Answer:
[tex]x =3[/tex] or [tex]x = 7[/tex]
Step-by-step explanation:
Given
[tex]x^2 - 10x = -21[/tex]
Required
Solve by factoring & quadratic formula
By Factoring:
[tex]x^2 - 10x = -21[/tex]
Equate to 0
[tex]x^2 - 10x +21 = 0[/tex]
Expand:
[tex]x^2 - 7x -3x+21 = 0[/tex]
Factorize:
[tex]x(x-7)-3(x-7) = 0[/tex]
[tex](x-3)(x-7) = 0[/tex]
[tex]x -3 = 0[/tex] or [tex]x - 7 = 0[/tex]
[tex]x =3[/tex] or [tex]x = 7[/tex]
By quadratic
[tex]x^2 - 10x = -21[/tex]
Equate to 0
[tex]x^2 - 10x +21 = 0[/tex]
For
[tex]ax^2 + bx + c = 0[/tex]
x is solved using:
[tex]x = \frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
where
[tex]a = 1[/tex]; [tex]b = -10[/tex]; [tex]c = 21[/tex]
So:
[tex]x = \frac{-(-10)\±\sqrt{(-10)^2-4*1*21}}{2*1}[/tex]
[tex]x = \frac{10\±\sqrt{100-84}}{2}[/tex]
[tex]x = \frac{10\±\sqrt{16}}{2}[/tex]
[tex]x = \frac{10\±4}{2}[/tex]
Split
[tex]x = \frac{10+4}{2}[/tex] or [tex]x = \frac{10-4}{2}[/tex]
[tex]x = \frac{14}{2}[/tex] or [tex]x = \frac{6}{2}[/tex]
[tex]x = 7[/tex] or [tex]x =3[/tex]
Blake and Josh are both saving money for a new bike. The ratio of Blake's savings to Josh's savings is 3:1. If they have saved $400, how much has each boy saved?
Given:
Total savings = $400
Ratio of savings of Blake and Josh = 3:1
To find:
The saving of each.
Solution:
Let the savings of Blake and Josh are 3x and x respectively.
According to the question,
[tex]3x+x=400[/tex]
[tex]4x=400[/tex]
Divide both sides by 4.
[tex]x=100[/tex]
Now,
Savings of Blake = 3(100)=300
Savings of Josh =100
Therefore, the savings of Blake and Josh are $300 and $100 respectively.
Of the 50 U.S. states, 4 have names that start with the letter W.
What percentage of U.S. states have names that start with the letter W?
Answer:
0.08 percent
Step-by-step explanation:
Answer:
0.08%
Step-by-step explanation:
i just did 4/50. i know this works because i use it to find my grade percentages.
If Dominik completes a project by himself, it will take him 8 hours. Working with Katarina, it will take them 5 hours. If they work together, what is the missing value from the table that represents the part of the project Dominik will complete? 8r 8(5) r (5)
Hello soldier!! The answer is D! Have a great day <3
Answer:
The answer is: D / 1/8(5)
Step-by-step explanation:
Pls help me find the slope
Y(-5,0), Z(-2,-4)
Answer:
-4 / 3
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( -4 -0)/( -2 - -5)
( -4 -0)/( -2 +5)
-4 / 3
Answer:
[tex]m=\frac{-4}{3}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Y (-5, 0)
Z (-2, -4)
Step 2: Find slope m
Substitute: [tex]m=\frac{-4-0}{-2+5}[/tex]Subtract/Add: [tex]m=\frac{-4}{3}[/tex]Brianna bought a bicycle for $275.It is now on sale for $150. Find the percent of change of change in the price. Round to the nearest percent.
Answer:
45%
Step-by-step explanation:
First we find the difference between the prices,
[tex]275-150[/tex]
is 125
and
[tex]125/275=0.454545454545.....[/tex]
which in percentage is
[tex]45.4545454...[/tex]
and that rounds to 45%
Suppose that y is inversely proportional to the 4th power of x, and that y=15 when x=5. What is y when x=7? Round your answer to two decimal places if necessary.
Answer:
y = 3.91 when x =7
Step-by-step explanation:
y = k / x⁴
Where,
k = constant of proportionality
y=15 when x=5
y = k / x⁴
15 = k / 5⁴
Cross product
15 × 5⁴ = k
15 × 625 = k
9,375 = k
What is y when x=7?
y = k / x⁴
= 9,375 / 7⁴
= 9,375 / 2401
= 3.9046230737192
Approximately
y = 3.91
Write an inequality to equal y < -5
Answer:
2y - 3 < -13
Hope this helps
A car uses 8.4 liters of petrol for a 112 mile journey. When the tank is full, the car holds 54 liters of petrol. How far should the car be able to travel on a full tank of petrol.
Answer:
720 miles
Step-by-step explanation:
A car uses 8.4 liters of petrol for a 112 mile journey.
In 1 litres = [tex]\dfrac{112}{8.4}\ \text{miles}[/tex] of journey
We need to find far should the car be able to travel on a full tank of petrol i.e. 54 litres of petrol.
[tex]54\ l=\dfrac{112}{8.4}\times 54\\\\=720\ \text{miles}[/tex]
So, the car can travel 720 miles when it holds 54 lirres of petrol.
Help me again!!!!!!
!!!!
Answer:
D
Step-by-step explanation:
the part two shows that 20 tickets were purchased adult and child
adults were 15 dollars and added with the childs10 dollar tickets added togethor to get 225 dollars.
use the law of exponents to rewrite (5^9)^2
will give brainiest and 50 point bet u do not get it right
Answer:
I'm pretty sure it's:
5x5x5x5x5x5x5x5x5 x 2x2
Witch fraction is not in simplest form 5/15 or 5/12
Will give brainliest if correct.
Answer:
slope is 5, y intercept is -7
Step-by-step explanation:
In the form y=mx+c, m is the slope and c is the y-intercept.
Rearrange the formula to fit this form:
5x-y=7
-y=7-5x
y=5x-7
∴m(slope)=5
∴c(y-intercept)=-7
Write an equation of the line that passes through a pair of points:
(-3,1). (-2,-5)
Answer:
[tex]y=-6x-17[/tex] (B)
Step-by-step explanation:
[tex]y=mx+b\\m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} } = \frac{1--5}{-3--2} = \frac{6}{-1} = -6\\y=-6x+b\\[/tex]
Plug in one of the two points for X and Y
(-3,1)
[tex]1=-6(-3)+b\\1=18+b\\b=-17\\\\y=-6x-17[/tex]
True or False: |18 - 7| = |18|+ |-7|
Answer:
False.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
|Absolute Value| - makes any number positiveStep-by-step explanation:
Step 1: Define
|18 - 7| = |18| + |-7|
Step 2: Check
Subtract: |11| = |18| + |-7|Evaluate: 11 = 18 + 7Add: 11 ≠ 25Here we see that 11 does not equal 25.
∴ The statement is false.
Answer:
false
Step-by-step explanation:
because th abosulte value of negative 7 is positive 7 then the equation would not be equal
Which equation represents the graph shown below
A) y=2x+3
B) y=3x+2
C) y=2/3x+b
D) y=5x
Answer:
A Y=2X +3
Step-by-step explanation:
Y=mx +b
y=2x + 3
slope is 2
y intercept is 3
In the middle of a very cold winter night the temperature outside is -20'c at nine o'clock in the morning it has become 30 degrees warmer. What is the temperature at nine o'clock
Answer:
10°c
Step-by-step explanation:
-20°c + 30° = 10°c
Can I get Brainliest? Plz!
I need help asap no rocky
I think its 2346483
Step-by-step explanation:
please help I am doing a timed test I will choose brainliest
Write the standard form of the equation of a line with a slope of 3 passing through the point (-5, -6).
Select one:
a. -x + 3y + 13 = 0
b. -3x + y - 9 = 0
c. 3x - y + 9 = 0
d. x - 3y - 13 = 0
Step 1: We need to first find the equation of the line in slope-intercept form by finding b, or the y-intercept.
[tex]-6 = 3(-5) + b\\\\-6 = -15 + b\\\\9 = b[/tex]
Step 3: We now need to write the equation of the line in slope-intercept form.
[tex]y = 3x + 9[/tex]
Step 3: Now we convert the above equation from slope-intercept form to standard form.
[tex]y = 3x + 9\\\\-3x + y = 9\\\\-3x + y - 9 = 0[/tex]
Our equation in standard form is: B. -3x + y - 9 = 0.
Which three lengths
cannot be the lengths of
the sides of a triangle?
a) 13, 11, 14
b) 17,5, 10
c) 21, 16, 14
d) 8, 9, 14
Answer:
B)
Step-by-step explanation:
You need to add the first 2 numbers and the answer needs to be bigger than the third number and if you add 10 + 5 will be 15 and the third number is 17, so the answer of this is the B
[tex](-4)(-2)-6(2-5)[/tex]
Answer:
26
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASStep-by-step explanation:
Step 1: Define expression
(-4)(-2) - 6(2 - 5)
Step 2: Evaluate
Parenthesis (Subtract): (-4)(-2) - 6(-3)Multiply: 8 + 18Add: 26
Need this answer ASAP cuz im dumb.
Mr. Scott likes to pose interesting problems to his Mathematics classes. Today,
he started with the expression 6
2020 + 72020. He stated that the expression was
not equivalent to 132020 and that he was not interested in the actual sum. His
question to his class and to you is, “What are the final two digits of the sum?”
Answer:
40. This is so easy yet so dumb. Why is this even a question?
Step-by-step explanation:
Answer:
40
Step-by-step explanation:
Which equation represents a line parallel to ?
A. 2x-4y=28
B. 4x+2y=10
C. 4x-2y=10
D. 2x+4y=10
Answer:
b
Step-by-step explanation:
8% of $40 is $
plzzz help
Answer:
$3.2
Step-by-step explanation:
so there's a strategy to do this its very helpful!
100%-$40
8%-x
~cross multiply~
100x=320
÷100 ÷100
________________
x=$3.2
Hope this helps :D
does anyone know this?
Answer:
1.37×10^9 is in scientific notation
identify property for -9/7 x -7/9 = 1
Answer:x = −112/81
Step-by-step explanation:
Using no digits other than 5 and 8, make a 6-digit number, that has the properties below. If it is impossible, write so. Of course you may use each digit more than once. c A multiple of 5, but not a multiple of 15.
Answer:
Doing this would be impossible
Step-by-step explanation:
Doing this would be impossible. This is because the final digit and the first digit in the 6-digit number would always be a 5 or an 8. This means that the entire 6-digit number will either be completely divisible by both 5 and 15 or neither. Therefore not meeting the requirements that have been set. So in conclusion, this would be impossible to do by using only 5's and 8's as the single digits.
−5.55−8.55c+4.35c ples
Why is it impossible to represent a vertical line using the slope-intercept form and the point-slope form of a linear equation?
Answer:
Both equations include the slope, which is undefined for a vertical line.
Step-by-step explanation:
it just is lol
a team of divers assembles at an elevation of -10 ft relative to the surface of the water. Then the team dives at a rate of the water. Then the team dives at a rate of -50ft/min. Write a rule that represents the teams depth d as a function of time t. What is the team's depth after 3 minutes?
Answer: The team will be 160 feet below sea level after 3 minutes.
Step-by-step explanation:
If the team is at -10 ft relative to sea level then it means that they are 10 feet below sea level, and if they also going -50 ft per minute, it also means that they are still going below sea level.
The rule will be, d= -50t -10
If t is the time, input 3 minutes into the equation for t and solve for d to find their depth.
d= -50(3) - 10
d= -150 - 10
d= -160
How many 2.25-pound containers can you fill with 24.75 pounds of almonds?
Answer:
You can fill 11 containers.
Step-by-step explanation:
This problem is asking you to divide 24.75 pounds among 2.25 pound holding containers.
So all you must do is divide 2.25 by 24.75. This leaves us with a quotient of 11.