The number you thought of is -1.
To solve this problem, you can use algebra to represent the unknown number as a variable (let's call it x) and the given information as equations. The first step is to determine what the problem is asking for. In this case, it is asking to find the original number before it was doubled and 3 was added. To do this, you can use the information given in the problem to set up equations.
The first equation is (2x+3)*4 = 52. You can then solve this equation for x. First, you can simplify the left side of the equation by distributing the 4 to the 2x and the 3: 4x + 12 = 52. Then, you can subtract 12 from both sides to get 4x = 40. Finally, you can divide both sides by 4 to get x = 10. however, this is not the solution, since the problem does have not a unique solution. x=-1 is also the solution.
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Gwen scans a photo that is 4inches wide by 6 inches long into her computer. If she scales the length down to 3inches how wide should the similar photo be?
The similar photo should be 4.5 inches wide.
What is scale factor?Direct variation of a quantity {y} with respect quantity {x} means that the value of {y} increases as the the value of {x} increases. Mathematically -
y = Kx
K = y/x
where -
{K} is scale factor. It also tells by how many times is {y} greater than {x}.
Given is that Gwen scans a photo that is 4 inches wide by 6 inches long into her computer. Now, she scales the length down to 3 inches.
We can write -
y₁/x₁ = y₂/x₂
6/4 = 3/x₂
x₂ = 6 x 3/4
x₂ = 6 x 0.75
x₂ = 4.5
Therefore, the similar photo should be 4.5 inches wide.
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What is the length of PQ
Check the picture below.
[tex]\sin(30^o)=\cfrac{\stackrel{opposite}{PQ}}{\underset{hypotenuse}{4}}\implies 4\sin(30^o)=PQ\implies 4\left( \cfrac{1}{2} \right)=PQ\implies 2=PQ[/tex]
Two alien pacehip tart traveling toward each other from pace tation that are 710,000 km apart. The firt pacehip tarted an hour before the econd pacehip and i traveling at 110,000 km/hr. In how many hour will the two pacehip meet if the econd pacehip i traveling at 90. 000 km/hr?
The two spaceships will meet in 8 hours if the second spaceship is traveling at 90. 000 km/hr.
To calculate the time it will take for the two spaceships to meet, you must use the equation Distance = Rate x Time. Since the first spaceship has a higher rate of speed, it will reach the second spaceship in less time than it would take the second spaceship to reach the first.
This means that the time it takes for the two spaceships to meet will be equal to the time it takes for the first spaceship to travel the distance between the two space stations. We can use the equation to solve for time: Time = Distance/Rate. In this case, the distance is 710,000 km and the rate is 110,000 km/hr, so the time is 6.45 hours.
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Let C be between D and E. Use the Segment Addition Postulate to solve for n.
DC = 5n – 30
CE = 6n – 25
DE = 44
A. N = 13
B. N = 4
C. N = –5
D. N = 9
Segment Addition Postulate states that n has a value of 9 when DC = 5n - 30 and CE = 6n - 25 and DE = 44.
what is equation ?A mathematical equation is a formula that connects two statements using the equal sign (=) to denote equivalence. An algebraic equation is a mathematical statement that establishes the equality of two mathematical expressions. For example, the variables 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14. Mathematical equations are used to express the connection between two phrases on either side of a letter. There is frequently just one variable, which is also the symbol. example: 2x - 4 = 2.
given
DE = DC + CE
44 = 5n – 30 + 6n – 25
44 = 11n - 55
44 + 55 = 11n
n = 9
Segment Addition Postulate states that n has a value of 9 when DC = 5n - 30 and CE = 6n - 25 and DE = 44.
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A different computer is advertised as 30% off of the original price. After the discount, the tax is $78.75
• Determine the original price of this computer.
Show your work or explain your answer.
The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
How to calculate original price of computer?The original price of the computer is 112.5 .The amount saved is 33.75The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
Here,
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
Coupon = 30% off
Coupon = 30% off= 78.75
This means that the cost of the computer is only 70% since 30% is off.
70% = 78.75
We know that the original price is 100%.
So,
70% = 78.75
Multiply 100/70 on both sides.
100/70 x 70% = 100/70 x78.75
100% =112.5
The original price of the computer is 112.5
The amount saved is:
112.5-78.75=33.75
Thus,
The original price of the computer is 112.5
The amount saved is 33.75
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Please help me understand
The transformation is shifted up 2 units.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is f(x)=-2x+3.
Here, the slope m of a line is -2 and y-intercept is 3
A) If the function g(x)=f(x)+k, where k=2.
Now, g(x)=-2x+3+2
g(x)=-2x+5
Here, the slope m of a line is -2 and y-intercept is 5
B) The slope of both functions are same
To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.
Shifted up 2 units
Therefore, the transformation is shifted up 2 units.
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How do you use log and e?
The value of e (exponential) is approximately equal to 2.718281 which is rounded to 6 digits. The exponential constant frequently happens in mathematics every time the exponential functions are involved.
Log mention to a logarithm to the base 10. Ln mentions a logarithm to the base e. This is also known as a common logarithm. This is also known as a natural logarithm.
The first common log is represented as log 10 (x) The second natural log is represented as log e (x) The exponent form of the common logarithm is 10 x =y.
An exponential function is a function in which a number or data is raised to the power of another number or a variable.
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help i cant solve it
Answer:
Step-by-step explanation:
We have,
x = 3y - 3 ---> x - 3y = -3 ------(1)
5x + 4y = 23 -----(2)
Multiplying eq. (1) by 5:
5x - 15y = -15 ------(3)
5x + 4y = 23
Subtracting (1) from (3):
-19y = - 38
y = 2
therefore, x - 6 = -3
x = 3
whoever helps me with this will get 10 points.
Answer:
The answer is 1/4.
I wish you good luck.
Answer: it's hard i thought i could do it but nope dang it
Find the value of xif V√81 = 3.
OA) 4
OB) 2
OC) 8
OD) 27
The value of exponent x, if [tex]$\sqrt[\text X]{81} = 3[/tex], is 4, in the given equation.
What is exponent?
Exponent is the process of expressing large numbers as powers, according to the definition. Accordingly, the exponent describes the number of times a number has been multiplied by itself. Using 6 as an example, multiply it by itself four times, or 6×6×6×6. 6⁴ can be used to represent this. In this case, the base is 6 and the exponent is 4. You can interpret this as 6 raised to the power of 4.
Exponents are represented by the symbol. The word "carrot" refers to this symbol (). 4 raised to a power of two, for instance, can be expressed as 4^2 or 4². Thus, 4^2 = 4 × 4 = 16. A few exponent-based numerical expressions are represented in the table below.
The value of x, if [tex]$\sqrt[\text X]{81} = 3[/tex]
3 × 3 = 9
9 × 3 = 27
27 × 3 = 81
Thus, The value of x, if [tex]$\sqrt[\text X]{81} = 3[/tex], is 4.
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The KOT club has 5 pledges. They will send at least 2 and no more than 4 pledges to work at Goodwill on Helping-Out Day. In how many ways can this be done?
Answer:
The KOT club has 5 pledges and can send between 2 and 4 pledges to work at Goodwill on Helping-Out Day. This can be done in 10 different ways
Step-by-step explanation:
David owns a food truck that sells tacos and burritos. He only has enough ingredients to make 87 tacos or burritos.Write an inequality that could represent the possible values for the number of tacos sold, tt, and the number of burritos sold, bb, that would satisfy the constraint.
For triangle ABC use the Triangle Proportionality Theorem to solve for x
1. what is the value of x?
2. What is the perimeter of triangle ABC?
show ALL work-- PLEASE HELP!
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here's the solution ~
The two triangles in the shown figure are similar, therefore conclusion can be made that :
Ratio of its it's corresponding sides is equal.
[tex]\qquad \sf \dashrightarrow \: \dfrac{2x - 4 + 6}{6} = \dfrac{24}{4} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{2x + 2}{6} = 6[/tex]
[tex]\qquad \sf \dashrightarrow \: 2x + 2 = 6 \times 6[/tex]
[tex]\qquad \sf \dashrightarrow \: 2x + 2 = 36[/tex]
[tex]\qquad \sf \dashrightarrow \: 2x = 36 - 2[/tex]
[tex]\qquad \sf \dashrightarrow \: 2x = 34[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 17[/tex]
Therefore, The value of x is " 17 "
Now, the measure of side BC is :
[tex]\qquad \sf \dashrightarrow \: 2x - 4[/tex]
[tex]\qquad \sf \dashrightarrow \:2 (17) - 4[/tex]
[tex]\qquad \sf \dashrightarrow \: 34 - 4[/tex]
[tex]\qquad \sf \dashrightarrow \: 30 \: \: units[/tex]
So, its perimeter will be :
[tex]\qquad \sf \dashrightarrow \: p = AB + AB + BC [/tex]
[tex]\qquad \sf \dashrightarrow \: p = 24 + 26 + 30[/tex]
[tex]\qquad \sf \dashrightarrow \: p = 80 \: \: units[/tex]
Answer:
1) x = 17,2) P = 86 units.------------------------------------
Part 1According to Triangle Proportionality Theorem we have the following equal proportions:
(24 - 4)/4 = (2x - 4)/620/4 = (x - 2)/35 = (x - 2)/3x - 2 = 5*3x - 2 = 15x = 17Part 2The missing side is:
BC = 6 + 5*6 = 6 + 30 = 36 unitsThe perimeter is:
P = 24 + 36 + 26 = 86 unitsChee and her children went into a grocery store and she bought $12 worth of bananas and mangos. Each banana costs $0.50 and each mango costs $2. She bought twice as many bananas as mangos. Graphically solve a system of equations in order to determine the number of bananas, x,x, and the number of mangos, y,y, that Chee bought.
We get the number of bananas as 8 and the number of mangoes as 4.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is that Chee and her children went into a grocery store and she bought $12 worth of bananas and mangos. Each banana costs $0.50 and each mango costs $2. She bought twice as many bananas as mangos.
We can write the system of equations as -
x = 2y ..... (1)
(1/2)x + 2y = 12 ..... (2)
We can write equation (2) as -
(1/2) x 2y + 2y = 12
3y = 12
y = 4
then -
x = 8
Therefore, we get the number of bananas as 8 and the number of mangoes as 4.
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Find the area of the largest rectangle that can be inscribed in the ellipse x2 / a2 + y2 / b2 = 1.
The maximum area of the rectangle inside the ellipse is 2ab.
Given that,
Ellipse = x2 / a2 + y2 / b2 = 1
we know the general coordinates of any point in an ellipse of the equation
x2 / a2 + y2 / b2 = 1 is (acosθ,bsinθ)
So, we take general vertices of rectangles as
(acosθ,bsinθ), (acosθ,-bsinθ), (-acosθ,bsinθ), and (-acosθ,-bsinθ)
So, we can see that length and breadth of the rectangle is 2acosθ and 2bsinθ
So, its area will be ab4sinθcosθ (Length x Breadth)
Applying trigonometric formula 2sinθcosθ=sin2θ, let area equals to A
Now A=2absin2θ
Now as the area is the maximum given in the question, we have to differentiate it with respect to θ
dA/dθ=2abcos2θ×2 (using dsin2θ / dθ=2cos2θ)
Equating dA / dθ=2abcos2θ×2=0, it means cos2θ=0 , which means 2θ = π / 2 and θ=π / 4
So now we to put θ=π / 4 in the equation of area which is A=2absin2θ
We get as A=2absin2π / 4=2absinπ / 2=2ab
Hence the max area of the rectangle inside the ellipse is 2ab.
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33
Problem 2
m, p, and z represent the lengths of the three sides of this right triangle.
m
i
Z
Р
Select all the equations that represent the relationship between m, p, and z.
On solving the provided question, we can say that since it it is right angled triangle so the relation that be formed is [tex]m^2 = p^2 + z^2[/tex]
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
since it it is right angled triangle
so the relation that be formed is
[tex]m^2 = p^2 + z^2[/tex]
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Combine like terms to simplify this expression:
8 + 7y + 2y + 4
Answer: The resulting expression is 8+9y+4, which simplifies to 12+9y.
Step-by-step explanation: To combine like terms, we add the coefficients of the terms that are the same. In this expression, the like terms are 2y and 7y. Their coefficients are 2 and 7, respectively, so when we add them we get 2+7=9. The resulting expression is 8+9y+4, which simplifies to 12+9y.
To indirectly measure the distance across a river, Houa stands on one side of the river and uses sight-lines to a landmark on the opposite bank. Houa draws the diagram below to show the lengths and angles that she measured. Find PRPR, the distance across the river. Round your answer to the nearest foot.
According to the Houa's drawing the distance across the river PR is
198.95 feetHow to measure the distance PRThe length of line PR is calculated using the knowledge of similar triangles
While similar triangles is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent.
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions
Examining the figure shown, the pair of equivalent sides are
PO and OC, PR and RE,
The solution is worked out using sides PO and OC, PR and RE,
PO / OC = PR / RE
let PR be equal to y such that PO = 140 + y
(140 + y) / 230 = y / 135
cross multiplying
135(140 + y) = 230y
Expanding
18900 + 135y = 230y
collecting like terms
18900 = 230y - 135y
95y = 18900
y = 198.95 feet
Hence PR = 198.95 feet
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On a certain hot summer day, 431 people used the public swimming pool. The daily prices are 1.50 for children and 2.00 for adults. The receipts for admission totaled to $788.50. How many children and how many adults swam at the public pool that day?
The number of adults at the public pool that day is 284 and the number of children is 147.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Let x be the number of adults and y be the number of children who used the swimming pool.
Total number of people used the swimming pool = 431
x + y = 431
Daily price for adults = $2.00
Daily price for children = $1.50
Total amount for admission = $788.50
2x + 1.5y = 788.5
We got two linear equations here :
x + y = 431 and 2x + 1.5y = 788.5
x + y = 431 ⇒ x = 431 - y
Substituting this in second equation,
2(431 - y) + 1.5y = 788.5
862 - 2y + 1.5y = 788.5
-0.5y = -73.5
y = 147
x = 431 - 147 = 284
Hence the number of adults is 284 and the number of children is 147.
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Graph the system of equations on the grid below. Y=4x+7 and 2=x-y
The two lines intersect at (-3,-5) and thus a common solution.
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here, the system of linear equations as Y=4x+7 and 2=x-y
On solving these two equations we get that the two lines intersect at (-3,-5) and thus a common solution.
The two equations are plotted in the attachment below.
Hence, The two lines intersect at (-3,-5) and thus a common solution.
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Write an equation for the sinusoid you graphed.
Max: 210
Min: 10
Time: 90 seconds (to go around the Ferris wheel 1 time)
Not sure if I graphed it correctly either…
Therefore , As a result, y=Sin will be the equation of the sinusoid that answers the supplied equation problem (2x).
Describe equationAn equation is a representation of two equal variables in mathematics, one on each side of a "equals" sign. Common difficulties can be solved using equations. We commonly seek pre algebra help to resolve problems in real life. Pre-algebra lessons address the fundamental concepts of mathematics.
Here,
Given: Maximum: 210
Minimum: 10
Time : 90
In order to create a sinusoid equation:
When x=0, sin(2*0)=sin(0)=0.
If x = 4 then sin(4 / 2) = 1.
Sin(π) = 0 if x =π/2 and
Consequently, the sinusoid's equation will be y=Sin (2x)
Therefore , As a result, y=Sin will be the equation of the sinusoid that answers the supplied equation problem (2x).
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In 200920092009, Usain Bolt set the world record for sprinting 100 \text{ m}100 m100, start text, space, m, end text in approximately 9\dfrac359
5
3
9, start fraction, 3, divided by, 5, end fraction seconds.
Find his average speed in meters per second.
meters per second
The average speed of Usain Bolt in meters per second is given as 10.42 meters
How to solve for the average speedThe formula for speed is given as distance / time
the distance is said to be 100m
the time as it is written here is said to be 9 3/5
this is written as an improper fraction = 48 / 5
We are to find the average speed in meter per second
speed = 100 / (48/5)
speed = 500 / 48
speed = 125 / 12
write this as a mixed fraction or in decimal
speed = [tex]10\frac{5}{12}[/tex] or 10.42
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Given g(x) = 1/2(3x-1) and f(x)=7 identify the value of x which makes f(x) = g(x)
Answer:x=5
Step-by-step explanation:
f(x) = g(x)
[tex]\frac{1}{2}(3x-1)=7\\\\ \frac{3}{2}x-\frac{1}{2} =7\\\frac{3}{2}x-\frac{1}{2}+\frac{1}{2} =7+\frac{1}{2} \\\\\frac{3}{2}x=\frac{15}{2} \\\frac{3}{2}x*\frac{2}{3} =\frac{15}{2}*\frac{2}{3} \\\\x=5[/tex]
An object is launched at an upward velocity of 9696 feet per second from the top of a building 160160 feet above the ground. Use the vertical motion model h=-16t^{2}+vt+c, where hh is the ending height of the object, cc is the initial height, in feet, of the object, tt is the time in seconds, and vv is the velocity of the object.
How long will it take the object to reach the maximum height and what is the maximum height? Fill in the blanks with the appropriate values.
The time that it will take for the object to reach maximum height is given as follows:
3 seconds.
The maximum height is given as follows:
304 feet.
How to model the object's height?The object's height is modeled by a quadratic function in the following format:
h = -16t² + v(0)t + h(0).
In which:
v(0) is the initial velocity.h(0) is the initial height.The parameters for this problem are given as follows:
v(0) = 96, h(0) = 160.
Hence the function is defined as follows:
h(t) = -16t² + 96t + 160.
Meaning that the coefficients of the quadratic function are given as follows:
a = -16, b = 96, c = 160.
The coefficient a is negative, meaning that this is a concave down quadratic function, thus the vertex of the quadratic function represents the maximum height.
The t-coordinate of the vertex is given as follows:
t = -b/2a = -96/-32 = 3 seconds.
Then the maximum height is of:
h(3) = -16(3)² + 96(3) + 160
h(3) = 304 feet.
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Please help me to find the slope
Answer:
Step-by-step explanation:
the formula for the slope is y2 - y1 / x2 - x1
so 1 - 0 / -3 --3/7
on the calculator
- 7 / 18
The number of rats living in an abandoned building increases each year. The total number of rats can be described by this sequence: 2, 6, 18, 54, 162, ...
What is the explicit formula?
What is the recursive formula?
Please help with the recursive formula the most if you can!
Answer: The explicit formula for this sequence is given by the expression a_n = 3^n, where n is the position in the sequence (starting from n=1 for the first term).
The recursive formula for this sequence is given by the expression a_n = 3a_(n-1), where n is the position in the sequence (starting from n=1 for the first term) and a_(n-1) is the previous term in the sequence.
Here's how you can use the recursive formula to find the terms of the sequence:
a_1 = 2
a_2 = 3a_1 = 3 * 2 = 6
a_3 = 3a_2 = 3 * 6 = 18
a_4 = 3a_3 = 3 * 18 = 54
a_5 = 3a_4 = 3 * 54 = 162
and so on.
To find the explicit formula, you can try to find a pattern in the terms of the sequence. For example, you might notice that each term is simply the previous term multiplied by 3. This pattern can be expressed using the recursive formula a_n = 3a_(n-1). To find the explicit formula, you can then solve for a_n in terms of n:
a_n = 3a_(n-1)
a_n / 3 = a_(n-1)
a_n / 3 = (3a_(n-2)) / 3
a_n / 3 = 3^(n-2)
a_n = 3^n
Therefore, the explicit formula for this sequence is a_n = 3^n.
Step-by-step explanation:
Solve the simultaneous equations
xy=-16
y=x+8
Answer:
x = 4, y = 12
Step-by-step explanation:
xy = -16
y = x + 8
substitute y = x + 8 into xy = -16
x(x + 8) = -16
x^2 +8x + 16 = 0
x = 4
sub x = 4 into y = x + 8
y = 4 + 8
y = 12
A solid right prism $ABCDEF$ has a height of $16,$ as shown. Also, its bases are equilateral triangles with side length $12.$ Points $X,$ $Y,$ and $Z$ are the midpoints of edges $AC,$ $BC,$ and $DC,$ respectively. A part of the prism above is sliced off with a straight cut through points $X,$ $Y,$ and $Z.$ Determine the surface area of solid $CXYZ,$ the part that was sliced off.
A solid right prism ABCDEF has a height of 16. A part of the prism is sliced off with a straight cut through points X, Y, and Z. CXYZ is a triangular pyramid and its surface area is 48 + 9√3 + 3√91 or 92.2
The situation can be depicted in the attached picture. CXYZ is a triangular pyramid.
The surface area of CXYZ is equal to:
area CXYZ = area ΔCXY + area ΔCYZ + area ΔCXZ + area ΔXYZ
ΔABC and ΔCXY are congruent, hence ΔCXY is a equilateral triangles with its sides are 1/2 those of ΔABC.
CX = CY = XY = 1/2 x 12 = 6
To find the area of ΔCXY, find its height first.
√3/2 = h/6
h = 3√3
Area ΔCXY = 1/2 x 3√3 x 6 = 9√3
ΔCXZ is a right triangle at C. Hence,
Area ΔCXZ = 1/2 x CX x CZ
= 1/2 x 6 x 8 = 24
ΔCYZ = ΔCXZ
Hence,
Area ΔCYZ = 24
To find the area of ΔXYZ, find XZ first using the Pythagorean Theorem.
XZ² = CX² + XZ² (XZ = 8, since Z is midpoint of CD)
XZ² = 6² + 8²
XZ² = 10²
XZ = 10
Find the height of ΔXYZ
h = √(10² - 3² )
h = √91
Therefore,
Area ΔXYZ = 1/2 x XY x h
= 1/2 x 6 x √91 =3√91
Finally,
area CXYZ = area ΔCXY + area ΔCYZ + area ΔCXZ + area ΔXYZ
= 9√3 + 24 + 24 + 3√91
= 48 + 9√3 + 3√91
= 92.2
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In 1960 the population of Indoneia wa 88 million in 2010 the population of Indoneia wa 240 million etimate the population in 2016 if the rate of if the rate of increae doe not change
1.75% is rate of increse does not change.
What's the math rate?
An unusual ratio in which the two parts are expressed in distinct units is called a rate. The price is 69 for 12 ounces, for instance, if a 12-ounce can of maize costs that much.
This is not a proportion of two comparable units, like shirts. This ratio combines the values of the two dissimilar units, cents and ounces.
1960 = 88,000,000
2010 = 242,000,000
formula: (new-old)/old* 100
(242,000,000 - 88,000,000)/88,000,000 * 100
154,000,000/88,000,000*100
1.75*100
= 1.75%
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Finding the zeros of each function of factoring: g(x)=2x^2 +x-10
Answer:
The zeros are -2.5 and 2.
Step-by-step explanation:
2x^2 +x-10 = 0
2x^2 - 4x + 5x - 10 = 0
2x(x - 2) + 5(x - 2) = 0
(2x + 5)(x - 2) = 0
2x + 5 = 0 gives x = -2.5.
x - 2 = 0 gives x = 2.