Answers:
Sarah has $12.50Sam has $27.50Casey has $55======================================================
Explanation:
x = amount of money Sarah has
x+15 = amount of money Sam has, since he has $15 more than her
2(x+15) = amount of money Casey has, since he has twice as much as Sam.
Let's add up those three expressions and set that sum equal to 95
Solve for x.
Sarah + Sam + Casey = 95
x+(x+15) + 2(x+15) = 95
x + x + 15 + 2x + 30 = 95
4x+45 = 95
4x = 95-45
4x = 50
x = 50/4
x = 12.50
This says that Sarah has $12.50
That must mean Sam has x+15 = 12.50+15 = 27.50 dollars
And Casey must have 2*27.50 = 55 dollars.
----------------
As a check,
Sarah+Sam+Casey = 12.50+27.50+55 = 95
So the answer is confirmed.
Answer:
Step-by-step explanation:
Let Sarah have x dollars.
Then Sam has x + 15
Casey had 2(x + 15)
x + x + 15 + 2(x + 15) = 95 Remove the brackets.
2x + 15 + 2x + 30 = 95 Collect like terms
4x + 45 = 95 Subtract 45 from both sides.
4x = 95 - 45
4x = 50 Divide by 4
x = 50/4
x = 12.5
Sarah has 12.50
Sam has 16.67 + 16 = 27.50
Casey has 55.00
Total 95
see screenshot below
Answer:
[tex] \displaystyle B) {x} = \log_{6} 118[/tex]
Step-by-step explanation:
we would like to solve the following exponential equation:
[tex] \displaystyle 2 \cdot {6}^{x} = 236[/tex]
to do so divide both sides by 2 which yields:
[tex] \displaystyle {6}^{x} = 118[/tex]
take log of base 6 in both sides so that we can solve the equation for x by using [tex]\log_ab^c=c\log_ab[/tex] and that yields:
[tex] \displaystyle \log_{6} {6}^{x} = \log_{6} 118[/tex]
use the formula:
[tex] \displaystyle {x} = \log_{6} 118[/tex]
hence,
our answer is B)
Answer:
[tex]\boxed{\sf Option \ B }[/tex]
Step-by-step explanation:
A equation is given to us and we need to find out the value of x . The given equation is ,
[tex]\sf\dashrightarrow 2 \times 6^x = 236 [/tex]
Transpose 2 to RHS , we have ,
[tex]\sf\dashrightarrow 6^x = \dfrac{236}{2} [/tex]
Simplify ,
[tex]\sf\dashrightarrow 6^x =118 [/tex]
Use log both sides with base "6"
[tex]\sf\dashrightarrow log_6 ( 6^x) = log_6 118 [/tex]
Using the property of log ,
[tex]\sf\longmapsto \bigg\lgroup \red{\bf log_p q^r = r log_p q}\bigg\rgroup[/tex]
[tex]\sf\dashrightarrow x \ log_6 6 = log_6 118 [/tex]
Again we know that ,
[tex]\sf\longmapsto \bigg\lgroup \red{\bf log_p p= 1}\bigg\rgroup[/tex]
We have ,
[tex]\sf\dashrightarrow x \times 1 = log_6 118 [/tex]
Therefore ,
[tex]\sf\dashrightarrow\boxed{\blue{\sf x = log_6 118 }} [/tex]
Hence option B is correct .
What is Index Law 1?
please give a definition
Answer:
LAW 2: The second law of indices tells us that when dividing a number with an exponent by the same number with an exponent, we have to subtract the powers. In algebraic form, this rule is as follows . ... Example: In this example, the powers were multiplied together to give the answer which is 3 to the power of 6.
Analyze the diagram below and complete the instructions that follow.
Quadrilateral LMNO is a rectangle. Find MN.
A.
7
B.
10
C.
18
D.
27
Answer:
there is no diagram ......
Which expression is equivalent to
8x^7y^8? Assume x>0.
Answer:
2x^3y^3Sqrt2 is the expression
The sequence 3,9,15,21,27 is an arithmetic sequence. What is the common difference d of this sequence
Answer:
6
Step-by-step explanation:
We can find the common difference by subtracting one number in the sequence from the one ahead of it.
27-21=6
21-15=6
15-9=6
9-3=6
The differences between each number is 6.
Because the difference is the same between each number in the sequence, that makes 6 the common difference.
[tex]\fbox{Hii\:student!}[/tex]
__________________________________________________________
[tex]\multimap\parallel\boldsymbol{Answer.}\parallel\gets[/tex]
[tex]\textsl{the common difference is 6!}[/tex]
__________________________________________________________
[tex]\multimap\parallel\boldsymbol{Explanation.}\parallel\gets[/tex]
[tex]\textsl{here's how we find the common difference in the sequence:}[/tex]
[tex]\sf 27-21=6 \\ 21-15=6 \\ 15-9=6 \\ 9-3=6 \\the\;result\;is\;the\;common\;difference}[/tex]
[tex]\maltese\boldsymbol{\therefore,\:6\:is\;the\;common\;dif\!ference}[/tex]
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}[/tex]
[tex]\boldsymbol{-Greetings!-}[/tex]
________________________________________________________
If Q = 5+2i, E = i, and D = 5-2i, find Q.E.D
Answer:
Q.D.E=(5+2i).(5-2i).i = (25-4i²)i = 25i-4i³
Step-by-step explanation:
Helppp and explain pls and ty
ahmed is sitting on a dock watching a float plane in a harbour. At a certain time, the plane is 350 m above the water and 470 m from Ahmed. Determine the angle of elevation of the plane measured from Ahmed, to the nearest degree
Answer:
The angle of elevation of the plane measured from Ahmed is approximately 36.67°
Step-by-step explanation:
The given parameters of the float plane are;
The height of the float plane above the water, y = 350 m
The horizontal distance of the float plane from Ahmed, x = 470 m
Given that Ahmed is sitting on the dock, by the water, by trigonometric ratios, we have;
The height of the float plane, the distance of the plane from Ahmed and the line of sight forming the angle of elevation of the plane measured from Ahmed, form a right triangle
[tex]tan\angle X = \dfrac{Opposite \ leg \ length}{Adjacent \ Leg\ length}[/tex]
Therefore
[tex]tan(\theta) = \dfrac{y}{x}[/tex]
Where;
θ = The angle of elevation of the plane measured from Ahmed
y = The leg of the right triangle opposite the reference angle
x = The leg of the right adjacent to reference angle
Therefore;
θ = arctan(y/x) which gives;
θ = arctan(350/470) ≈ 36.67°
The angle of elevation of the plane measured from Ahmed, θ ≈ 36.67°.
Find the equation of the line through the points (-5,11) and (2,-3)
y=
Answer:
y = -2x + 1
Step-by-step explanation:
y2 - y1 / x2 - x1
-3 - 11 / 2 - (-5)
-14/ 7
= -2
y = -2x + b
-3 = -2(2) + b
-3 = -4 + b
1 = b
6. The right triangles ABC and DEF
are similar. The hypotenuse of ABC
measures 12 cm and the hypotenuse
of DEF measures 24 cm. If one of
the legs of ABC measures 9 cm,
what does the corresponding leg
of DEF measure?
A 4.5 cm
B 18 cm
Answer:
B. 18 cm
Step-by-step explanation:
24 / 12 = 2.
9 x 2 = 18 cm.
Hope this helps!
What is the solution to this inequality?
X-7-6
O A. x>-13
O B. x < -13
O C. x>1
O D. x< 1
Answer:
x> 1
Step-by-step explanation:
X-7>-6
Add 7 to each side
X-7+7>-6+7
x> 1
The difference between the square of two numbers is 11. Twice the square of the first number increased by the square of the second number is 97 find the numbers
Answer:
Below in bold.
Step-by-step explanation:
x^2 - y^2 = 11
2x^2 + y^2 = 97
From the first equation:
y^2 = x^2 - 11
Substituting in the second equation:
2x^2 + x^2 - 11 = 97
3x^2 = 108
x^2 = 36
x = 6, -6.
Substituting for x in the first equation:
(6)^2 - y^2 = 11
y^2 = 36 - 11 = 25
y = 5, -5.
What is the minimum perimeter of a rectangle with an area of 625 mm^2
Question 2 options:
100 mm
125 mm
156.25 mm
312.5 mm
Show your work:
Answer:
100 mm
Step-by-step explanation:
Square root the area to find the length of each side
[tex]\sqrt[]{625} =25[/tex]
Multiply 25 by 4 to get the sum of all four sides for the perimeter
25 x 4 = 100
Use the figure to find the angle m
Answer:
Measure of angle M = 41°
Step-by-step explanation:
From the figure attached,
NM ≅ NO [Given]
Therefore, ∠O ≅ ∠M [Opposite angle of the equal sides]
By triangle sum theorem,
m∠O + m∠N + m∠M = 180°
m∠O + m∠N + m∠O = 180° [Since, ∠M ≅ ∠O]
By substituting the values of the given angles,
(4y - 15)° + (7y)° + (4y - 15)° = 180°
(15y - 30) = 180
15y = 210
y = 14
Therefore, m∠M = (4y - 15)°
= 4(14) - 15
= 56 - 15
= 41°
1) Evaluate the following function for x = -7
3x + 10 =
Answer:
-11
Step-by-step explanation:
x = -7
To find = 3x + 10
= 3(-7) + 10
= -21 + 10
= -11
Answered by GauthMath if you like please click thanks and comment thanks.
Question 2 of 10
What is the length of MN?
M
4x
x + 3
250"
50
N
A. 4
o
B. 1
C. 7
ОО
D. 8
Answer:
4
Step-by-step explanation:
Since the base angles are the same, the side have to be the same
ML = MN
4x = x+3
Subtract x from each side
4x-x = x+3-x
3x= 3
Divide by 3
3x/3 = 3/3
x = 1
We want the length of MN
MN = x+3 = 1+3 = 4
The measurement of MN side is 4
What are the properties of Triangle?The properties of the triangle are:
1. The sum of all the angles of a triangle (of all types) is equal to 180°.
2. The sum of the length of the two sides of a triangle is greater than the length of the third side.
3. In the same way, the difference between the two sides of a triangle is less than the length of the third side.
Since the base angles are the same, the side have to be the same
ML = MN
4x = x+3
Subtract x from each side
4x-x = x+3-x
3x= 3
Divide by 3
3x/3 = 3/3
x = 1
We want the length of MN
MN = x+3 = 1+3 = 4
Learn more about triangles here:
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make 24 with the numbers below :
5, 10, .5, 1
Answer:
0.5(5 × 10) - 1
Step-by-step explanation:
((5 × 10) × 0.5) - 1
((50) × 0.5) - 1
25 - 1
24
If a rectangle has a length of 10 and an area of 50 Units squared what is the perimeter
Answer:
The perimeter is 10+10+5+5, or 30.
Step-by-step explanation:
The formula to find area is A=LW. Since the area is 50, we can assume that the width is 5, because 10x5=50. The perimeter is made up of the sides of a rectangle, or L+L+W+W. This is 10+10+5+5.
Use the cross product property to determine witch of the following equalities are proportions:
6.6/1.1 = 0.3/0.05
Answer:
proportion
Step-by-step explanation:
6.6/1.1 = 0.3/0.05
Using cross products
6.6 * .05 = 1.1 * .3
.33 = .33
Since this is a true statement, the statement is a proportion
What is the midpoint of AB?
A
F GHI
B
+
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3
3 4 5 6 7
5 6 7 8 9
+
+
point F
point G
point H
O point
Answer:
the answer is point G
It is found that Point G is the midpoint of AB.
What does a midpoint mean?Midpoint, as the word suggests, means the point which lies in the middle of something. Midpoint of a line segment means a point which lies in the mid of the given line segment.
We are Given two points A and B which are located at -6 and 8 on the number line. We need to find the midpoint of AB.
First we have to calculate the distance between AB which can be calculated as;
8-(-6)=14 units
Now, to find the midpoint we have to divide the total distance by 2.
Hence, the mid point of AB is 7 units apart from both points A and B then G.
Learn more about midpoint here;
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Find the domains of the following functions:
Can someone help me with this math homework please!
9514 1404 393
Answer:
(-1, 1)
Step-by-step explanation:
Find the differences between an f(x) value and the previous one
3 -18 = -15
0 -3 = -3
3 -0 = 3
6 -3 = 3
3 -6 = -3
Where the differences are positive, the function is increasing on the interval. Here, it is increasing on the intervals (-1, 0) and (0, 1). Then the longest increasing x-interval is (-1, 1).
using trig solve for the missing angle
Answer:
The answer is 26.4
What is the inequality shown
Answer:
We can also graph inequalities on the number line. The following graph represents the inequality x≤2 . The dark line represents all the numbers that satisfy x≤2 . If we pick any number on the dark line and plug it in for x, the inequality will be true.
Answer:
Step-by-step explanation:
If it's for x:
-4 ≤ x ≤ 3
(-6)+(-1)+4+9+...+64 sequence
Answer:
n
Step-by-step explanation:
hb
How many solutions does-3x = -x – 2x have?
Answer:
infinite solutions
Step-by-step explanation:
-3x = -x – 2x
Combine like terms
-3x = -3x
Add 3x to each side
-3x+3x = -3x+3x
0 =0
This is always true so there are infinite solutions
Given that BD is the perpendicular bisector of AC , set up the equation needed to solve for x and find the value of x
Answer:
below
Step-by-step explanation:
that is the procedure above
Step-by-step explanation:
4x = 6x-10
10 = 6x-4x
2x = 10
x = 5
(4 x 10 ^ 7) ÷ (8 x 10 ^ 4) in standard form PLZ ANSWER QUICK
Answer:
4.67×10
4
=4.67×10000=46700
[tex]4.67 \times {10}^{4} [/tex]
[tex] = \: 4.67 \times 1000[/tex]
[tex] = \: 46700[/tex]
If somebody can give me the answer!!!
Please I need help
Answer:
Its B
Step-by-step explanation:
You're correct
What is the area of trapezoid DEFG with coordinates D (4, 3), E (4, 0), F (2, 1), and G (2, 3)?
10 square units
5 square units
3 square units
2 square units
The area of the trapezoid is 10 square units
How to find the area of a trapezoid?The formula for finding the area of the trapezoid is expressed as:
A = 0.5(a+b)h
where:
a and b are the sides
h is the height
Given the following
a = 3
b = 2
h = 4
Determine the requried volume of the trapezoidSubstitute
A = 0.5(3 + 2)*4
A = 0.5(20)
A = 10 square units
Hence the area of the trapezoid is 10 square units
Learn more on area of trapezoid here: https://brainly.com/question/1463152
Answer:
B) 5 Square Units
Step-by-step explanation:
Answered from another colleague :)
B1 = 2
B2 = 3
H = 2
A = 1/2 (B1 + B2) H
1/2 (2+3) 2
1/2 (5) 2
(2.5)2
5
