Answer:
y=1/4x + 7
Step-by-step explanation:
To find the perpendicular equation of an equation, you need to find the reciprocal of the slope (reciprocal is the opposite fraction and it's opposite sign (negative or positive)). Then you use both points in the point slope form. y-y1=m(x-x1), y-5=m(x--8), subtracting -8 from x is the same as +8, so the equation becomes y-5=m(x+8), m is the slope and our new slope is 1/4 (the reciprocal of -4x). Now your equation is y-5=1/4(x+8). All you have to do now is solve. first you multiply 1/4 by x and 8 to get rid of the parenthesis. so the equation is now y-5=1/4x+2. Now you move the 5 to the other side, so it becomes a +5 instead of -5, and you add it to 2. now the equation is y=1/4x+7.
Solve this equation algebraically.
Write both sides as powers of 16:
[tex]\log_4(2-x)=\log_{16}(13-4x) \implies 16^{\log_4(2-x)}=16^{\log_{16}(13-4x)}[/tex]
Since 16 = 4², we can rearrange the left side to get
[tex]16^{\log_4(2-x)}=(4^2)^{\log_4(2-x)}=4^{2\log_4(2-x)}=4^{\log_4(2-x)^2}[/tex]
Then, recalling that [tex]b^{\log_ba}=a[/tex], we have
[tex]4^{\log_4(2-x)^2}=16^{\log_{16}(13-4x)}\implies(2-x)^2=13-4x[/tex]
Now solve for x :
[tex](2-x)^2=13-4x[/tex]
[tex]4-4x+x^2=13-4x[/tex]
[tex]x^2-9=0[/tex]
[tex](x+3)(x-3)=0[/tex]
[tex]\implies x=-3\text{ or }x=3[/tex]
Notice that if x = 3, then log₄(2 - x) = log₄(-1) is undefined, so we throw out this solution. We don't run into this problem with x = -3, so that's the only (real) solution.
I need help fast ! What is the slope of y=-x+7
Answer:
-1 this equation is in slope intercept for y=mx+b. the slope is variable m, which in this case is -1. the one is always invisible in front of variable
Please and thank you
Answer:
5 inches since you can divide 15 and 20 by 5
Answer:
yea im following this guy and just double checked yea 5
Step-by-step explanation:
"11 less than three times a number is the same as 75 less than the product of -1 and the number"
Answer:
x=-16
Step-by-step explanation:
Let the number be x.
11 less than three times a number would be represented as 3x - 11.
75 less than the product of -1 and the number would be represented as -x - 75
Those two expressions are the same.
3x - 11 = -x - 75
3x = -x - 64
4x = -64
x = -16
Hope this helps!! :)
∠1 and ∠2 are complementary angles. Given m∠1=83°, find m∠2.
Reasoning: Complementary angles always add to 90 degrees.
If angle 2 was x, then x+83 = 90 solves to x = 7
The measure of m∠2 is 7° due to the pair of angles being complementary.
What are complementary angles?The complementary angles are defined as when pairing of angles addition to 90° then they are called complementary angles. There are two types of supplementary angles.
Adjacent angles: Adjacent angles are the type of supplementary angles. Adjacent angles have a common side and vertex, for example, a corner point. Their points do not overlap in any way. In other terms, adjacent angles are pairs of two angles next to each other.
We have been given that the pair of angles as
m∠1 = 83° and m∠2 = x
Here, the pairing of angles sums up to 90° then they are called complementary angles.
So x + 83 = 90°
⇒ x = 90° - 83°
⇒ x = 7°
Therefore, the value of m∠2 is 7°.
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francis made a rectangular path from her driveway to the porch . the width of the path is 2 ft and the length is 28 ft longer than the width . what is the perimeter of the path
The perimeter of the rectangular path is 64 ft
What is a Rectangle?Rectangle is a type of quadrilateral that has its parallel sides equal to each other, opposite sides are equal to each other, and all the angle are equal to 90 degrees.
How to determine this
The perimeter of a Rectangle = 2 ( Length + Width)
Where the Width = 2 ft
Length = 28 ft longer than Width
i.e W + 28
Length = 2 + 28 = 30 ft
To calculate the perimeter if the path
Perimeter = 2( 30 + 2)
Perimeter = 2(32)
Perimeter = 64 ft
Therefore, the perimeter of the rectangular path is 64 ft
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Last Friday Kevin had $2. Over the weekend he found some money in his old jeans. He now has $10. How much money did he find?
Line A has a slope of −3 . Line B has a slope of 4. Line C has a slope of 2
Which Line Is The Closest To Being Horizontal?
- Line A
- Line B
- Line C
- I dont Know
The line whose absolute value of the slope is least will be the slope which is close to being horizontal. Hence, line C is the answer.
An horizontal line has will have a slope value of 0. Hence, the steeper the slope, the greater the absolute value of the slope obtained. This means that a line deviates more from being horizontal as the absolute value of the slope increases.Therefore, the line with least absolute value would be the closest to being horizontal, hence, line C with an absolute value of 2.
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Suppose you need to borrow $90000 at an APR of 5.25% to buy a home.
a) What will your monthly payment be if you opt for a 15-year mortgage?
b) What percentage of your first month's payment will be interest if you opt for a
15 - year mortgage? (Round your answer to two decimal places as a percentage.)
c) How much interest will you have paid by the end of the 15-year loan?
Which number is the largest?
1.2 × 10^4
4.5 × 10^−3
3.8 × 10^3
7.5 × 10^3
Answer:
1.2 x 10^4 = 12,000
4.5 x 10^-3 = 4.5 x 1/(10^3) = 4.5/1000 = 0.0045
3.8 x 10^3 = 3,000
7.5 x 10^3 = 7,000
largest is 1.2 x 10^4
Hope this helps!!
Step-by-step explanation:
5 x 2/3 in simplest form
Answer:
10/3
Step-by-step explanation:
Answer:
10/3
Step-by-step explanation:
5/1 x 2/3= 10/3
5 x 2 = 10
1 x 3 = 3
You cannot simplify 10/3.
5 people are meeting for the first time and shake each others hand once. determine the number of handshakes
Step-by-step explanation:
5
Answer:
10 B
Step-by-step explanation:
you would just start with 4 and each time count down.which gives you 10
Nerissa's car can travel between 380
and 410 miles on a full tank of gas. She
filled her gas tank and drove 45 miles.
How many more miles can she drive
without running out of gas?
Answer:
Step-by-step explanation:
20 miles
The table below shows the illuminated percentage of the moon on a lunar cycle of 28 days. The relationship can be described using a cosine function.
A 2-column table with 5 rows. Column 1 is labeled d with entries 0, 7, 14, 21, 28. Column 2 is labeled percent with entries 0, 48, 96, 48, 0.
Use the drop-down menus to complete each statement.
The amplitude of the function is
.
The period of the function is
.
The graph has a vertical shift of
units.
Answer:
StartSet (negative 8, negative 2), (negative 4, 1), (0, negative 2), (2, 3), (4, negative 4) EndSet
Step-by-step explanation:
The function is when there are sets of input and output values given and each input value hem has one corresponding output. Input values are unique but output values can be same for more than one input value.
A.........................................
A 2-column table with 5 rows. The first column is labeled x with entries negative 5, negative 3, negative 3, 0, 5. The second column is labeled y with entries 10, 5, 4, 0, negative 10.
Not a function as input values repeated: negative 3
B.........................................
StartSet (negative 8, negative 2), (negative 4, 1), (0, negative 2), (2, 3), (4, negative 4) EndSet
Yes, it is a function
C.........................................
A 2-column table with 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 0, 1. The second column is labeled y with entries negative 3, negative 2, negative 1, 0, negative 1.
Not a function as input values repeated: 0
D.........................................
StartSet (negative 12, 4), (negative 6, 10), (negative 4, 15), (negative 8, 18), (negative 12, 24) EndSet
Not a function as input values repeated: negative 12
So correct one is option B
HELP FAST!!!!!!! f(x)=−x ²−14 PLZ HELP
Answer:
what's x?
Step-by-step explanation:
substitute whatever you have for x in the equation. I was taught f(x) is no different from y=.
can anyone help i don’t know how to do it and it’s GEMDAS not PEMDAS?
Answer:
GEMDAS rate. (Abbreviation) A mnemonic used to the order of operations in math problems; Grouping (such as parentheses), Exponents, Multiplication, Division, Addition, Subtraction.
Step-by-step explanation:
its pemdas just with a different name!!
do you still need help?
Please help me with this problem
Answer:
line l
line m
Step-by-step explanation:
[tex]line \: l \: and \: line \: m \: are \: the \: \\ transversals \: of \: \angle 15 \: and \: \angle \: 5\:\\ respectively. [/tex]
If the pattern indicated below continued, what would be the total number of cubes in the 8th stage of the pattern?
1, 1+4=5, 1+4+9=14
Answer:
The number of cubes in the 8th stage of the pattern is 204
Step-by-step explanation:
Here, we want to calculate simply the 8th term of the pattern
T1 = 1
T2 = 1 + 4 = 1 + 2^2 = 5
T3 = T2 + 3^3 = 5 + 9 = 14
T4 = T3 + 4^2 = 14 + 16 = 30
T5 = T4 + 5^2 = 30 + 25 = 55
T6 = T5 + 6^2 = 55 + 36 = 91
T7 = T6 + 7^2 = 91 + 49 = 140
T8 = T7 + 8^2 = 140 + 64 = 204
A motorboat heads upstream a distance of 24 miles on the Guadalupe River, whose current is flowing at 3 miles/hour. Which expression can represent the total time it takes to complete a round-trip up and back, where b is the speed of the boat in miles/hour?
Answer:
24/b-3 + 24/b+3
Step-by-step explanation:
For PLATO users!!!!
This expression represents the total time, Time = [tex]\frac{24}{b-3} + \frac{24}{b+3}[/tex]
What is distance?Distance is defined as the product of the speed and time.
Given,
b = the speed of the boat in miles/hour
let, effective speed upstream = (b+3)
effective speed downstream = (b-3)
∵Time = distance/ speed
Given that, upstream a distance of 24 miles
Time = [tex]\frac{24}{b-3} + \frac{24}{b+3}[/tex]
This expression represents the total time it takes to complete a round-trip up and back.
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In a group of 150 people, 39 of them wear glasses. What is the probability of randomly selecting a person who does not wear glasses?
A. 111/150
B. 39/111
C. 111/189
D. 189/150
E. 39/150
Answer:
A. 111/150
Step-by-step explanation:
Because we know that 39 people out of the 150 in the group wear glasses, we need to subtract that from the total. This gives us 111 people that don't wear glasses.
Therefore, the probability of choosing someone not wearing glasses is 111/150.
Denise earns $30 an hour. She works 40 hours per week. Denise would like to purchase a computer that costs $2000. Create and solve an inequality in order to determine the least amount of hours she must work in order to be able to purchase the computer?
Answer:
67hours hoursStep-by-step explanation:
Given
she works $30 for 1 hour
in 40 hours she will earn 40*30= $1200
this means that a week she earns $1200
let the number of weeks she needs to work be x
40x*(30)<=2000
1200x<=2000
x<=2000/1200
x<=1.66
the number of hours in a week is 40
40*1.66=66.66
67hours
hence she must work for at least 67hours
Gerald ran 240 yards. Which answer choices are equivalent to the distance he ran?
Select all that apply.
20 inches
2.880 inches
O 8, 640 inches
0 80 feet
720 feet
7 miles
Answer:
720 feet
Step-by-step explanation:
A yard is equivalent to 3 feet, so 1 yard = 3 feet.
240 yards * 3 = 720 feet
Jenny is organising a party,
She buys some paper plates and some plastic cups.
Paper plates are sold in packs.
There are 25 plates in a pack,
Each pack costs 78p.
Plastic cups are sold in packs.
There are 35 cups in a pack.
Each pack costs £1.10
Jenny buys exactly the same number of plates and cups.
What is the least amount of money she pays?
5 Marks
7x-7=2x-2 what is the answer
Answer:
x = 1
Step-by-step explanation:
7x-7=2x-2
5x = 5
x = 1
1. A submarine was situated 620 feet below sea level. It ascended 250 feet. What
is its new elevation?
Answer: 370 feet below sea level
Step-by-step explanation: The submarine was 620 feet below and ascend means go up so you add 250 to -620 which would be 370.
Answer:
100 feet
Step-by-step explanation:
620 - 250
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
The right arrow symbol used to show the transition from a point to its image after a transformation is not contained within the Equation Editor. If such a symbol is needed, type "RightArrow." For example: P(0, 0) RightArrow P′(1, 2).
Triangle ABC has coordinates
A
(
1
,
4
)
;
B
(
3
,
−
2
)
;
and
C
(
4
,
2
)
.
A
(
1
,
4
)
;
B
(
3
,
-
2
)
;
and
C
(
4
,
2
)
.
Find the coordinates of the image
A
'
B
'
C
'
A
'
B
'
C
'
after a reflection over the x-axis.
Answer:
A'(1, -4)B'(3, 2)C'(4. -2)Step-by-step explanation:
GivenTriangle ABC with coordinates
A(1, 4), B(3, -2), C(4, 2)To findCoordinates of the image A'B'C' after a reflection over the x-axisSolutionRule for reflection over x-axis is
R(x) = (x, y) → (x, -y)The coordinates will change as follows
A(1, 4) → A'(1, -4)B(3, -2) → B'(3, 2)C(4, 2) → C'(4. -2)I know it’s simple but can someone explain to me the percents that go over 100?
Answer:
Look below.
Step-by-step explanation:
Not exactly sure what is being asked here, but I'm going to assume you need to convert them into decimals.
7.) 0.51
8.) 3.95
9.) 0.49
10.) 0.11
11.) 0.39
12.) 7.39
13.) 9.70
14.) 2.56
15.) 2.77
16.) 0.37
17.) 0.04
18.) 7.73
19.) 0.14
20.) 2.19
Any percent that goes over 100, goes into the unit place.
If I didn't answer the question right, then let me know.
$98.45 − $10.63 + $2.82 − $20.26
Answer:
70.38
Step-by-step exp7lanation:
$98.45 − $10.63 + $2.82 − $20.26 = 70.38
Answer:70.38
Step-by-step explanation:
what is the slope or the line going through (0,0) (6,8) A: -6/8 B: -3/4 C: 3/4 D: 8/6
Answer:
D: 8/6
Step-by-step explanation:
Slope = y 2 - y 1
x2 - x1
= 8 - 0
6 - 0
=8
6
Answer: D. 8/6
Step-by-step explanation:
To solve this, we can use the slope formula, which is
[tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex] ← this is [tex]\frac{rise}{run}[/tex]
Plugging in the values of the two points, we get:
[tex]\frac{8 - 0}{6 - 0} = \frac{8}{6} = \frac{4}{3}[/tex]
In your case though, it is D. 8/6
Convert 76.4% to a fraction in simplest form and a decimal.
Answer:
In Fraction, it is 76 1/25
In decimal, it is 76.04
Step-by-step explanation:
