Answer:
Large number: 20
Small number: 12
Step-by-step explanation:
Hello!
This problem is a word problem, and if we assign variables to find each of the numbers, it could help.
A variable is usually an unknown number that stands for that unknown.
Since in this problem we know there is a small and large number, let's assign the large number as the variable x and small number as variable y.
For the first part, it says two numbers whose difference is 8, which means the large number minus the smaller number equals 8.
x-y=8
For the second part is tricky. It's saying that the small number times three is 16 more than the large number itself. When constructing a equation, this is what we get:
x+16=3y x plus 16 equals 3 times y
To solve this equation together so we can make it super easy, let's do the method of substitution, which is where we make an equation equal to a variable and input that equation into the second equation.
We can use x-y=8 to input, we can rearrange y and plug it to the right side to get x=8+y
Since x equals 8+y, let's input this into the second equation.
(8+y)+16=3y input the rearranged equation into the second
24+y=3y combine like terms
-y -y
24=2y divide by two to get y by itself
12=y
We aren't done yet! We have to find x still; let's use the previous first equation to find x. We know y=12, so let's plug it in.
x-y=8 original formula
x-12=8 plug it in
+12 +12
x=20
Therefore, the large number is 20, and smaller number is 12.
Answer:
12 and 20
Step-by-step explanation:
small=x
big= (x+8)
(x+8) = 3x -16
24 = 2x
x=12 (small)
12+8 = 20(big)
Concert tickets cost $70 each. A college student ordered some tickets online. There
was a service fee of $3.50 per ticket. The student has $367.50. How many tickets
did can he order?
Answer:
The college student can get 5 concert tickets
Step-by-step explanation:
$367.50÷(70+$3.50)
what's the área of this triangle?
Answer:
192 SQUARE FEET
Step-by-step explanation:
Area of a triangle= 1/2 ×base×height
1/2 of the base =32/2 ft
=16 ft
Let the height be A ft and another side(16 ft) be B ft
We know that, A^2 + B^2 =Hypotenuse^2
OR, A^2 + 16^2 = 20^2
OR, A^2= 400-256
OR, A^2 =144
OR, A= Square root of 144
OR, A=12 ft
By the problem,
1/2 ×Base×Height =Area of half of the triangle
1/2 ×16×12= Area of half of the triangle
96=Area of half of the triangle
AREA OF THE TRIANGLE=96 ×2
AREA OF THE TRIANGLE=192 SQUARE FEET.
HOPE IT HELPS
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Solve the linear inequality. Other than ∅, graph the solution set on a number line.
Find the solution set in interval notation.
12x-8≤6x-15
The solution for the linear inequality, in interval notation, is [tex]\:(-\infty \:,\:-\frac{7}{6}][/tex].
InequalityIt is an expression mathematical that represents a non-equal relationship between a number or another algebraic expression. Therefore, it is common the use of follow symbols: ≤ (less than or equal to), ≥ (greater than or equal to), < (less than) and > (greater than).
The solutions for inequalities can be given by: graph in a number line or numbers.
For solving this exercise, it is necessary to find a number solution for the given inequality.
12x-8≤6x-15
12x-6x≤ -15+8
6x≤-7
x≤ -7/6
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–5.4(–0.7 + u) =
What is the answer?
Answer:
u = 7\/10
Step-by-step explanation:
What does AB congruent symbol CD mean? AB and CD here have lines over them How is it different than AB=CD?
Answer:
Suppose that we have two line segments, AB and CD. We know that they have the same length.
I know that AB¯¯¯¯¯¯¯¯=CD¯¯¯¯¯¯¯¯ means AB is identical to CD (aka. They are the same lines), and also that AB¯¯¯¯¯¯¯¯≅CD¯¯¯¯¯¯¯¯ means that AB and CD have the same size, but what does AB=CD mean?
Step-by-step explanation:
consider the graph
6
4
2
What is the midline? urte as an equation)
What is the period of the function?
What is the amplitude of the function?
What is the equation of the function? f(x)=
Help please
Answer:
[tex]\displaystyle \boxed{y = -3} \\ \boxed{\pi} \\ \boxed{N/A} \\ f(x) = \boxed{-2cot\:(x + \frac{\pi}{2}) - 3}[/tex]
Step-by-step explanation:
[tex]\displaystyle f(x) = Acot(Bx - C) + D \\ \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \\ Amplitude \hookrightarrow |A| \\ \\ \\ Vertical\:Shift \hookrightarrow -3 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{2}} \hookrightarrow \frac{-\frac{\pi}{2}}{1} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{2} \\ Amplitude \hookrightarrow N/A[/tex]
OR
[tex]\displaystyle f(x) = \boxed{2tan\:x - 3} \\ \\ f(x) = Atan(Bx - C) + D \\ \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \\ Amplitude \hookrightarrow |A| \\ \\ \\ Vertical\:Shift \hookrightarrow -3 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{2} \\ Amplitude \hookrightarrow N/A[/tex]
Here is all the information you will need. Now, what you need to know is that ALL tangent, secant, cosecant, and cotangent functions have NO amplitudes. Also, keep in mind that although this IS a tangent graph, if you plan on writing your equation as a function of cotangent, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle f(x) = 2cot\:x - 3,[/tex]in which you need to replase "tangent" with "cotangent", then figure the appropriate C-term out that will make the graph horisontally shift and map onto the tangent graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two graphs, we can tell that the cotangent graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{2}\:unit[/tex]to the right, which means that in order to match the tangent graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{2}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{2}} = \frac{-\frac{\pi}{2}}{1},[/tex]but we are NOT YET DONE. Although we shifted the graph back into position, remember, cotangent is graphed in REVERCE, so we need to insert a negative in front of the amplitude term, and with that, the cotangent graph of the tangent graph, accourding to the horisontal shift, is [tex]\displaystyle f(x) = -2cot\:(x + \frac{\pi}{2}) - 3.[/tex]Now, with all that being said, we can move forward. To find the period in this case, you need to take a look at the distanse between each vertical asymptote. Now, accourding to this graph, the vertical asymptotes are at [tex]\displaystyle -\frac{\pi}{2} = x\:and\:\frac{\pi}{2} = x.[/tex]From here, you will then find the distanse between these asymptotes by simply perfourming the operation of Deduction, and doing that will give you [tex]\displaystyle \boxed{\pi} = \frac{\pi}{2} + \frac{\pi}{2}.[/tex]So, the period of this function is [tex]\displaystyle \pi.[/tex]Now, you will instantly get the jist of the horisontal shift by looking at the above formula. Just keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must pay cloce attention to what is given to you inside those parentheses. Finally, the midline is the centre of your graph, also known as the vertical shift, which in this case is at [tex]\displaystyle y = -3.[/tex]
Well, that just about wraps it up. Now that everything has been explained, you should understand it better. If you still have questions, do not hesitate to comment any you have.
I am delighted to assist you at any time.
Which set of coordinate pairs do NOT represent a linear function?
(-4, -12), (-3,-10), (-2, -8), (-1,-6)
O (-4, -17), (-3, -10), (-2,5), (-1,2)
O (1, -7), (2, -10), (3, -13), (4, -16)
O (1, 1), (2, 4), (3, 7), (4, 10)
Answer:
(-4, -17), (-3, -10), (-2,5), (-1,2)
Step-by-step explanation:
All the coordinates are represent linear function.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The coordinates are,
⇒ (-4, -12), (-3,-10), (-2, -8), (-1,-6)
⇒ (-4, -17), (-3, -10), (-2,5), (-1,2)
⇒ (1, -7), (2, -10), (3, -13), (4, -16)
⇒ (1, 1), (2, 4), (3, 7), (4, 10)
Now,
We know that;
A relation between a set of inputs having exactly one output each is called a linear function.
Clearly, All the coordinate have exactly one output for every input.
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Find the area (hint: find the value of x first)
Answer:
C. 128 in²
Step-by-step explanation:
We know that the opposite sides of rectangles are congruent, so 8 = 2x. If we divide 8 by 2 and 2x by 2, we get x = 4.
This means that the other side length, (3x + 4), equals 3(4) + 4 = 12 + 4 = 16 inchesNow, the area of a rectangle is l × w, where l = length and w = width. The dimensions of this rectangle are 8 and 16, so 8 × 16 = 128 in².
Brainliest if correct
Answer:
22/24 or 11/12
Step-by-step explanation:
Answer:
9/12, 2/12, 11/12
Step-by-step explanation:
The lowest common denominator of 3/4 and 1/6 is 12.
3/4 * 3/3 = 9/12
1/6 * 2/2 = 2/12
Now that both of the fractions have the same denominator, we can add them.
9/12 + 2/12 = 11/12
I hope this helps! Have a lovely day! :)
Damon plotted a point on the grid. He says that the first number of the ordered pair is negative and the second number of the ordered pair is positive. Based upon this information, which of the points below could be Damon's?
A. H
B. J
C. K
D. L
Answer:
A) H you have to run before you can climb is what my teacher told me when looking at a graph so when reading the problem you have to run left for negative then climb for positive leaving the answer being a) h
*URGENT*
Find the Equation of the line that contains the point (-2,-8) and is parallel to the line 6x + 5y = 11. Write the equation in slope-intercept form.
Point :
Parallel lines have same slopes.
_________________________________
[tex]6x + 5y = 11[/tex]
Subtract sides -6x
[tex] - 6x + 6x + 5y = - 6x + 11[/tex]
[tex]5y = - 6x + 11[/tex]
Divided sides by 5
[tex] \frac{5}{5}y = \frac{ - 6}{5}x + \frac{11}{5} \\ [/tex]
[tex]y = - \frac{6}{5}x + \frac{11}{5} \\ [/tex]
Look :
This is the slope-intercept of the given line. We know that the coefficient of x is the slope of the linear functions in slope-intercept form.
Thus the slope of the line which we want is :
[tex]slope = - \frac{6}{5} \\ [/tex]
_________________________________
We have following equation to find the point-slope form of the linear functions.
[tex]y - y(given \: point) = (slope) \times (x - x(g \: p) \: ) \\ [/tex]
Now just need to put the slope and the coordinates in the above equation.
[tex]y - ( - 8) = - \frac{6}{5} \times (x - ( - 2) \: ) \\ [/tex]
[tex]y + 8 = - \frac{6}{5}(x + 2) \\ [/tex]
To find the slope-intercept form of the above equation we need to take the y alone and then simplifies the equation.
Look :
[tex]y + 8 = - \frac{6}{5}x - \frac{12}{5} \\ [/tex]
Subtract sides by -8
[tex]y + 8 - 8 = - \frac{6}{5}x - \frac{12}{5} - 8 \\ [/tex]
[tex]y = - \frac{6}{5}x - \frac{12}{5} - \frac{40}{5} \\ [/tex]
[tex]y = - \frac{6}{5}x - \frac{52}{5} \\ [/tex]
This is what we want...
_________________________________
Now we must Check the equation by using the given point :
[tex]( - 8) = - \frac{6}{5}( - 2) - \frac{52}{5} \\ [/tex]
[tex] - 8 = \frac{12}{5} - \frac{52}{5} \\ [/tex]
[tex] - 8 = \frac{ - 52 + 12}{5} \\ [/tex]
[tex] - 8 = \frac{ - 40}{5} \\ [/tex]
[tex] - 8 = - 8[/tex]
So the equation is right.
_________________________________
And we're done.♥️♥️♥️♥️♥️
How many solutions does the equation: 4x+2=12x+6 have?
Use the Pythagorean Theorem to find the whole number estimate of the unknown side of the right triangle shown below.
A:3
B 10
C 9
D 4
Answer:
Option C.Step-by-step explanation:
This is Right Angled Triangle.So,
We'll solve this using the Pythagorean Theorem.
Let
6cm be BC, where BC is the perpendicular.7cm be AB, where AB is the Base. AC be the Hypotenuse.We know that,
[tex]{ \longrightarrow \bf \qquad (AC) {}^{2} = (AB) {}^{2} +( BC) {}^{2} }[/tex]
[tex]{ \longrightarrow \sf \qquad (AC) {}^{2} = (7) {}^{2} +( 6) {}^{2} }[/tex]
[tex]{ \longrightarrow \sf \qquad (AC) {}^{2} = 49 +36 }[/tex]
[tex]{ \longrightarrow \sf \qquad (AC) {}^{2} = 85 }[/tex]
[tex]{ \longrightarrow \sf \qquad AC = \sqrt{85} }[/tex]
[tex]{ \longrightarrow \sf \qquad AC \approx 9.21 }[/tex]
⠀
Therefore,
The length of the unknown side is 9 cm. (Estimated)What is the value of x in the figure?
Enter your answer in the box.
x=
A little square marked on angle means that the angle is 90 degrees.
By the vertical angle theorem, angles opposite each other are equal thus the angle opposite the angle with the little square is also 90 degrees.
That angle is split into two angles that is off measure 22 degrees and x degrees
-- x + 22 = 90 --> x = 68.
Hope that helps!
Answer:
68
Step-by-step explanation:
[tex] \hookrightarrow \: x + 22 = 90(complementary \: angles) \\ [/tex]
[tex] \hookrightarrow \: x + 22 = 90 \\ \hookrightarrow \: x = 90 - 22 \\ \hookrightarrow \: x = 68[/tex]
(a-b+c)-(c+b)
I literally tried so many times i dont get it
Answer:
a - 2b
Step-by-step explanation:
❖ Step 1: Distributive negative sign.
[tex](a-b+c)+(-1)(c)+(-1)(b)[/tex] [tex]a-b+c-c-b[/tex]❖ Step 2: Combine like terms.
[tex](a)+(-b-b)+(c-c)[/tex] [tex]a-2b[/tex]Therefore, the answer is a - 2b.
Have a lovely rest of your day/night, and good luck with your assignments! ♡
Answer:
a-2b
Step-by-step explanation:
(a-b+c)-(c+b)
Distribute the minus sign to the terms in the second parenthesis
a-b+c-c-b
Combine like terms
a-b+c-c-b
a-b-b+c-c
Cancel like terms
a-2b
Which statement correctly describes the expression (-60)(-5)?
A. One factor is positive and one factor is negative, so the product
will be positive.
B. Both factors are negative, so the product will be positive.
C. One factor is positive and one factor is negative, so the product
will be negative.
D. Both factors are negative, so the product will be negative.
Answer:
If you're multiplying then the answer would be B.
Step-by-step explanation:
If you multiply two negative numbers, your product would be positive.
If you multiply 1 positive and 1 negative then your product will be negative.
What is the probability of getting a 7 of spades in a deck of 52 cards?
Answer:
I'm sure it's 1/52
Step-by-step explanation:
because if there is 52 cards and one 7 of spades then it would be a 1 out of 52 chance
Find the value g(-2), where g is defined below.
g(x) = 2x^2- 4x – 4
Answer:
12
Step-by-step explanation:
For this question, simply plug in -2 for x:
[tex]g(-2)=2(-2)^2-4(-2)-4\\g(-2)=2(4)+8-4\\g(-2)=8+8-4\\g(-2)=12[/tex]
Hope this helps!!
helpoppppollpppppppppppppppppppppp
Answer:
Given:
1 mile = 1.6 km
So, to find how many miles are in 100 km, we need to divide 100km by 1.6km because one single mile contains 1.6km.
100km/1.6km = 62.5 miles
if CP of an item is Rs 7000, If SP of item is Rs 9100 Find the profit percentage.
Step-by-step explanation:
please mark me as brainlest
plss help me plss #2
Answer:
8
Step-by-step explanation:
2 ÷ 1/4 = 8
You can draw 2 squares and make them into quarters for your diagram. Hope this helped!
Answer: There are 8 1/4 inches in 2 inches.
Step-by-step explanation:
1/4 x 4 = 1, so 1/4 x 8 = 2
Diagram can be made to look as splitting 2 inches into 8 parts.
This figure represents a platform in an auditorium. The crew needs to paint it green. One gallon of paint will cover 40 square yards. How many full gallons of paint does the crew need to buy in order to paint the entire platform? Enter your answer in the box. gallons Complex solid composed of rectangular prisms in an L shape. The bottom face is labeled with a length of 7 yd and a width of 3 yd. The height of the shorter side of the L shape is labeled 2 yd. The height between the shorter side and taller side of the L shape is labeled 4 yd. The width of the taller section of the L shape is labeled 2 yd.
Step-by-step explanation:
1 yd = 3 ft
1 yd² = 2ft²
1 gallon covers: 15 · 9 = 135 ft²
955 : 135 ≈ 7.074 gal
7.1 gallons
# Jerry Don is here#
The quantity of paint required to paint the platform is 3 gallons.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. Here we have three shapes a triangle, a rectangle and a parallelogram.
Given that the attached figure represents a platform in an auditorium. The crew needs to paint it green. One gallon of paint will cover 40 square yards. One gallon of paint will cover 40 square yards.
The area of the platform is,
Area = (3x2) + 2 ( 7x 2 ) + ( 4 x 2 )2 + 3(6) + ( 5 x 3 ) + ( 4 x 3 ) + ( 2 x 3 ) + ( 7 x 3 )
Area = 6 + 28 + 16 + 18 + 15 + 12 + 6 + 21
Area = 122 square yards.
The quantity of paint required will be calculated as,
Q = 122 / 40
Q = 3 gallons
Therefore, the quantity of paint is 3 gallons.
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Find the volume of a rectangular prism with a base of area B=x^2+5x+4 in^2 and a height of h=x+3 in.
I will give Brainliest.
Please help
The volume of the rectangular prism is the amount of space in the prism
The volume of the rectangular prism is x^3+8x^2+19x+12 cubic inches
How to determine the volume?The given parameters are:
Base area = x^2+5x+4
Height = x + 3
The volume is then calculated as:
Volume = Base area * Height
So, we have:
Volume = (x^2+5x+4) * (x + 3)
Expand
Volume = x^3+5x^2+4x + 3x^2+15x+12
Collect like terms
Volume = x^3+5x^2+ 3x^2+4x +15x+12
Evaluate the sum
Volume = x^3+8x^2+19x+12
Hence, the volume of the rectangular prism is x^3+8x^2+19x+12 cubic inches
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pls i need help ASAP PLS
g(x)=8x. then g(x) isSingle choice.
Answer:
X=0
Step-by-step explanation:
Swap the side of the equation
8x=0 then divide both sides by eight
x=0
Angle MNP ~ Angle HJK.
Both triangles are isosceles. if m
Answer:
Angles H, J, M, N
Step-by-step explanation:
Since m<p is 90 degrees it must be the largest angle so both triangles have angle 45-45-90. m<P is equal to m<K. This means that angle h, j, m, and n are equal.
angles M, N, and J.
try drawing diagrams to help you figure out the problem :)
Write the ratio 4/5 over 7/5 in its simplest form! Need Answer ASAP
Answer:
[tex]\frac{4}7[/tex]
Step-by-step explanation:
Just as a reminder, to find the ratio of 2 numbers, you divide the first by the second, and to divide 2 fractions, you multiply the dividend by the reciprocal of the divisor.
In this case, that would be:
[tex]\frac{\frac{4}{5}}{\frac{7}{5}}[/tex]
[tex]= \frac{4}{5} \cdot\frac{5}{7}[/tex]
=[tex]\frac{4}7[/tex]
I hope this helped you.
*Suppose you drop a tennis ball from a height of 15 feet. After the ball hits the floor, it rebounds to 12 feet, then hits the floor and rebounds to 9.6 feet.
Write an explicit formula for the sequence.
Also, How high will the ball rebound after its fourth bounce?
Answer:
The explicit formula is [tex]a_n=15(\frac{4}{5})^{n-1}[/tex].
Step-by-step explanation:
First, we need to find the common ratio. We know this is a geometric sequence because the decrease from one term to the next is not a constant number.
To find the constant ratio, we can take the [tex]2^{nd}[/tex] term and divide by the [tex]1^{st}[/tex] term:
[tex]\frac{2nd}{1st}=\frac{12}{15}=\frac{4}{5}[/tex]
So, our common ratio is [tex]r=\frac{4}{5}[/tex].
We already know our initial term, [tex]a_0[/tex] is 15, so we get:
[tex]a_n=a_0(r)^{n-1}\\a_n=15(\frac{4}{5})^{n-1}[/tex]
Find the value of:
a) 8
9
×
−3
4
Step-by-step explanation:
89 multiplied by negative 34 gives a negative answer, since positive multiplied by negative is negative hence,
(89) × (-34) = -3026
Jack wants to buy carpet to cover his whole living room, except for the tiled floor. The tiled floor is 5
3
4
Mixed number
ft by 3
1
2
ft. Find the area the carpet needs to cover.
The area of the floor the carpet needs to cover is 20 1/8 cm².
What is the area the carpet needs to cover?The floor has the shape of a rectangle. A rectangle is a 2-dimensional quadrilateral with four right angles.
Area of a rectangle = length x width
5 3/4 x 3 1/2
23/4 x 7/2 = 161/8 = 20 1/8 cm²
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Find the length of the line below.
A. 2 in.
B. 2 3/16 in.
C. 2 5/16 in.
D. 3 in.
Answer:
A)
Step-by-step explanation:
Starting point is at o and ending point at 2.
So, 2 in