9514 1404 393
Answer:
k+4
Step-by-step explanation:
48 = 16×3 = 2^4×3
log2(48) = log2(2^4) +log2(3)
log2(48) = 4 + k
Given a rectangle with length of (2x+9)cm and width of (3x+1)cm.Two squares, each with sides x cm is removed from the rectangle.The remaining shape has an area of 83cm².Find the value of length and width of the rectangle.
Answer: The length is 13cm and the width is 7cm
Step-by-step explanation:
For a rectangle of length L and width W, the area is:
A = W*L
In this case we have:
L = (2*x + 9) cm
W=(3*x + 1) cm
Then the area of the rectangle is:
A = (2*x + 9)*(3*x + 1) cm^2
A = (6*x^2 + 2*x + 27*x + 9) cm^2
A = (6*x^2 + 29*x + 9) cm^2
now we remove two squares with sides of x cm
The area of each one of these squares is (x cm)*(x cm) = x^2 cm^2
Then the area of the figure will be:
area = (6*x^2 + 29*x + 9) cm^2 - (2*x^2 ) cm^2
area = (4*x^2 + 29*x + 9) cm^2
Now we know that the area of this shape is 83 cm^2, then we need to solve:
83 cm^2 = (4*x^2 + 29*x + 9) cm^2
0 = (4*x^2 + 29*x + 9) cm^2 - 83 cm^2
0 = (4*x^2 + 29*x - 74) cm^2
Then we need to solve:
0 = 4*x^2 + 29*x - 74
Here we can use Bhaskara's equation, the solutions of this equation are given by:
[tex]x = \frac{-29 \pm \sqrt{29^2 - 4*4*(-74)} }{2*4} = \frac{-29 \pm 45}{8}[/tex]
Then the two solutions are:
x = (-29 - 45)/8 = -9.25 (for how the length and width are defined, we can not have x as a negative number, then this solution can be discarded).
The other solution is:
x = (-29 + 45)/8 = 2
x = 2
Then the length and width of the rectangle are:
Length = (2*2 + 9)cm = 13 cm
Width = (3*2 + 1)cm = 7cm
Find the slope pleaseeee hurry
Answer:
slope is -1
Step-by-step explanation:
Answer:
Step-by-step explanation:
Let ( x1 , y1) = ( -4 ,1 )
(x2 , y 2) = ( -2 , -1 )
Now
slope (m)
= ( y2 - y1) / (x2 -x1)
= ( -1 - 1) / ( - 2 + 4)
= -2 /2
= - 1
Hope it helps :)
Nick wants to build a banister for the staircase in his home. The height of the staircase is 8 feet, and the horizontal distance from the bottom to the top of the staircase is 15 feet.
What is the length of the banister? Round to the nearest tenth, if necessary.
Answer:
Step-by-step explanation:
By the Pythagorean Theorem
c^2=a^2+b^2 ( where c is the hypotenuse and a and b are the legs of a right triangle)
c^2=15^2+8^2
c^2=225+64
c^2=289
c=17 feet
In ΔSTU, the measure of ∠U=90°, ST = 67 feet, and TU = 14 feet. Find the measure of ∠T to the nearest degree.
Answer:
78
Step-by-step explanation:
Answer:
78
Step-by-step explanation:
Robert bought a pair of shoes that was on sale for 30% off
the original price of $79.95. Which is closest to the sale
price of the pair of shoes?
Answer:
The sale price of the shoes is $55.96
Step-by-step explanation:
1: 30% of $79.95 is 23.985.
Which would round to $23.99.
Then subtract 23.99 from 79.95.
79.95-23.99= 55.96
[tex] \sqrt{18} - \sqrt[x]{2 } = \sqrt{32} [/tex]
solve for x
Tres empleados de una empresa tienen que pagar 3100€ de impuestos entre todos de forma inversamente proporcional a su sueldo mensual. Si Javier cobra 1500€, Antonio, 2000€, y Elvira, 1800€, ¿cuánto tiene que pagar cada uno?
Answer:
La cantidad que Javier paga como impuesto, A es de 1.200 €
La cantidad que Antonio paga como impuesto, B es 900 €
El importe que paga Elvira como impuesto, C es de 1.000 €
Step-by-step explanation:
Dejemos que 'A', 'B' y 'C', representen la cantidad que pagan Javier, Antonio y Elvira respectivamente, y que 'k' represente la constante de proporcionalidad, por proporcionalidad inversa, tenemos;
A = k / 1500, B = k / 2000, C = k / 1800
A + B + C = 3100
∴ k / 1500 + k / 2000 + k / 1800 = 3100
Simplificando la ecuación anterior usando una calculadora gráfica da;
31 · k / 18 000 = 3100
k = 18.000 × 3.100 / 31 = 1.800.000
k = 1.800.000
La cantidad que Javier paga como impuesto, A = 1.800.000 / 1.500 = 1.200
La cantidad que Antonio paga como impuesto, B = 1.800.000 / 2.000 = 900
La cantidad que paga Elvira como impuesto, C = 1.800.000 / 1.800 = 1.000
Solve for x in the diagram below.
Answer:
x = 20
Step-by-step explanation:
The sum of the two angles is 90 degrees
x+3x+10 = 90
Combine like terms
4x+10 = 90
Subtract 10 from each side
4x+10-10 = 90-10
4x= 80
Divide each side by 4
4x/4 = 80/4
x = 20
Answer:
x = 20
Step-by-step explanation:
x and 3x + 10 form a right angle, then
x + 3x + 10 = 90
4x + 10 = 90 ( subtract 10 from both sides )
4x = 80 ( divide both sides by 4 )
x = 20
A shark is swimming 25 feet below the surface of the water. It goes down another 12 feet. What is the new depth the shark is swimming at?
Answer:
37 feet below the surface or -37 ft
Step-by-step explanation:
To find the total cost ( c ), substitute the value of (p) you just found, 285.7 , into one of the equations in the system
Answer:
c = 214.28 OR 214.275
Step-by-step explanation:
You could do c = 0.75(285.7) and you would get c = 214.275
Triangle AB is 15 BD 9 what is area ABC
Answer:
it is your answer...... if it is helpful plzz like ans comment
f(x) = x2. What is g(x)?
What is the Mean of the data below 2,4,5,6,8,2,5, 6
the answer is 4.75
Step-by-step explanation:
The mean of a set of numbers, sometimes simply called the average , is the sum of the data divided by the total number of data. Example 1 : ... There are 8 numbers in the set. Add them all, and then divide by 8 . so just add all you numbers and divide it by 8. simple
HELP PLEASE!! i need help on A and B. PLEASE DONT ANSWER IF YOU DONT KNOW!!
Answer: B
Step-by-step explanation:
you use the coordinates to find the sides
0.5+69-69=180-69 plz help I will give brainlest
Answer: 0.5 = 111
Step-by-step explanation:
Answer:
Step-by-step explanation:69696969699696969696969696969699696965iu436745
Mr. Torres bought 3 chairs on Saturday. He paid d dollars for each chair. Mr. Torres received $15 dollars in change when he bought the chairs. Which expression can be used to find the total amount Mr. Torres paid for these chairs
Answer: c. 3d + 15
Step-by-step explanation:
Mr. Torres paid d dollars for each of the three chairs which gives the expression of:
= 3 * d = 3d
He then paid with an amount that was greater than this 3d and got a change of $15.
That total amount that he paid is therefore, the price of the three chairs added to the $15 that he received back.
= 3d + 15
Determine the approximate average rate of change in the number of tickets sold between the 3rd and 10th days after the release.
OA.
OB.
The number of tickets sold changed at an average rate of approximately -20 tickets per day.
The number of tickets sold changed at an average rate of approximately – 7 tickets per day.
The number of tickets sold changed at an average rate of approximately –10 tickets per day.
The number of tickets sold changed at an average rate of approximately –3 tickets per day.
Ос.
D.
Answer:
-3 Is the average rate
Step-by-step explanation:
The number of tickets sold changed at an average rate of approximately -20 tickets per day. The correct answer is option A.
What is the average rate of change?The average rate of change is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.
The rate of change is calculated by the formula below:-
Rate of change = Final value - initial value.
From the given graph the value of tickets on the 3rd day is 100 and on the 10th day is 80. The final value of tickets is 80 and the initial value is 100.
The average rate of change in the number of tickets sold between the 3rd and 10th days after the release will be calculated as below:-
Rate of change = Final value - initial value.
Rate of change = 80 - 100
Rate of change = -20
Therefore, the number of tickets sold changed at an average rate of approximately -20 tickets per day. The correct answer is option A.
To know more about the average rate of change follow
https://brainly.com/question/8728504
#SPJ2
which statement is true about the extreme value the given quadratic equation? y = -3x^2 + 12x - 33 Oa. The equation has a maximum value with a y coordinate of -27 Ob. The equation has a minimum value with a y coordinate of -21 Oc. the equation has a minimum value with a y coordinate of -27 Od. The equation has a maximum value with a y coordinate of -21
Answer:
D. The equation has a maximum value with a y coordinate of -21Step-by-step explanation:
The quadratic equation has the extreme value at vertex with x-coordinate of
x = -b/2aFor the given equation the vertex is:
x = -12/2(-3) = 2The value of y at x = 2 is:
y = -3(2²) + 12(2) - 33 = -12 + 24 - 33 = -21Since the leading coefficient is negative, the extreme is the maximum for the given equation.
Correct choice is D
A taxi service charges a flat fee of $4.20 per ride plus an additional $.80 per mile.
If a taxi ride costs $6.60, how many miles did the taxi travel?
A. 2
B. 3
C. 3.5
D. 4
Answer:
B.)
6.60
4.20
-______
what is the dividend of 20 times 50
Answer:
1000
Step-by-step explanation:
Answer:
20 × 50
= 1000
Although u say dividend, which is division, not too sure here
If – 2/3X – 1 = 4, then x =
Answer:
2/5
Step-by-step explanation:
The value of x will be x = -15/2
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
We are given that the equation – 2/3X – 1 = 4
Here, we need to solve for x,
– 2/3X – 1 = 4
Now combine the like terms;
– 2/3X = 4 + 1
-2/3x = 5
x = -15/2
Therefore, the solution will be as;
x = -15/2
The value of x will be; x = -15/2
Learn more about equations here;
brainly.com/question/25180086
#SPJ2
Two angles are vertical if one is 5x - 15 and the second angle is 3x + 1, what is the value of x
What is the measure of each angle
Answer:
Step-by-step explanation:
If they are vertical angles, they are opposite to each other where two lines intersect. Vertical angles are equal to each other so
5x-15=3x+1
2x-15=1
2x=16
x=8 degrees.
The angles are
a=5x-15, and x=8 so
a=5(8)-15
a=40-15
a=25 degrees.
A baker has 15 cups of flour. He sets aside 4 cups of flour, and uses the rest for a cookie recipe that calls for 1/2 cup of flour. How many batches of cookies can the baker make? pls help ana2928
YO please help actually been waiting for an hour and a half cuz so many trolls lol. <3 giivng brainliest, and ty in advance guys
Hello!
For this problem we are given that quadrilateral ABCD is congruent to quadrilateral GJIH, meaning that all sides and angle measures will be equivalent to its corresponding side.
This means that to find [tex]x[/tex], we can look at quadrilateral GJIH's corresponding side to quadrilateral ABCD's side AD, which is side GH, which has a value of 9.
This means that 9 should also be the side length of side AD, which we're given a value of [tex]x/3[/tex].
[tex]x/3=9[/tex]
Solve.
[tex]x=27[/tex]
Hope this helps!
-(4-x)=3/4(x-6)
solve for x
show work please!!!
(not test, this is hw)
Traveon is walking dogs for his neighbors, to make money. This week, he walked Mr. Jackson's dog 3.5 times farther than he walk Ms. Evans' dog. If the total distance that he walked both dogs is 17.5 miles, how far did he walk Ms. Evans' dog? *
Answer:
He walked Ms. Evans' dog 3.89 miles.
Step-by-step explanation:
From the information provided, you know that the total distance that he walked both dogs is 17.5 miles, which can be expressed as:
x+y=17.5, where:
x is the distance he walked Mr. Jackson's dog
y is the distance he walked Ms. Evans' dog
Also, the statement indicates that he walked Mr. Jackson's dog 3.5 times farther than he walk Ms. Evans' dog and you can write the following equation:
x=3.5y
Now, you can replace x=3.5y in the first formula and solve for y to find how far he walked Ms. Evans' dog:
3.5y+y=17.5
4.5y=17.5
y=17.5/4.5
y=3.89
According to this, the answer is that he walked Ms. Evans' dog 3.89 miles.
someone please do this for me... i will mark brainliest. all work needs to be shown. (picture shown above)
Step-by-step explanation:
just use step by step process so dum
Sorry its long but ill give brainlist to the right one just look at the images and multiple choice parts
If the mother's name is Mrs.62,Her son's name is 52 & her daughter's name is 42 ,then what is the name of father????
Answer:
Either Mr.62 or 72
Because if her name is 62 that means thats his name, but also it went down 10 so therefore his name could be 10 above
Answer:
72
Step-by-step explanation: beacuse the mother is 62 so the fartheher has to be older
Gilded Gifts Company hires employees to make handmade greeting cards. The manager is determining how the time spent training new employees affects their production of greeting cards. The scatter plot below shows how many greeting cards each employee made the past month and the number of hours of training the employee received. A line of best fit is drawn.
Complete the statements based on the scatter plot.
The slope of the line of best fit is
. This means that for every additional hour of training,
more greeting cards are expected to be made per month.
Without any training, an employee is expected to make
greeting cards per month.
If an employee has 70 hours of training, the employee is expected to make
greeting cards per month.
Answer:
I think its A
Step-by-step explanation:
a. The equation of the trend line is c=5x+100.
b. The equation of the trend line is c=-5x+100.
c. As the hours of training increase by 5, the greeting cards made increases by 25.
d. As the hours of training increase by 5, the greeting cards made decreases by 25.
Answer:
The slope of the line of best fit is 5.
Without any training, an employee is expected to make 100 greeting cards.
If an employee has 70 hours of training, the employee is expected to make 450 greeting cards per month.
Step-by-step explanation:
First, find the slope of the line of best fit by substituting any two points on the line into the slope formula. The following calculation uses (10,150) and (20,200).
So, the slope of the line of best fit is 5.
The y-intercept is the point at which the line crosses the y-axis or when x = 0. So, the y-intercept of the line of best fit is 100.
The equation of the line of best fit can be represented in slope-intercept form, where the slope, m, is 5 and the y-intercept, b, is 100.
A slope of 5 in this situation means that for every additional hour of training, 5 more greeting cards are expected to be made per month. The y-intercept is 100 when the number of hours of training is 0. So, without any training, an employee is expected to make 100 greeting cards.
To find the number of greeting cards an employee would produce after receiving 70 hours of training, substitute x = 70 into the equation for the line of best fit and solve for y.
So, if an employee has 70 hours of training, the employee is expected to make 450 greeting cards per month.