We are given:
The line passes through (2,-3)
Slope of the line = 4
Finding the equation of the line:
We know that the general form of the slope-intercept form is:
y = mx + b [where m is the slope and b is the y-intercept]
y = 4x + b [since slope = 4]
Finding the y-intercept:
Now, we are given that the line passes through the points: (2,-3)
which can be written as: x = 2 and y = -3
Since the line passes through these points, these values must satisfy the equation
So,
y = 4x + b
-3 = 2(4) + b
-3 = 8 + b
b = -11 [subtracting 8 from both sides]
Hence, the y-intercept is -11
Equation of the line:
We wrote the equation of the line as:
y = 4x + b (where b is the y-intercept)
now that we know the value of b,
y = 4x - 11
Therefore, the equation of the line is: y = 4x - 11
3.3^(2x+1)-103^x+1=0 need value of x
Answer:
The value of [tex]x[/tex] is approximately -1.531.
Step-by-step explanation:
Let [tex]3.3^{2\cdot x + 1}-103^{x+1} = 0[/tex], we proceed to solve this expression by algebraic means:
1) [tex]3.3^{2\cdot x + 1}-103^{x+1} = 0[/tex] Given
2) [tex]3.3^{2\cdot x}\cdot 3.3 -103^{x}\cdot 103 = 0[/tex] [tex]a^{b}\cdot a^{c} = a^{b+c}[/tex]
3) [tex](3.3^{x})^{2}\cdot 3.3 -\left[\left( \sqrt{103} \right)^{2}\right]^{x}\cdot 103 = 0[/tex] [tex](a^{b})^{c} = a^{b\cdot c}[/tex]
4) [tex](3.3^{x})^{2}\cdot 3.3 - \left[\left(\sqrt{103}\right)^{x}\right]^{2}\cdot 103 = 0[/tex] [tex](a^{b})^{c} = a^{b\cdot c}[/tex]/Commutative property
5) [tex]\left[\left(\frac{3.3}{\sqrt{103}}\right)^{x}\right] ^{2}-\frac{103}{3.3} = 0[/tex] Existence of multiplicative inverse/Definition of division/Modulative property/[tex]a^{b}\cdot a^{c} = a^{b+c}[/tex]
6) [tex]\left(\frac{3.3}{\sqrt{103}} \right)^{2\cdot x}=\frac{103}{3.3}[/tex] Existence of additive inverse/Modulative property/[tex](a^{b})^{c} = a^{b\cdot c}[/tex]
7) [tex]\log \left(\frac{3.3}{\sqrt{103}} \right)^{2\cdot x}=\log \frac{103}{3.3}[/tex] Definition of logarithm.
8) [tex]2\cdot x\cdot \log \left(\frac{3.3}{\sqrt{103}} \right)= \log \frac{103}{3.3}[/tex] [tex]\log_{b} a^{c} = c\cdot \log_{b} a[/tex]
9) [tex]2\cdot x \cdot [\log 3.3-\log \sqrt{103}] = \log 103 - \log 3.3[/tex] [tex]\log_{b} \frac{a}{d}[/tex]
10) [tex]x\cdot (2\cdot \log 3.3-\log 103) = \log 103 - \log 3.3[/tex] [tex]\log_{b} a^{c} = c\cdot \log_{b} a[/tex]/Associative property
11) [tex]x = \frac{\log 103-\log 3.3}{2\cdot \log 3.3-\log 103}[/tex] Existence of multiplicative inverse/Definition of division/Modulative property
12) [tex]x \approx -1.531[/tex] Result
The value of [tex]x[/tex] is approximately -1.531.
A rectangle I has a perimeter of 28 units, an area of 48 square units, and sides that are either horizontal or vertical. If one vertex is the point (-5,-7) and the origin is in the interior of the rectangle, fi the vertex of the rectangle is opposite of (-5,-7).
Answer:
B, C, E
Step-by-step explanation:
On edge 2021
The ratio of teachers needs to be 1:30. If there were 120 students, how many teachers would be needed?
Answer:
4:120
Step-by-step explanation:
for 120 student they would be 4 teacher needed per 30 student
4:120
Asap, show the shaded area of the graf of lines 7x+10y=70, x-2y=0, 2x+y=0...
Answer:
The answer is i have no clue
Tom got on a scale while on a vacation in France and noticed he weighed 75 kg. He read in a guidebook that 1 lb. = 0.45 kg. How much does Tom weigh in pounds
Answer:
166.67 pounds
Step-by-step explanation:
Set up a proportion where x is Tom's weight in pounds:
[tex]\frac{75}{x}[/tex] = [tex]\frac{0.45}{1}[/tex]
Cross multiply and solve for x:
75 = 0.45x
166.67 = x
So, Tom weighs approximately 166.67 pounds
. Ruiz wants to buy a coffee machine that costs
$45.00. How much would the cashier give Ruiz if she
gives the cashier a $100 bill?
Ruiz would get back 55 dollars 0 cents
BRAINLIST HELP TIMED
Answer:
its the second one
Step-by-step explanation:
u just mulitply the terms together and add the exponents
Find percentage of .20
Answer: The percentage of 0.20 is 20%.
Step-by-step explanation: 0.20 represents the 20% of 100%.
Answer: 20%
Step-by-step explanation: You just move the dot 2 times to the right and it will be 20%
Can anyone help with this it is for Geometry
Answer:
three angle one slide
Step-by-step explanation:
Solve for the value of f: ½(6 + 4) + 5f = 10
Answer:
Start by combing any like variable and distributing the values.5+5f=10 5f=5f=11/ The Hotel is 163 miles from your house.your car travels 10.5 miles for every litre of petrol. Work out approximately how many litres of petrol the journey will use.
2/The price of petrol is 138.9 pence per litre Work out the approximate cost for the petrol to the hotel .
3/ you expect to travel 50 miles in each hour of a jurney how long the whole journey should take
please help.
Answer:
1. The journey will use 15.52 liters of petrol.
2. The approximate cost of petrol to hotel will be 2155.73 pence
3. The whole journey will take 3.36 hours
Step-by-step explanation:
Given that:
Distance of hotel from house = 163 miles
Distance covered by per liter = 10.5 miles
1/ The Hotel is 163 miles from your house.your car travels 10.5 miles for every litre of petrol. Work out approximately how many litres of petrol the journey will use.
Petrol used for total distance = [tex]\frac{Total\ distance}{Distance\ per\ liter}[/tex]
Petrol used for total distance = [tex]\frac{163}{10.5}=15.52\ liters[/tex]
The journey will use 15.52 liters of petrol.
2/The price of petrol is 138.9 pence per litre Work out the approximate cost for the petrol to the hotel .
Cost of per liter petrol = 138.9 pence
Cost for petrol to hotel = Petrol used for journey * Price per liter
Cost of petrol = 138.9 * 15.52 = 2155.73 pence
The approximate cost of petrol to hotel will be 2155.73 pence
3/ you expect to travel 50 miles in each hour of a jurney how long the whole journey should take.
Distance covered per hour = 50 miles
Time taken in whole journey = [tex]\frac{total\ distance}{distance\ per\ hour}[/tex]
Time taken in whole journey = [tex]\frac{168}{50}[/tex]
Time taken in whole journey = 3.36 hours
The whole journey will take 3.36 hours
Hence,
1. The journey will use 15.52 liters of petrol.
2. The approximate cost of petrol to hotel will be 2155.73 pence
3. The whole journey will take 3.36 hours
Solve The Equation !
‐5x – 3 < 2x – 18
Answer:
x>15/7
Step-by-step explanation:
If two sides of a triangle are 7 and 14, the third side may be?
In the figure, if the measure of ∠1 = 112o, what's the measure of ∠12?
Answer:
the measure of angle 12 is 68degrees
2x+y=42
8x+7y=36
Using the process of eliminations.
Answer:
x=43,y=-44
Step-by-step explanation:
hey i hope it helps you
2x+y=42(7)
8x+7y=36(1)
14x+7y=294
8x+7y=36
6x=258
divide both sides by 6
x=43
to get y
2x+y=42
equate x=43
8(43)+7y=36
344+7y=36
344-36=7y
308=7y
divide both sides by 7
y=-44
what is equivalent to 1/2 (2x + 7)
What is 3/8 divided by 4/1
The inter quartile range of a distribution is 7. If the 25th percentile is 16. Find the upper quartile
Given:
Inter quartile range(IQR) of a distribution = 7
25th percentile = 16
To find:
The upper quartile.
Solution:
We have,
IQR = 7
25th percentile = lower quartile = 16
We know that,
IQR = Upper quartile - Lower quartile
Let the upper quartile be [tex]Q_3[/tex].
Using the above formula, we get
[tex]7=Q_3-16[/tex]
Adding 16 on both sides, we get
[tex]7+16=Q_3-16+16[/tex]
[tex]23=Q_3[/tex]
Therefore, the upper quartile of the distribution is 23.
Pretty please help!!!
The table shows the relationship of how many pounds of apples are needed to make a certain number of pies:
Number of pies: 5 10 15
Pounds of apples: 2 4 6
What is a equivalent expression for 10(y² + 2.45)
Answer:
10y²+24.5
Step-by-step explanation:
distribute.
10y²+24.5
Hope this helps plz hit the crown :D
The equivalent expression for the given expression is 10y²+24.5.
The given expression is 10(y² + 2.45).
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The equivalent expression is
10(y² + 2.45)
=10y²+24.5
Therefore, the equivalent expression for the given expression is 10y²+24.5.
To learn more about an equivalent expression visit:
https://brainly.com/question/28170201.
#SPJ2
`y=2x+1` was a positive slope because...
Step-by-step explanation:
.....because the coefficient of x is 2, a positive number.
5) A student answered 81 problems on a test correctly and received a grade 90%.
How many problems were on the test, if all the problems were worth the same
number of points?
Answer:
90
Step-by-step explanation:
81/x=90/100
8100=90x
90=x
The total number of problems given in exam was 90.
PercentageWhat is percentage?Percentage, which is a relative figure used to denote hundredths of any quantity. One percent (symbolised as 1%) is equal to 100 parts; hence, 100 percent denotes the complete amount, and 200 percent designates double the amount specified.
How to calculate percentage?Divide one number by the other, then multiply the result by 100 to get the percentage of the two numbers.
Calculation for the total number of question given:A student correctly answered 81 problems.
Grade received by student is 90%
Let the total number of question given in the test be 'x'.
Thus,
90% of x = 81
(90/100)x = 81
x = (81×100)/90
x = 90
Therefore, the total number of question allotted to the student is 90.
To know more about how to conver percent to fraction?, here
https://brainly.com/question/317717
#SPJ2
6) Calculate the slope of a line containing the points (-3,5) and (-7,11).
slopev=
[tex]diffrence \: in \: y \: coordinate \\ diffrence \: in \: x \: coordinate[/tex]
so
Y=11_5 =6
X = -7_(-3) = -4.
slope = (-4,6)
make as brainlist
Solve five ninths minus two sixths
options:
twelve fifty fourths
twenty fifty fourths
six thirds
three over one
Find the value of x
a)105°
b)85
c)75
d)25
Answer:
c) 75
Step-by-step explanation:
180-155 = 25
80+25+x=180
x = 75
Step-by-step explanation:
By Exterior Angle Theorem,
x = 155° - 80° = 75° (C).
Please help me ASP
Give me a Fraction Mixed number word problem
WORD PROBLEM:
Flock of birds flew for 2 3/4 hours. The next day , they flew for 3 4/5 hours. How many hours did the birds fly in total?PROBLEM:2 3/4 + 3 4/5In triangle $XYZ,$ $\angle Y = 45^\circ$ and $\angle Z = 60^\circ.$ If $XZ = 4,$ then what is $XY$?
[asy]
unitsize(3 cm);
pair X, Y, Z;
X = (0,1);
Y = (-1,0);
Z = (1/sqrt(3),0);
draw(X--Y--Z--cycle);
label("$45^\circ$", Y + (0.3,0.1), fontsize(10));
label("$60^\circ$", Z + (-0.2,0.1), fontsize(10));
label("$X$", X, N);
label("$Y$", Y, SW);
label("$Z$", Z, SE);
label("$4$", (X + Z)/2, NE);
[/asy]
Answer:
[tex]XY = 4.9[/tex]
Step-by-step explanation:
[tex]\angle Y = 45^\circ[/tex]
[tex]\angle Z = 60^\circ[/tex]
[tex]XZ = 4[/tex]
Required
Determine the length of XY?
This question is supported with the attachment.
To solve for the length of XY, we make use of the sine law which states:
[tex]\frac{sin\ A}{a} = \frac{sin\ B}{b} = \frac{sin\ C}{c}[/tex]
In this case:
[tex]\frac{sin\ \angle Y}{XZ} = \frac{sin\ \angle Z}{XY} = \frac{sin\ X}{YZ}[/tex]
Substitute in, the following values:
[tex]\angle Y = 45^\circ[/tex]
[tex]\angle Z = 60^\circ[/tex]
[tex]XZ = 4[/tex]
The expression becomes:
[tex]\frac{sin\ 45}{4} = \frac{sin\ 60}{XY}[/tex]
Cross multiply
[tex]XY * \sin\ 45 = 4 * \sin\ 60[/tex]
Make XY the subject
[tex]\frac{XY * \sin\ 45}{\sin\ 45} = \frac{4 * \sin\ 60}{\sin\ 45}[/tex]
[tex]XY = \frac{4 * \sin\ 60}{\sin\ 45}[/tex]
[tex]XY = \frac{4 * 0.8660}{0.7071}[/tex]
[tex]XY = \frac{3.4640}{0.7071}[/tex]
[tex]XY = 4.89888276057[/tex]
[tex]XY = 4.9[/tex] --- approximated
Answer:
XY = 4.9
Step-by-step explanation:
Find the slope of the line containing the points in the table below
Answer:
slope = 3
Step-by-step explanation:
Choose any two points: For example, (2, 4) and (4, 10)
Find the difference in y. This is called the "rise."
rise = 10 - 4 = 6
In the same order, find the difference in x. this is called the "run."
run = 4 - 2 = 2
slope = rise/run
slope = 6/2
slope = 3
There are 60 seconds in a minute use a tape diagram to find the total number of seconds in 5 minutes and 45 seconds
60 x 5 + 45 = 345 Seconds
Estimate the quotient for:
4,819÷68
Answer:
≈ 70.87 (rounded to the nearest hundredth)
Step-by-step explanation:
-When you do 4,819 ÷ 68, you’ll get:
70.867647058....
-So, just round it to the nearest hundredth:
70.87