a function h(x) is [tex](-\infty, \infty)[/tex]
4) As x approaches -∞, h(x) approaches -∞
Learn more about the function here:
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can i get some help? i tried figuring it out myself already but i must have done something wrong. please help!
First, we'll set up two equations. One for the amount of each coin and another for the value of the coins.
N will represent nickels
D will represent dimes
N + D = 30
---The problem tells us that there are 30 total coins
0.05N + 0.10D = 2.95
---Nickels are worth 5 cents and dimes are worth 10 cents, and the total value of the coins is 2.95
Now that we have our equations, we need to solve for one of the variables in the first equation. I will solve for N.
N + D = 30
N = 30 - D
Then, we take that equation and substitute our new value for N into the second equation (value) and solve for D.
0.05(30 - D) + 0.10D = 2.95
1.5 - 0.05D + 0.10D = 2.95
1.5 + 0.05D = 2.95
0.05D = 1.45
D = 29
Now that we know how many dimes there are, we can plug that value into our equation for N and solve for N.
N = 30 - D
N = 30 - 29
N = 1
Therefore, there are 29 dimes and 1 nickel.
Hope this helps!
2. Peter wants to order tickets to a production of Charles Dickens' A Christmas Carol. Each ticket
costs $30 and there is a one time service fee of $12 for the transaction. What is an expression that
would find the total cost for any number of tickets that Peter orders? Use t for the variable to
represent the number of tickets he purchased.
Answer
Answer:
There is overwhelming evidence that human activities, especially burning fossil fuels, are leading to increased levels of carbon dioxide and other greenhouse gases in the atmosphere, which in turn amplify the natural greenhouse effect, causing the temperature of the Earth's atmosphere, ocean, and land surface to ...
solve -7x^2+x+9=-6x quadratic formula
Answer:
[tex]-7x^2+x+9=-6x[/tex]
[tex]-7x^2+x+9+6x=-6x+6x[/tex]
[tex]-7x^2+7x+9=0[/tex]
[tex]quadratic\: formula[/tex]
[tex]x_{1,\:2}=\frac{-7\pm \sqrt{7^2-4\left(-7\right)\cdot \:9}}{2\left(-7\right)}[/tex]
[tex]\sqrt{-7^{2} -4(-7)\times9} =\sqrt{301}[/tex]
[tex]x_{1,\:2}=\frac{-7\pm \sqrt{301}}{2\left(-7\right)}[/tex]
[tex]\frac{-7+\sqrt{301}}{2\left(-7\right)}[/tex]
[tex]=\frac{-7+\sqrt{301}}{-2\cdot \:7}[/tex]
[tex]=\frac{-7+\sqrt{301}}{-14}[/tex]
[tex]\frac{-7-\sqrt{301}}{2\left(-7\right)}[/tex]
[tex]=\frac{-7-\sqrt{301}}{-2\cdot \:7}[/tex]
[tex]=\frac{-7-\sqrt{301}}{-14}[/tex]
[tex]answer=\frac{7+\sqrt{301}}{14}[/tex]
[tex]OAmalOHopeO[/tex]
Instructions: Find the missing side of the triangle.
48
50
Answer:
x = 14
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
48 ^2 + x^2 = 50^2
2304+x^2=2500
x^2 = 2500-2304
x^2 =196
Taking the square root of each side
sqrt(x^2) = sqrt(196)
x = 14
Answer:
14
Step-by-step explanation:
Use A^2+B^2=C^2
A=48
C=50
So B=sqrt(C^2-A^2)
B=sqrt(50^2-48^2)
B=sqrt(2500-2304)
B=sqrt(196)
B=14
Solve the system by substitution
y= 5x− 22
y= 4x− 17
Answer:
x=5, y=3
Step-by-step explanation:
Which set of ordered pairs does NOT represent a function?
{(0, 0), (1, 1), (2, 2), (3, 3)}
(0, 0), (0, 1), (1, 2), (1, 3)}
{(1,0), (2, 0), (3, 0), (4, 0)}
{(0, 1), (1, 2), (2, 3), (3, 4)}
Answer: (0, 0), (0, 1), (1, 2), (1, 3) does NOT represent a function
Step-by-step explanation:
to tell whether a set of ordered pairs are functions or not, all domains must have different ranges!
range: x-axis (0,0)
domain: y-axis (0,0)
pair 1:
all the ranges - 0, 1, 2, 3 - are different, which means it IS a set of ordered pairs
pair 2:
all the ranges - 0, 0, 1, 1 - are NOT all different, which means it is NOT a set of ordered pairs
pair 3:
all the ranges - 1, 2, 3, 4 - are different, which means it IS a set of ordered pairs
pair 4:
all the ranges - 0, 1, 2, 3 - are different, which means it IS a set of ordered pairs
let me know if you have any more questions or if i made any mistakes. hope this helped, and good luck! ˶ˆ꒳ˆ˵
5. Find the measures of the following. Round to the nearest whole number. (2 points)
a. HT
H
b. 2T
15 cm
C. ZH
W
8 cm
T
Answer:
HT = 17 cm
<T = 58°
<H = 32°
Step-by-step explanation:
✔️Find HT:
Since it's a right triangle, we would apply the Pythagorean Theorem given as c² = a² + b²
Where,
a = HW = 15 cm
b = WT = 8 cm
c = HT
Plug in the values:
HT² = 15² + 8²
HT² = 289
HT = √289
HT = 17 cm
✔️Find <T by applying trigonometric ratio formula:
Recall: SOH CAH TOA
Reference angle (θ) = <T
HW = 15 cm = Opposite side length
WT = 8 cm = Adjacent side length
Apply CAH:
Cos θ = Adj/Hyp
Substitute
Cos T = 8/15
T = [tex] cos^{-1}(0.5333) [/tex]
T ≈ 58°
✔️Find <H:
Sun of interior angles of a triangle = 180°
Therefore,
m<H + m<T + m<W = 180°
Substitute
m<H + 58° + 90° = 180°
m<H + 148° = 180°
m<H = 180° - 148°
m<H = 32°
What the length of segment LM
Answer: LM = 23
Step-by-step explanation:
Solve the algebraic equations:
Line KN: (solve for x)
[tex]14x-3=25[/tex]
move the 3 to the other side with addition
[tex]14x=28[/tex]
divide by 14 to get x by itself
[tex]x=2[/tex]
Now that we have x we can find line KL:
[tex]9(2)+5\\18+5\\23[/tex]
So we now know that KL is 23 units. And we know that KL = LM
Jamie bought a new pair of jeans for $\$10$ because the price marked was $75\%$ off the original price. What was the original price of the pair of jeans?
Answer:
$40
Step-by-step explanation:
Let
Original price = x
Selling price = $10
Discount = 75%
Selling price = original price - (Discount * original price)
10 = x - 75% of x
10 = x - 0.75 * x
10 = x - 0.75x
10 = 0.25x
x = 10/0.25
x = 40
Original price = x = $40
Please help me anyone
Answer:
Step-by-step explanation:
y = x^2 + 4
x = 11 Put this value in wherever you see an x on the right.
y = 11^2 + 4
11^2 = 11 * 11 = 121
y = 121 + 4
y = 125
Eric and Shiloh each have a savings account. The ratio of Eric’s account balance to Shiloh’s account balance is 4:3. Together they have a total of $140 in their accounts. Use the tape diagram below to help you determine the balance of Eric’s account. [Type your answer as a number.]
Answer:
Eric 80
Step-by-step explanation:
Take 4+3 = 7
140 /7 = 20
There is 20 in each block
Eric gets 4 of the blocks so 4*20 = 80
Shiloh gets 3 of the blocks 3*20 = 60
Answer:
80
Step-by-step explanation:
4 : 3
4x + 3x = 140
7x = 140
x =20
4*20 = eric's amount
= 80
In the graph, what does A represent?
major axis
vertices
minor axis
foci
An ellipse is a plane curve that surrounds two focus points and has a constant sum of the two distances to the focal points at all places on the curve. In the graph, the A represents the minor axis of the ellipse.
What is the equation of ellipse if its major and minor axis and center are given?Suppose that the major axis is of the length 2a units, and that minor axis is of 2b units, and let the ellipse is centered on (h,k) with major ellipse parallel to x-axis, then the equation of that ellipse would be:
[tex]\dfrac{(x-h)^2}{a^2} + \dfrac{(y-k)^2}{b^2} =1[/tex]
Coordinates of its foci would be: (h±c, k) where c² = a² - b²
If its major axis is parallel to y-axis, then,
coordinates of its foci would be: (h, k±c) where c² = a² - b² and its equation would be:
[tex]\dfrac{(x-h)^2}{b^2} + \dfrac{(y-k)^2}{a^2} =1[/tex]
An ellipse is a plane curve that surrounds two focus points and has a constant sum of the two distances to the focal points at all places on the curve. Since an ellipse has two diameter, the major and the minor diameter. Therefore, in the graph, the A represents the minor axis of the ellipse.
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How to change the decimal 4.5 into a fraction
4.5
= 4.5/1
= 4.5/1.0
= 45/10 [Shifting the decimal to right]
= 9/2 [Reducing to the simplest form]
So, the answer is 9/2.
(5,8) and (x, 12) slope is -2, find x
PLEASE HELP ASAP
A school is painting its logo in the shape of a triangle in the middle of its sports field. The school wants the height of the triangle to be 8 feet. The area of the logo must be at least 36 square feet. (The logo has to be seen from all the seats.) Write an inequality that describes the possible base lengths (in feet) of the triangle.
Use b for the base length of the triangular logo.
SOMEONE PLS HELP ME! THANK YOU!
Answer:
[tex]b\geq 9[/tex]
In other words, the base must be at least 9 feet long.
Step-by-step explanation:
The schools wants the height of the triangle to be eight feet, and the area of the logo to be at least 36 square feet.
Recall that the area of a triangle is given by:
[tex]\displaystyle A = \frac{1}{2}bh[/tex]
Since we want to area to be at least 36 square feet:
[tex]\displaystyle \frac{1}{2}bh \geq 36[/tex]
We are given that the height is eight feet. Substitute:
[tex]\displaystyle \frac{1}{2}(8)b\geq 36[/tex]
Simplify:
[tex]4b\geq 36[/tex]
Divide both sides by four. Hence, our inequality is:
[tex]b\geq 9[/tex]
In words, this means that the base must be at least 9 feet long.
If you don’t know the answer please don’t respond. I actually need help :)
Answer:
I don't know the answer to this question
Select the expression that shows the distributive property applied to
13(2+9).
18 of 29 QUESTIONS
13(9+2)
13. 2+ 9
13. 2+ 13.9
13. 2+ 2.9
3rd option is correct
13 × 2 + 13 × 9
In the following table of values, the first differences are
x y First Difference
-2 34
-1 27
0 20
1 13
2 6
Answer:
-7
Step-by-step explanation:
Given
[tex]\begin{array}{ccc}x & {y} & {First\ difference} & {-2} & {34} & {}&{-1} & {27} & {} &{0} & {20} & {} & {1} & {13} & {} & {2} & {6} &{} \ \end{array}[/tex]
Required
The first difference
To do this, we simply calculate the difference between the consecutive y-values.
i.e.
[tex]d = y_{n+1} - y_n[/tex]
So, we have:
[tex]d = y_2 - y_1 = 27 - 34 = -7[/tex]
[tex]d = y_3 - y_2 = 20 - 27 = -7[/tex]
[tex]d = y_4 - y_3 = 13 - 20 = -7[/tex]
[tex]d = y_5 - y_4 = 6-13 = -7[/tex]
Hence, the first differences are -7 (all through)
Help Please Now!!!
Find the volume of the rectangle prism
Answer:
V =48 cm^3
Step-by-step explanation:
The volume of a prism is given by
V = l*w*h
V = 3*4*4
V =48 cm^3
V =48 cm^3
Step-by-step explanation:
The volume of a prism is given by
V = l*w*h
V = 3*4*4
V =48 cm^3
Find the volume of a sphere with a diameter of 17.2 cm. Use 3.14 for it Round your answer to the nearest
tenth
Answer:
2663.0 cm³ (3 s.f.)
Step-by-step explanation:
[tex]\boxed{volume \: of \: sphere = \frac{4}{3}\pi {r}^{3} }[/tex]
Radius= diameter ÷2
Radius of sphere
= 17.2 ÷2
= 8.6 cm
Volume of sphere
[tex] = \frac{4}{3} (3.14)(8.6)^{3} [/tex]
= 2663.0 cm³ (3 s.f.)
I could really use some help
Answer:
045
Step-by-step explanation:
North is equal to 360 or 0 degrees. East is equal to 90 degrees because that is 1/4 of 360.
Thus, northeast is 45 degrees. This image may help.
Which numbers belong to the solution set of the inequality?
6x < 48
A. 1,3,5,8
B. 2,4,5,7
C. 7,9,13,16
D. 9, 12, 14, 20
Answer:
B. 2, 4, 5, 7
Step-by-step explanation:
6x<48
Divide by 6 on both sides:
x < 8 (excluding 8)
You can test values greater than 8, and if it yields false, then try different numbers.
Hope this helps!
Suppose you have D12000 to save . You have to save some amount at 10% and the rest at 15% how much should be saved at each rate to yield 12% on the total amount saved
Answer:
$7200 at 10%
$4800 at 15%
Step-by-step explanation:
help which one is the correct one
Answer:
B.) x^12
Step-by-step explanation:
You don't multiply the exponents when multiplying x^7 × x^5, you add them.
If we add the exponents, we get x^12.
Hope this helps!
If there is something wrong, just let me know.