Answer:
1363.6
Step-by-step explanation:
let the basic salary be = x
10% of x = 10/100x
So the equation = x + 10/100x = 1500
= x + 0.1x = 1500
= 1.1x = 1500
= x = 1500/1.1
= x = 1363.6
Christopher has breakfast at a cafe and the cost of his meal is $36.00dollar sign, 36, point, 00. Because of the service, he wants to leave a 10%, percent tip.
Answer: $39.60
Step-by-step explanation:
Here is the correct question:
Christopher has breakfast at a cafe and the cost of his meal is $36.00 . because of the service he wants to leave a 10% tip.What is his total bill including tip?
His total bill will be the addition of the cost of his meal and the tip. This will be:
= $36.00 + (10% × $36.00)
= $36.00 + $3.6
= $39.60
His total bill including tip is $39.60
Given directed line segment PR below, find the coordinates of Q on PR
such that the ratio of PQ to QR is 2:1.
Answer:
[tex](\frac{4}{3},-3)[/tex]
Step-by-step explanation:
The location of a point O(x, y) which divides line segment AB in the ratio a:b with point A at ([tex]x_1,y_1[/tex]) and B([tex]x_2,y_2[/tex]) is given by the formula:
[tex]x=\frac{a}{a+b}(x_2-x_1)+x_1\\ \\y=\frac{a}{a+b}(y_2-y_1)+y_1[/tex]
From the graph, the location of the point is P(2, 5), R(1, -7). Let point Q be (x, y) which divides PR in ratio 2:1. Coordinates of point Q is at:
[tex]x=\frac{a}{a+b}(x_2-x_1)+x_1=\frac{2}{2+1}(1-2)+2=\frac{2}{3}(-1)+2=\frac{4}{3} \\ \\y=\frac{a}{a+b}(y_2-y_1)+y_1=\frac{2}{2+1}(-7-5)+5= \frac{2}{3}(-12)+5=-3[/tex]
Point Q is at [tex](\frac{4}{3},-3)[/tex]
in the adjoining figure, ABC is a right-angled triangle, where
B = 90°, AB = 3 cm and AC
3V2 cm, find the size of ®.
Answer:
the value of theta i 45°
Which expression represents the measure of segment RS? A.7x – 3 B.7x + 5 C.x + 5 D.x – 3
Answer:
D) x-3
Step-by-step explanation:
(4x+1)-(3x-4)=
4x-3x+1-4=
x-3
What's the only place in this world who's Fahrenheit and Celsius degrees can be equal?
Antarctica , I think
Step-by-step explanation:
Evaluate the expression for the given value of x.
−7x + 6 for x = −7
Answer:
[tex]\Huge \boxed{\mathrm{55}}[/tex]
Step-by-step explanation:
[tex]-7x + 6[/tex]
Put x as -7 and evaluate the expression.
[tex]-7(-7)+6 \\\\\\ 49+6 \\\\\\ 55[/tex]
what is 5/13 rounded to the nearest tenth
Answer:
5 thirteenth ti the nearest tenth Is .6
Answer:
0.4
Step-by-step explanation:
First make it a decimal:
5/13 (divide)
0.38 (round)
So you get 0.4
help me with this please! I haven’t found the solution since 11:30 am
Answer:
PT = 22
Step-by-step explanation:
Given that T is the midpoint of PQ, then
PT = TQ , substitute values
5x + 2 = 7x - 6 ( subtract 5x from both sides )
2 = 2x - 6 ( add 6 to both sides )
8 = 2x ( divide both sides by 2 )
4 = x
Thus
PT = 5x + 2 = 5(4) + 2 = 20 + 2 = 22
solve the given equation: 2 x ( x + 3 ) − 6 ( x + 3 ) = 0 2 x ( x + 3 ) - 6 ( x + 3 ) = 0
Answer:
x = 3 or x = -3
Step-by-step explanation:
Solve for x over the real numbers:
2 x (x + 3) - 6 (x + 3) = 0
Expand out terms of the left hand side:
2 x^2 - 18 = 0
2 x^2 - 18 = 2 (x^2 - 9):
2 (x^2 - 9) = 0
Divide both sides by 2:
x^2 - 9 = 0
x = (0 ± sqrt(0^2 - 4 (-9)))/2 = ( ± sqrt(36))/2:
x = sqrt(36)/2 or x = (-sqrt(36))/2
sqrt(36) = sqrt(4×9) = sqrt(2^2×3^2) = 2×3 = 6:
x = 6/2 or x = (-6)/2
6/2 = 3:
x = 3 or x = (-6)/2
(-6)/2 = -3:
Answer: x = 3 or x = -3
Answer those please
11.) 0.5.
12.) 0.25.
13.)1/2,0.49,55%.
14.)2/5,0.6,35%.
15.) To get a whole number from a fraction you have to multiply the fraction by the denominator of the fraction=5/9×9=5.
or you can say that can add 4/9 to 5/9=9/9=1 a whole number also
A map has a scale of 6 in. = 8 mi. If you measured the distance between two cities to be 25 in. On the map, how many miles would it actually be?
Answer:
33 2/6 miles
Step-by-step explanation:
So we know that every 6 inches equals 8 miles. To find one mile, we would divide both sides by 8, so every 6/8 of an inch is 1 mile. if the two cities are 25 in apart on a map, that means that we can first do 6*4:8*4 for the ease of it to get 24 inches and 32 miles. So so far it's already 32 miles. Then we have to calculate the leftover one inch. To find out how many miles one inch is, we can divide both sides by 6, so one inch=8/6 of a mile.
So then we add 32+8/6=33 2/6
Tell me if that works for you
Answer the two please 1. A monopoly playing board is in the shape of a square.The sides measure 19 inches. What is the area of the monopoly board? Use the golf scores below to answer quest 2 72,75,82 75,72,74 2. What is the median golf score? A.74.5 B.74 C.75.5 D.75
Korey completely covered a square counter top using 103.5 ft² of tile without any overlap. Which measurement is closest to the side length of this counter top in feet? A. 10 ft B. 11 ft C. 27 ft D.55 ft
The measurement is closest to the side length of this counter top in feet is 10.17ft
Area of a squareThe formula for calculating the area of a square is expressed as:
area of a square = L^2
where
L is the length of a square
Given the following parameter
A = 103.5ft^2
Substitute
103.5ft^2 = L²
L = √103.5
L = 10.17ft
Hence the measurement is closest to the side length of this counter top in feet is 10.17ft
he measurement is closest to the side length of this counter top in feet is 10.17ft
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Use calculator to decide whether each statement is true or false. It may be that a true statement will lead to results that differ in the last decimal place due to rounding error.
tan² 72° 25' + 1 = sec² 72° 25'
Answer: 72.416
Step-by-step explanation:
For what value of a is a(2x+3)=9x+15+x an identity?
Answer:
Expand the left side, group like terms on both sides, and get
(2a)x + 3a = 10x + 15
To be true for all x, equate like terms from both sides and get
2a = 10
3a = 15
Solution: a = 5
You can test the answer.
Step-by-step explanation:
Expand the left side, group like terms on both sides, and get
(2a)x + 3a = 10x + 15
To be true for all x, equate like terms from both sides and get
2a = 10
3a = 15
Solution: a = 5
You can test the answer.
Express the formula d=rt in teens of the time, t use your formula to find the time the distance is 49 and the rate is 8.
Answer:
d=rt
rt=d
t= d/r
t= 40/8
t= 5
perform the indicated operation. 2i(3-4i)+8(4-5i)(4+5i)
Answer: 336+6i
The key to solving this problem is to choose which parts you should solve first.
2i(3-4i)+8(4-5i)(4+5i)
let's divide this expression to three parts:
2i(3-4i), 8 and (4-5i)(4+5i)
first let's solve 2i(3-4i):
2i(3-4i) =
2i × 3 + 2i × -4i =
6i - 8i² =
6i + 8
(4-5i)(4+5i):
(4-5i)(4+5i) =
16 + 20i - 20i -25² =
16 + 25 =
41
8(4-5i)(4+5i):
8(4-5i)(4+5i) = 8 × 41 = 328
Now let's put back these parts:
2i(3-4i)+8(4-5i)(4+5i) =
6i + 8 + 328 =
6i +336 OR 336 +6i
When I take half of my number and add two, I get twenty-four. What is my number?
90 POINTS PLEASE HELP Describe the three main trigonometry functions, their ratios and reciprocal functions.
Answer and Step-by-step explanation:
There are three reciprocal trigonometric functions
making a total of six including cosine, sine, and tangent.
→The reciprocal cosine function is secant: sec(Ф)=1/cos(Ф).
→The reciprocal sine function is cosecant, csc(Ф)=1/sin(Ф).
→The reciprocal tangent function is cotangent, expressed two ways: cot(Ф)=1/tan(Ф) or cot(Ф)=cos(Ф)/sin(Ф).
We've already learned the basic trig ratios:
sin(A) = a/c
cos(B) = b/c
tan(C) = a/b
But there are three more ratios to think about:
→Instead of a/c, we can consider c/a
→Instead of b/c, we can consider c/b
→Instead of a/b, we can consider b/a
These new ratios are the reciprocal trigonometric ratios, and we’re about to learn their names.
The cosecant (csc)
The cosecant is the reciprocal of the sine. It is the ratio of the hypotenuse to the side opposite a given angle in a right triangle.
sin(A) = opp / hyp = a/c
csc(A) = hyp / opp = c/a
The secant (sec)
The secant is the reciprocal of the cosine. It is the ratio of the hypotenuse to the side adjacent to a given angle in a right triangle.
cos(A) = adj/hyp = b/c
sec(A) = hyp/adj = c/b
The cotangent (cot)
The cotangent is the reciprocal of the tangent. It is the ratio of the adjacent side to the opposite side in a right triangle.
tan(A) = opp/adj = a/b
cot(A) =adj/opp = b/c
How many solutions does the equation −4a + 4a + 3 = 8 have?
Answer:
none
Step-by-step explanation:
Answer:
It does not have any solution because 3 is not equal to 8
A new top-selling DVD is marked 20% off at Discount DVD, where it normally sells for $29.90. The same disc sells for $28.60 at Value Video, where you have a coupon for 15% off anything in the store. Where would you buy the DVD? Explain how you decided and be sure to include work to support your answer.
Answer:
You would buy the DVD at Discount DVD.
Step-by-step explanation:
To decide where to buy the DVD, you have to determine the price at each store after the discount is applied.
-Discount DVD: $29.90*0.2=$5.98
$29.90-$5.98=$23.92
-Value Video: $28.60*0.15=$4.29
$28.60-$4.29=$24.31
According to this, you would buy the DVD at Discount DVD because it is where you will get the lower price.
Michael solved this inequality as shown: Step 1: -6(x + 3) + 10 < -2 Step 2: -6x − 18 + 10 < -2 Step 3: -6x − 8 < -2 Step 4: -6x < 6 Step 5: x > -1 What property justifies the work shown between step 3 and step 4? A. transitive property B. division property of inequality C. distribution property D. addition property of inequality
Answer:
D. addition property of inequalityStep-by-step explanation:
Given the step 3 and 4 of the solution Step 3: -6x − 8 < -2 Step 4: -6x < 6
From step 3;
-6x − 8 < -2
Michael got the step 4 by adding 8 to both sides of the inequality as shown;
-6x − 8 + 8 < -2 + 8
-6x < 6 (Step 4)
Since Michael added 8 to both sides of the inequality, the property that justifies the transition from step 3 to step 4 is the addition property of inequality. Addition property is the property that adds an integer to both sides of an inequality without altering the inequality sign and also retaining the inequality equation.
Every natural number is an integer. True or false?
Answer:
yes every natural number is integer
because intezer is collection of positive and negative numbers....
Answer:
Step-by-step explanation:
Hello friend!!!
It's TRUE
Natural numbers are the range of numbers from 1 to infinite.
Integers are made up of positive as well as negative numbers.
Since natural numbers are positive numbers, they are also integers.
Hope this helps
plz mark as brainliest!!!!!
After heating up in a teapot, a cup of hot water is poured at a temperature of 210°F. The cup sits to cool in a room at a temperature of 70° F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between the temperature of the water and the temperature of the room, as given by the formula below: T = T. + (To - Tale To = the temperature surrounding the object To = the initial temperature of the object t = the time in minutes T= the temperature of the object after t minutes k = decay constant The cup of water reaches the temperature of 197°F after 1.5 minutes. Using this information, find the value of k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 4 minutes. Enter only the final temperature into the input box.
Newton's Law of Cooling:
[tex]T(t)=T_{s}+(T_{o}-T_{s})e^{-kt}[/tex]
[tex]T(t) =[/tex] Temperature given at a time
[tex]t =[/tex] Time
[tex]T_{s} =[/tex] Surrounding temperature
[tex]T_{o}=[/tex] Initial temperature
[tex]e =[/tex] Constant (Euler's number) ≈ 2.72
[tex]k =[/tex] Constant
Using this information, find the value of [tex]k[/tex], to the nearest thousandth, then use the resulting equation to determine the temperature of the water cup after 4 minutes.
First, plug in the given values in the equation and solve for [tex]k[/tex]:
[tex]T(t) =[/tex] 197°, [tex]t =[/tex] 1.5 minutes, [tex]T_{s} =[/tex] 70° and [tex]T_{o}=[/tex] 210°
[tex]T(t)=T_{s}+(T_{o}-T_{s})e^{-kt}\\197=70+(210-70)e^{-1.5k} \\197 -70 = (140)e^{-1.5k} \\127 =(140)e^{-1.5k}\\\frac{127}{140}=e^{-1.5k} \\ln(\frac{127}{140})=-1.5k\\-0.097=-1.5k\\0.0649 = k[/tex]
[tex]k[/tex] ≈ [tex]0.065[/tex]
Let the temperature of the water cup after [tex]t = 4[/tex] minutes be [tex]T(t) = x[/tex]
Now, let's plug the new time and [tex]k[/tex] constant in the equation and solve for [tex]x[/tex]:
[tex]T(t)=T_{s}+(T_{o}-T_{s})e^{-kt}\\\\\x=70+(210-70})e^{-0.065*4}\\\\x=70+(140})e^{-0.26}, -0.26=-\frac{26}{100}=-\frac{13}{50} \\[/tex]
[tex]x=70+(140})e^{-\frac{13}{50}}\\\\[/tex]
[tex]x=70+(140})e^{\frac{1}{\frac{13}{50}}\\\\\\[/tex]
[tex]x=70+e^{\frac{140}{\frac{13}{50}}\\\\\\[/tex]
[tex]x=70+{\frac{140}{\sqrt[50]{e^{13}}}\\[/tex]
[tex]x = 70 +\frac{140}{1.3} \\x=70+107.947\\[/tex]
[tex]x=177.95[/tex] ≈ [tex]178[/tex]
Temperature of water after 4 minutes is 178°
sorry if there's any misspelling or wrong step but I hope my answer is correct ':3
4 solutions for z<-6
Answer:
-7, -8, -9, -10
Step-by-step explanation:
Is this actually the whole problem? If so, the answer is anything less than -6. z < -6 includes all the numbers less than -6, so that would include -7, -8, -1000, -6.000001, etc.; you get what I mean. This would NOT include -6, though, because z is less than, not equal to, -6.
You can visualize it on a number line. If every value that could possibly equal z had a dot on it, you would see an infinite number of dots starting from -6 and going left to infinity. Like: <-------------o, if o was -6.
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solve the equation (2^2x +2) (2^3x -7)= 2^25
Answer:
[tex]\Huge \boxed{x=6}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
[tex](2^{2x +2}) (2^{3x -7})= 2^{25}[/tex]
When multiplying same bases, add the exponents.
[tex](2^{2x +2+3x -7})= 2^{25}[/tex]
[tex](2^{5x -5})= 2^{25}[/tex]
Cancelling the same bases from both sides.
[tex]5x-5=25[/tex]
Adding 5 to both sides.
[tex]5x=30[/tex]
Dividing both sides by 5.
[tex]x=6[/tex]
[tex]\rule[225]{225}{2}[/tex]
Please help, find what X is. 42 - X = 29
Answer:
X = 13
Step-by-step explanation:
42 - X = 29
Subtract 42 from each side
42-42 - X = 29-42
-X = -13
Multiply each side by -1
X = 13
Employees in 2012 paid 4.2% of their gross wages towards social security (FICA tax). How much will someone earning $43,047 a year pay towards social security?
Answer:
$1807.94
Step-by-step explanation:
Given that:
Annual income = $43047
Social security (FICA tax) = 4.2% of the gross wages
To find:
Social security paid = ?
Solution:
Social security (FICA tax) is calculated by finding the 4.2% of the Total Gross Annual income.
i.e. for the given value, the social security paid can be calculated as:
4.2% of $43047
[tex]\Rightarrow \dfrac{4.2}{100}\ of \ \$43047\\\Rightarrow \dfrac{42}{1000}\times 43047\\\Rightarrow 0.042\times 43047\\\Rightarrow \bold{\$1807.97}[/tex]
Therefore, the Social Security paid is $1807.94.
What are the roots of the equation 9x^2 + 54x +82 = 0 in simplest a + bi form?
Answer:
The roots are
[tex]x = - 3 + \frac{1}{3} i \: \: \: or \: \: \: x = - 3 - \frac{1}{3} i \\ [/tex]Step-by-step explanation:
9x² + 54x + 82 = 0
Using the quadratic formula
That's
[tex]x = \frac{ - b\pm \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]From the question
a = 9 , b = 54 , c = 82
Substitute the values into the above formula and solve
That's
[tex]x = \frac{ - 54\pm \sqrt{ {54}^{2} - 4(9)(82)} }{2(9)} \\ x = \frac{ - 54\pm \sqrt{2916 - 2952} }{18} \\ x = \frac{ - 54\pm \sqrt{ - 36} }{18} \\ x = \frac{ - 54\pm 6i}{18} [/tex]Separate the real and imaginary parts
That's
[tex]x = - \frac{54}{18} \pm \frac{6}{18} \: i \\ x = - 3\pm \frac{1}{3} i[/tex]We have the final answer as
[tex]x = - 3 + \frac{1}{3} i \: \: \: or \: \: \: x = - 3 - \frac{1}{3} i \\ [/tex]Hope this helps you
Can a translation, a reflection, or a rotation of a figure ever result in an image with
a different size or shape? Explain.
Answer:
no, it will always be the same size and image just in a different placement.
Step-by-step explanation:
No, a translation, a reflection, or a rotation of a figure never results in an image with a different size or shape.
What is a translation?Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.
Each point in a figure is transformed into a rotation by rotating it a specific amount of degrees around another point.
Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point.
Hence, a translation, a reflection, or a rotation of a figure never results in an image with a different size or shape.
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