Hey ! there
Answer:
First Integer is 97Second Integer is 98Step-by-step explanation:
The question says that two consecutive Integer have a sum of 195 . And we are asked to find the integers.
For finding integers we are assuming them . So ,
Let the first integer be x .Let the second integer be x + 1 ( This is because in question it's given that they are consecutive integers )Solution : -
According to question ,
First Integer + Second Integer = 195So ,
[tex] \dashrightarrow \qquad \: x + x + 1 = 195[/tex]
Step 1 : Adding like terms ( x and x ) on left side :
[tex] \dashrightarrow \qquad \: 2x + 1 = 195[/tex]
Step 2 : Subtracting 1 on both sides :
[tex] \dashrightarrow \qquad \: 2x + \cancel{1} - \cancel{1} = 195 - 1[/tex]
Simplifying it ,
[tex] \dashrightarrow \qquad \: 2x = 194[/tex]
Step 3 : Dividing with 2 on both sides :
[tex] \dashrightarrow \qquad \: \dfrac{ \cancel{2}x}{ \cancel{ 2}} = \cancel{\dfrac{194}{2} }[/tex]
On further calculations , We get :
[tex] \dashrightarrow \qquad \: \purple{\underline{\boxed{\frak{ x = 97}}}} \quad \: \bigstar[/tex]
We know that ,
x = first number✰ Therefore , first number is 97 .
x + 1 = second number97 + 1 98✰ Therefore , second number is 98.
Verifying : -
Now , we are verifying our answer by substituting value of first and second number and equating it with 195 . So ,
97 + 98 = 195195 = 195L.H.S = R.H.SHence , Verified .Therefore , our solution is correct .
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[tex]\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]
Two consecutive integers have a sum of 195. Find the integers
[tex]\blue{\textsf{\textbf{\underline{\underline{Answer:-}}}}[/tex]
The integers are 97 and 98.
[tex]\blue{\textsf{\textbf{\underline{\underline{How to Solve:-}}}}[/tex]
If integers are [tex]\textbf{consecutive,}[/tex] they stand right next to each other.
Example:- 7 and 8. 7 and 8 are consecutive integers because they stand right next to each other.
Now, let the integer be n.
The integer next to n is 1 greater than n, or n+1.
So we set up the following equation:-
[tex]\bigstar{\fbox{n+n+1=195}[/tex]
[tex]\textsf{\underline}}[/tex]Add the n's:-
[tex]\Longrightarrow[/tex] [tex]\sf{2n+1=195}[/tex]
Subtract 1 on both sides:
[tex]\sf{2n=195-1}[/tex]
[tex]\sf{2n=194}[/tex]
Divide by 2 on both sides:-
[tex]\bigstar{\fbox{n=97}[/tex]
Now that we've found the first integer, finding the second integer is easy, because we can subtract the first integer from the sum of both integers:-
195-97=98
So the second integer is 98.
Quick Check:-
97 and 98 are consecutiveThey add up to 195:-97+98=195[tex]\textbf{195=195}[/tex]Since the LHS (left-hand side) equals the RHS (right-hand side), the integers are indeed 97 and 98.Good luck.
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which equation represents a linear function 2ry+y= 9 , y=12r-5 , 3y+r2+t=0, 4r+2(y-1)=0
The equation which represents a linear function for the variable y is y=12r-5. Option B is the correct option.
What is linear function?Linear function is the function in which the highest power of the unknown variable is one. Linear functions are used to model the real life problem in the mathematical expressions.
The linear function with dependent variable y and independent variable x can be written as,
y=mx+c
Here, m is the slope of the line represented by the function and c is the y intercept.
The equation given in the problem are,
2ry+y= 9
y=12r-5
3y+r2+t=0
4r+2(y-1)=0
The second option is similar to the standard linear function.
Hence, the equation which represents a linear function for the variable y is y=12r-5. Option B is the correct option.
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Lamar pays 15.60 for a pack of 6 towels. Find the unit price in dollars per towel. If necessary, round your answer to the nearest cent.
Divide total price by quantity:
15.60 / 6 = 2.60
Unit price = $2.60
Find the value of x in the figure.
Line segment st is dilated to create line segment s't' using the dilation rule dq,2.25. point q is the center of dilation. line segment s t is dilated to create line segment s prime t prime. the length of q t is 1.2 and the length of q s is 2. the length of s s prime is x and the length of t t prime is 1.5. what is x, the distance between points s' and s? x = 2.25 units x = 2.5 units x = 4.25 units x = 4.5 units
The value of x when the line segment st is dilated to create line s't' about point q is 2.5 units
How to determine the value of x?The given parameters are:
qs = 2
qt = 1.2
tt' = 1.5
ss' = x
To calculate the value of x, we make use of the following equivalent ratio
ss' : qs = tt' : qt
So, we have:
x : 2 = 1.5 : 1.2
Express as fractions
x/2 = 1.5/1.2
Multiply both sides by 2
x = 2 * 1.5/1.2
Evaluate the product
x = 2.5
Hence, the value of x is 2.5 units
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Answer:
2.5
Step-by-step explanation:
Find the distance between the two points on the graph
Answer: The side highlighted is 6.3 units long
Step-by-step explanation:
You can use Pythagorean therum to solve this problem
a² + b² = c²
We already know the length of two of the sides, a and b. So we will replace those variables with the given values
2² + 6² = c²
And now we solve
2² + 6² = c²
4 + 36 = c²
c² = 40
√40 = 6.3
someone pls help with this
Answer: B
Step-by-step explanation:
Substituting in the coordinates into the lines which they lie on,
[tex]r=p+b\\\\5r=4p+b[/tex]
Subtracting the equations,
[tex]-4r=-3p \implies \frac{r}{p}=\frac{3}{4}[/tex]
8x-3y times 5x5y over 10x6y2
Answer:
8x-5/4
Step-by-step explanation:
Cancel 5y x 5y/10 x 6y²=5/12y
8x-3y 5/12y
apply fraction rule a× b/c = a×b
____
c
8x-3y⁵/12y
8x-3y×5/12y
8x-3×5/12y
8x-3×5/12
=8x-5/4
Ayúdenme en esto porfavor
Answer:
The distance from point A(x, 1) to point B(0, 7) is equal to 10. Calculate the value of the abscissa x.
Para resolver un problema como este lo primero que tenemos que hacer es sacar regla de tres:
----- 48
----- [tex]\bold{\cfrac{3}{4}}[/tex]
----- X
Una vez sacado la regla de tres debemos Saber los datos que son los siguientes
[tex] \underline{\bold{Ahora \: \: Planteamos \: \: la \: \: ecuacion \: : } }[/tex]
En este caso debemos hallar el 3/4% de 48.
Ahora Usamos la regla de tres simple.
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \Rightarrow\bold{\cfrac{3}{4} * 48 }[/tex]
Comenzamos a Resolver :[tex] \: \: \: \: \: \: \: \: \: \bold{\cfrac{3}{4} * 48 = \cfrac{ \cfrac{3}{4} }{100} * 48 }[/tex]
[tex] \bold{\cfrac{3}{400} \: * 48 = \cfrac{3}{25}* 3 = \cfrac{9}{25} }[/tex]
Ahora Hallamos el decimal de 9/25
[tex] \: \: \: \: \: \bold{\cfrac{9}{25} = 9 \div 25 = 0.36 }[/tex]
Entonces podemos decir que:
En total a Susana le faltan 0.36km para llegar a casa.
what is x in 2x − 3 + 4x = 21
Answer: x = 4
Step-by-step explanation:
2x - 3 + 4x = 21
6x - 3 = 21
6x - 3 (+3) = 21 (+3)
6x = 24
24/6
x = 4
Find the equation of the straight line with the gradient -2/3 and passing through the point(1,1)
Answer:
y = -2/3 x + 5/3
Step-by-step explanation:
y = mx + b
y = -2/3 x + b
1 = -2/3 × 1 + b
3/3 + 2/3 = b
b = 5/3
y = -2/3 x + 5/3
Gary and Jessica exercise for a total of 18 hours per week. Jessica exercises 2 less than 3 times the hours that Gary exercises. How many hours per week does Gary exercise?
Enter your answer in the box.
Work Shown:
g = number of hours that Gary exercises
3g-2 = number of hours that Jessica exercises
(g) + (3g-2) = 18
4g-2 = 18
4g = 18+2
4g = 20
g = 20/4
g = 5
Gary exercises 5 hours per week.
help me with this math problem, please
Answer:
Refer the attachment
SO, OPTION (D) IS CORRECT
Answer:
Option (D) is the correct answer
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When you perform a rigid transformation on a figure, the figure's ________ change(s).
A
shape
B
side measurements
C
angle measurements
D
position on the coordinate plane
Answer: D
Step-by-step explanation:
This is just definition.
need help will give brainliest i am timed answer in 20 minutes
What is the y-value of the vertex of the function f(x)=−(x+8)(x−14)?
3
6
112
121
The function f(x) = –3x2 + 36x – 119 written in vertex form is f(x) = –3(x – 6)2 – 11. Which statements are true about the graph of f(x)? Select three options.
The axis of symmetry is the line x = 6.
The vertex of the graph is at (–6, –11).
The parabola has a minimum.
The parabola opens down.
The value of h, when the equation is written in vertex form, is positive.
Answer:
121
.
The axis of symmetry is the line x= 6
The parabola opens downwards.
The value of h when the equation is in vertex form is positive.
Step-by-step explanation:
In the pictures.
Hope it helps! :)
Is the mean most useful when there is an outlier?
Answer:
The median is more useful because the mean, which his the average can be affected by a large or small outlier.
Step-by-step explanation:
A perfect triangle is a triangle with two key characteristics: 1) all three side lengths are positive integers, and 2) the area of the triangle area is equal to its perimeter. is a triangle with sides of length 8, 9, and 16 a perfect triangle? set up expressions and show the work needed to solve in order to answer the question.
Answer: It is not a perfect triangle.
Step-by-step explanation:
3^5*2^-6 please answer fast
[tex]3^5 \cdot 2^{-6}=\dfrac{3^5}{2^6}=\dfrac{243}{64}[/tex]
What is the value of x
A)8
B)6
C)1
D)7
Answer:
D) 7
Step-by-step explanation:
Tangents from the same external point are equal in length.
8x - 7 = 6x + 7Add 7 on both sides.
8x - 7 + 7 = 6x + 7 + 78x = 6x + 14Subtract 6x from both sides.
8x - 6x = 6x + 14 - 6x2x = 14x = 7The correct option is D.
answer as soon as u can i need this
Answer:
25.12 cm.
Step-by-step explanation:
you take pie times the diameter (4)cm and times them together.
Answer:
4π cm
Step-by-step explanation:
Circumference of circled = 4 cm
Circumference = πd
= π*4
= 4π cm
An elevator starts at floor 9. It goes up 10 floors twice, and then it goes down 18 floors. A second elevator
starts on floor 28. It goes down 5 floors 2 times, and then it goes up 11 floors. Which elevator ends on a
higher floor?
Answer:
Higher floor- Elevator 2 ends on a higher floor
Elevator 1- ends on floor 11
Elevator 2- ends on floor 29
Step-by-step explanation:
What is the quotient of startfraction 7 superscript negative 1 baseline over 7 superscript negative 2 baseline endfraction?
The expression 7⁻¹ ÷ 7⁻² is a quotient expression, and the value of the quotient 7⁻¹ ÷ 7⁻² is 7
How to evaluate the exponents?The expression is given as:
7⁻¹ ÷ 7⁻²
Rewrite the expression using the product sign
7⁻¹ ÷ 7⁻² = 7⁻¹ * 7²
Apply the product rule of indices
7⁻¹ ÷ 7⁻² = 7⁻¹⁺²
Evaluate the sum of the exponents
7⁻¹ ÷ 7⁻² = 7¹
Evaluate the exponent
7⁻¹ ÷ 7⁻² = 7
Hence, the value of the quotient 7⁻¹ ÷ 7⁻² is 7
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Answer:
7
Step-by-step explanation:
Edge
Does anybody know this? I think know the second one but I'm not sure. ABCD is a square find the following.
Answer:
see explanation
Step-by-step explanation:
in a square
• all sides are congruent
• all angles are right
• diagonals bisect the angles
• diagonals are perpendicular bisectors of each other
Then
∠ BCA = [tex]\frac{1}{2}[/tex] × ∠ BCD = [tex]\frac{1}{2}[/tex] × 90° = 45°
∠ AWD = 90°
Solve the inequality 3(y-4)<6
The answer is y<6
Add 12 to both sides
Simplify
Divide both sides by the same factor
Simplify
Find the value of x that makes m ∥ n
Answer:
26
Step-by-step explanation:
When two lines are parallel, corresponding angles are equal.
Here,
m II n
5x + 13 and 143 are corresponding angles.
So,
5x + 13 = 143
Substract 13 on both sides,
5x = 143 - 13
5x = 130
Divide 5 on both sides,
x = 130 / 5
x = 26
An item is regularly priced at $35. It is now priced at a discount of 40% off the regular price. What is the price now?
Answer:
15
Step-by-step explanation:
Picasso's Phone Shop charges $65.54 for its activation fee plus $13.10 for every gigabyte, g, of data you use over your limit. The equation that
models the total cost (T) is T (g) = 13.10g +65.54 Which value in the equation represents the rate of change?
A
$65.54
B
$78.63
$13.10
the number of gigabytes used over
I don't know yet
4
04.02.05.1289
D
E
Com
5. SE
Answer:
$13.10 represents the rate of change
Step-by-step explanation:
13.1 is the only value in the equation with a variable (g). There is an additional $13.10 charge for every gigabyte used over the limit, and this is the rate of change.
For example, if 5 gigabytes were used over the limit, the charge would be 13.1(5) or $65.50
Historically, a given day at the beginning of March in upstate New York has a 18% chance of snow and a 12% chance of rain. If there is a 4% chance it will rain and snow on a day, then which of the following
represents the probability that a day in early March would have either rain or snow?
1.) .30
2.) .34
3.) .02
4.) .26
The Venn probability that a a day in early March would have either rain or snow is given by:
4.) .26
What is a Venn probability?In a Venn probability, two non-independent events are related with each other, as are their probabilities.
The "or probability" is given by:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
In this problem, we have that the probabilities are given as follows:
[tex]P(A) = 0.18, P(B) = 0.12, P(A \cap B) = 0.04[/tex]
Hence:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
[tex]P(A \cup B) = 0.18 + 0.12 - 0.04[/tex]
[tex]P(A \cup B) = 0.26[/tex]
Which means that option 4 is correct.
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welp pls.i’m so confused
Let's see
Area=Length×Breadth(2x+1)(x-7)=172x(x-7)+1(x-7)=172x²-14x+x-7=172x²-13x-24=0On solving
x=8So
length
2(8)+1=17Width
8-7=1A rectangle has a length of (2x+1) units, a width of (x-7) units and an Area of 17 square units. Find the dimensions of the rectangle.
✭ Explanation -:In this question we are provided with the length of a rectangle (2x + 1) units and the width of the rectangle (x - 7). It is also given that the area is 17 units². We are asked to calculate the length and width of the rectangle.
First we will find the value of x
We know,
[tex] \bull \: \small\boxed{ \rm{ Area_{(rectangle)} = Length × Width}}[/tex]
Substituting the values we get
[tex] \small\sf{ (2x + 1 ) (x - 7) = 17}[/tex]
[tex] \small\rm{ 2x( x - 7) + 1(x - 7) = 17}[/tex]
[tex] \small\rm{ 2 {x}^{2} - 14x + 1(x - 7) = 17}[/tex]
[tex] \small\rm{ 2 {x}^{2} - 13x - 7 = 17}[/tex]
[tex] \small\rm{2 {x}^{2} - 13x - 7 - 17 = 0 } [/tex]
[tex] \small\rm{2 {x}^{2} - 13x - 24 = 0} [/tex]
[tex] \small\rm{x = \dfrac{13 + 19}{2 \times 2} } [/tex]
[tex] \small\rm{ x = \dfrac{32}{4} = 8}[/tex]
[tex] \small\sf{x = 8} [/tex]
Now we will substitute the value of x
Length = (2x + 1) = 2 × 8 + 1 = 16 + 1 = 17 units
Width = (x - 7) = 8 - 7 = 1 units
Hence, the length of the rectangle is 17 units and the width is 1 units.2
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A line passes through the point (-2, 7) and has a slope of -5.
What is the value of a if the point (a,2) is also on the line?
Answer:
a is equal to 3 ...................
determine whether each pair of polygons is similar. Explain.
Answer:
they are similar because polygons have three or more sides