Answer:
It's 3
Step-by-step explanation:
if you go to desmos graphing calculator it'll help you get the solutions for these if you type it in every number and letter and for exponents type ^ its shift then type 6.
Calcular la edades actuales de una madre y sus dos hijos sabiendo que hace 14 años la dad de la madre era 5
veces la suma de las edades de los hijos en aquel momento, que dentro de 10 madre será la suma de las edades
que los hijos tendrán en ese momento y que cuando el hijo mayor tenga la edad actual de la madre, el hijo
menor tendrá 42 años.
The present age of mother and her daughter respectively are; 40 and 10 years respectively.
How to Solve Algebra Word Problems?Let x and y be the present age of mother and her daughter respectively.
Therefore;
x + y = 50
x = 50 − y .....(1)
After 20 years, mother's age will be twice her daughter's age at the time. Thus;
x + 20 = 2(y + 20)
x − 2y = 20 .....(2)
Plugging eq 1 into eq 2 gives us;
50 − y − 2y = 20
3y = 30
y = 10
Thus;
x = 50 − 10
x = 40
Thus, the present age of mother and her daughter is 40 and 10 years respectively.
Translation of the question into English is;
The sum of the present ages of mother and her daughter is 50 years. After 20 years, mother's age will be twice her daughter's age at the time. Find their present ages.
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In what table does y vary directly with x?
Answer:
The phrase “ y varies directly as x” or “ y is directly proportional to x” means that as x gets bigger, so does y, and as x gets smaller, so does y. That concept can be translated in two ways. for some constant k. The k is called the constant of proportionality. Therefore a chance of probability is a binary table.
Step-by-step explanation:
24. Demography A city has a population of 71,500. Ten years ago the population
was 32,500. What percent of the population 10 years ago is the population now?
Use the proportion method.
Answer:
45.5%
Step-by-step explanation:
The increase in population was 45.5%
What is the product of (x² + x + 2) and (x² − 2x + 3)
Answer:
[tex]x^4-x^3+3x^2-x+6[/tex]
Step-by-step explanation:
Multiply each term in the first equation by all the terms in the second and add them together.
Cooling towers are used to remove or expel heat from a process. A cooling tower's walls are modeled by x squared over 324 minus quantity y minus 90 end quantity squared over 1600 equals 1 comma where the measurements are in meters. What is the width of the cooling tower at the base of the structure? Round your answer to the nearest whole number.
36 meters
48 meters
80 meters
89 meters
The width of the cooling tower at the base of the structure will be A. 36 meters.
How to calculate the width?From the information given, the towers walls are modeled by x²/324 - (y² - 90)²/1600.
Therefore, the width of the cooling tower at the base of the structure will be:
= 2 × ✓324
= 2 × 18
= 36
In conclusion, the width is 36 meters.
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Answer:
It is actually D
Step-by-step explanation:
You are choosing between two different cell phone plans. The first plan charges a rate of
24 cents per minute. The second plan charges a monthly fee of $49.95 plus 11 cents per
minute.
Lett be the number of minutes you talk and C₁ and C₂ be the costs (in dollars) of the first
and second plans. Give an equation for each in terms of t, and then find the number of
talk minutes that would produce the same cost for both plans (Round your answer to one
decimal place).
C₁ =____
C₂ =____
If you talk for
_____ minutes the two plans will have the same cost.
If you talk for 384.23 minutes the two plans will have the same cost.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
x is the number of minutes that will be used during a month:
C₁ = 0.24x
C₂ = 49.95 + 0.11x
So, when 1st = 2nd
0.24x = 49.95 + 0.11x
0.24x - 0.11x = 49.95
0.13x = 49.95
x = 49.95/0.13
x = 384.23 minutes
Hence, If you talk for 384.23 minutes the two plans will have the same cost.
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Answer please! I need this!
Step-by-step explanation:
The top has been multiplied by 5 so multiply the bottom by 5, 2 x 5 = 10. also why is there a pig lol
what is the range of the ordered pairs shown in the graph?
D
Step-by-step explanation:
The points dx are at -1, 1, 2 and 3 so it must be D
Answer:
To find the range,
first see the value of each points -
first = (3,5)
second = (2,0)
third = ( 1,3)
fourth, ( -1, 2)
let's take X Axix to find the range
so the range is ( -1, 1 , 2 ,3)
Option D is correct
please solve using whatver method u want!
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ASAP
Answer:
System has no solutions.
Step-by-step explanation:
Double the first, change sign to the second. You get
[tex]6x-4y=8\\6x-4y=-7[/tex]
You need a quantity ([tex]6x-4y[/tex]) which, at the same time is both equal to 8 and -7, which is obviously impossible.
System has no solutions.
Which is the graph of f(x) = √x?
Look at the attached image.
the length of a cell is 2/3 mm. If the area of the cell is 1/12 square mm, whtat is the width of the cell
Answer:
0.125 mm
Step-by-step explanation:
A/L=W
W=0.125
Maria rides her bicycle to school at a constant speed of 15 miles per hour.If the distance to school is 6 miles,how many minutes will it take Maria to get to school?EXPLAIN PLEASE
E. 10
F.15
G.24
H.30
Answer:
24 minutes
Explanation:
Given:
speed: 15 miles/hdistance: 6 milesFormula:
time taken = distance/speed
Applying the formula:
time taken = 6/15 = 0.4 hours = 24 minutes
Now
Speed=Distance/TimeTime=Distance/SpeedTime =6/15=0.4h=24minf(a)=3a^2+2a+7 find the value of f(a)
Answer:
Step-by-step explanation:
If a = 0, f(a) = f(0) = 0 + 0 + 7 = 7;
If a = 1, f(1) = 3(1^2) + 2(1) + 7 = 12;
and so on. Normally an 'a' value would be given as part of this problem.
Actually, the value of f(a) is given and is f(a) = 3a^2+2a+7 for input value a.
What is the domain of the linear parent function?
Answer:
The parent function of linear functions is y=x and it passes through the origin.The domain and range of all linear functions are all real numbers.
Step-by-step explanation:
What is the vertex of the quadratic function given in the table?
Answer:
The vertex is (-3,-2)
The vertex is basically the very top or very lowest, so you will notice how values around (-3,-2) are relatively the same in the y coordinate, but -2 is the "highest/lowest" so that's how you know it's a vertex.
If you try picturing the points in your head, you will see it make a U and at the bottom of the U is the vertex.
A woman passed gas silently. I said "it stinks", and she said "I apologize. Excuse me". Why did she say both of those things?
Answer:
one possible way was because she knew what she did and started playing innocent
Solve the system of equation for y using Cramer's rule. Hint: The determinant of the coefficient matrix is -23.
Answer:
-4 option (c)
Step-by-step explanation:
Cramer rule : In this method, the values of the variables in the system are to be calculated using the determinants of matrices
if , D :determinant of the coefficient matrix
[tex]{D}_{x}:[/tex]determinant of the matrix with coefficients except x
then,
[tex]x=\frac{{D}_{x}}{D}[/tex]
similarly,
[tex]y=\frac{{D}_{y}}{D}[/tex]
[tex]z=\frac{{D}_{z}}{D}[/tex]
given,
D = -23
[tex]D_{y}[/tex] = [tex]det\left[\begin{array}{ccc}5&7&-1\\2&6&-2\\3&-7&2\end{array}\right][/tex]
[tex]D_{y}[/tex] = 92
therefore, y = 92/(-23)
y = -4 answer
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find arc length
x=t^(3)-2t
y=t^(2)-3
Answer:
Step-by-step explanation:
If the ordered pair (-5/2, y) lies on the graph of y=7-2x, find the value of y.
19/2
012
02
The correct answer is option B which is the value of Y will be 12.
What is an equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Given that:-
If the ordered pair (-5/2, y) lies on the graph of y=7-2x,
The value of Y will be calculated as:-
Y = 7 - 2x
Y = 7 - 2 ( -5/2 )
Y = 7 - ( - 5 )
Y = 7 + 5
Y = 12
Therefore the correct answer is option B which is the value of Y will be 12.
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The length of a golden rectangle is 35 cm. Find the width to the nearest centimeter.
17cm
25cm
22cm
29cm
16cm
Answer:
22 cm
Step-by-step explanation:
First we need to know that The golden number
= (1+√(5))÷2
= 1.61803398875 (in decimal)
………………………………………………
We get the length of a golden rectangle
by multiplying its width by the golden number itself.
Then
The width = 35÷ 1.61803398875
=21.631189606245
Which statement is correct when a scatterplot is constructed?
The independent variable is the input variable and should be represented by the x-axis.
The independent variable is the input variable and should be represented by the y-axis.
The dependent variable is the input variable and should be represented by the x-axis.
The dependent variable is the input variable and should be represented by the y-axis.
Option A is the correct answer.
The independent variable is the input variable and should be represented by the x-axis.
What is Variable?A variable is a symbol and placeholder for a quantity that may change, or any mathematical object. In particular, a variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set.
For the Scatterplot, out of given options,
Option A is the correct option which represents The independent variable is the input variable and should be represented by the x-axis.
Thus, The independent variable is the input variable and should be represented by the x-axis.
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An open rectangular box with a volume of 12 cubic meters has a length that is 5 times the width. Express the surface area of the box as a function of the length of a side of the base, x.
The area of a 2D form is the amount of space within its perimeter. The surface area of the prism is 5x²+(24/5x)+(24/x).
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
Let the width of the rectangular box be x. Therefore, the length of the box is 5x. Now, the height of the box can be written as,
Volume of the box = length × width × Height
12 = 5x² × H
H= 12 / 5x²
Further, the surface area of the open box is,
Surface area of the box
[tex]= (5x \times x) + 2(h \times x) + 2(5x \times h)\\\\= (5x^2) + 2(\dfrac{12}{5x^2} \times x) + 2(5x \times \dfrac{12}{5x^2})\\\\\\= 5x^2 + \dfrac{24}{5x} + \dfrac{24}{x}[/tex]
Hence, the surface area of the prism is 5x²+(24/5x)+(24/x).
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Using Triangle Congruence Theorems
There are a total of five theorems congruent triangles. They are summarized as:
SASSSSAASRHS and ASA.What are the definitions of the Theorems of Congruent Triangles?SAS - Side Angle Side
According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.
SSS - Side Side Side Rule
According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are proportional to the size three sides of the second triangle.
AAS - Angle Angle Side Rule
Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the comparable angles and sides of another triangle.
ASA - Angle Side Angle rule
According to the ASA rule, two triangles are said to be congruent if any two angles and the side contained between the angles of one triangle are proportional to the size two angles and side included in between angles of the second triangle.
RHS - Right Angle- Hypotenuse side Rule
According to the RHS rule, two right triangles are said to be equivalent if their hypotenuses and one of their sides are identical to those of another right-angled triangle.
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Answer:
AD=BC (given)
DC=DC (reflexive property)
DE=CE (converse of isosceles triangle thm)
<BCD=<ADC (given)
<ECD=<EDC (CPCTC)
TriangleADC=TriangleBCD (SAS)
An airplane is flying at an altitude of 26,843 feet. The plane descends (goes down) 1,284 feet. Then the plane ascends (goes up) another 5,832 feet.
Let a represent the altitude of the plane.
Which equation could be used to find the final altitude of the plane?
A. a = 26,843 + 1,284 + 5,832
B. a=26,843+1,284−5,832
C. a=26,843−1,284+5,832
D. a=26,843−1,284−5,832
Answer:
Hi
The answer is C
Step-by-step explanation:
Because it descend means goes down so it's minus and after that it ascends means goes up so it's plus so the answer will be -
26,843-1,284+5832
2x+3y=9 -2x+2y=6 The y cordinate
Answer:
y = 3
Step-by-step explanation:
2x + 3y = 9
-2x + 2y = 6
We have to add these two equations which gives us 5y = 15. Now, if you divide by 5 on both sides you get y = 3.
Find the sine and the cosine of 30°.
A. sin 30° =1/2, cos 30°= √3
B. sin 30°=1/2, cos 30° = √3/2
C. sin 30° = √3/3, cos 30°= √3/4
D. sin 30° = √3/3, cos 30° = √3/2
Answer:
Option B is correct.
Step-by-step explanation:
Trigonometry is defined as the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles. There are three basic trigonometric ratios: sine, cosine, and tangent. Trigonometry and its functions have an enormous number of uses in our daily life. For instance, it is used in geography to measure the distance between landmarks, in astronomy to measure the distance of nearby stars and also in the satellite navigation system.
The trigonometric function of sine for an acute angle is the ratio between the leg opposite the angle when it is considered part of a right triangle and the hypotenuse while the cosine is the ratio of the base and the hypotenuse.
Here, [tex]sin 30[/tex]° [tex]=\frac{4}{8}[/tex]
[tex]sin 30[/tex]° [tex]=\frac{1}{2}[/tex]
[tex]cos 30[/tex]° [tex]=\frac{4\sqrt{3}}{8}[/tex]
[tex]cos30[/tex]°[tex]=\frac{\sqrt{3} }{2}[/tex]
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Need help with this geometric question
Answer: 95 degrees (not an answer choice)
Step-by-step explanation:
Opposite angles of a parallelogram are congruent, so the left part of the angle is 40 degrees.
Adjacent angles of a parallelogram are supplementary, so the right part of the angle is 55 degrees.
Adding these together, we get 95 degrees.
Suppose line g is the line with the equation y = x. Given A (7,-3) , B (6,3), and C (-2,-7), what are the coordinates of the vertices of a’b’c’ for the reflection
Answer: A'(-3, 7), B'(3, 6), C'(-7, -2)
Step-by-step explanation:
Reflecting over y = x maps (x,y) onto (y,x).
If you currently makes 425 What is the gross they will earn If they work every week If the year
They will earn If they work every week If the year is $22100.
We have given that,
you currently make 425
We have to determine what is the gross they will earn If they work a week If the year.
We know that
A worker currently makes $425 per week
How many weeks in a year?1year=52 weeks
So by proportion find the amount that the worker will earn in one year
[tex]\frac{425}{x}\times \frac{\$}{weeks}[/tex]
[tex]=\frac{x}{52}\times \frac{\$}{weeks}[/tex]
[tex]x=52\times 425[/tex]
x=22,100
Therefore, The answer is $22100.
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What are the solutions to the quadratic equation below?
x²-2x-168 =0
Answer:
x= 14, –12
Step-by-step explanation:
The given question might make you believe that it's difficult due to it's frightening digit (168) but in fact in you use the following methods, it's going to be a pieces of cake.
the delta formula:
Δ=b²–4ac===> (–2)²–4(1)(–168)=676
[tex]x 1 = \frac{ - ( - 2) + \sqrt{676} }{2} = 14 [/tex]
[tex]x2 = \frac{ - ( - 2) - \sqrt{676} }{2} = - 12[/tex]
well this can be on of the methods and the other one is
The full square formula:
[tex]x ^{2} - 2x - 168 = 0 \\ {x}^{2} - 2x = 168[/tex]
[/tex]
now what you need to do is to put this on both side of the equation (½b)²=1
[tex] {x}^{2} - 2x + 1 = 168 + 1 \\ {(x - 1)}^{2} = 169 \\ x - 1 = 13 = = > x = 14 \\ x - 1 = - 13 = = = > x = - 12[/tex]