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]
Apples cost $1.47 per pound. Danielle buys an apple that weighs 0.62 pound. To the nearest cent, how much does Danielle’s apple cost?
Answer:
91 cents
Step-by-step explanation: Just a hunch
The amount that Danielle’s apple cost is $0.91.
Using this formula
Cost=Sales price per pound× Weight per pound
Where:
Sales price per pound=$1.47
Weight in pound=0.62 pound
Let plug in the formula
Cost=$1.47×0.62
Cost=$0.91
Inconclusion the amount that Danielle’s apple cost is $0.91.
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brainlest for whoever gets it right
3/4 - 1 and 1/2
Answer:
-0.75
Step-by-step explanation:
Answer: the answer would be -0.75, or -3/4
A backpack is normally $64.99 but is discounted ti $45.49. What percent of the original does Maria pay?
Answer:30%
Step-by-step explanation:
5) Ziegler is using paper for an art project
thatis 0.025 mm thick. If she glues a layer
of thepaper onto a construction board with
athickness of 7 * 10^-2 mm, what will the
total thickness of the paper and the
construction
board be? Write your ansicer
in scientific notation
Answer:
9.5 * 10^-2 mm
Step-by-step explanation:
To find the total thickness, we proceed to add the two thickness that we have
Mathematically, this will be;
0.025 mm + 7 * 10^-2 mm
7 * 10^-2 mm = 0.07
So we have;
0.025 mm + 0.07 mm = 0.095
In scientific notation, this is 9.5 * 10^-2 mm
(9x2 – 8) + (9x2 + 9x + 3)
Answer:
18x2 +9x -5
Step-by-step explanation:
combine like terms
Here is the other question
Part A and B are done
A. Lesson
1. Describe the formula for slope in words and with an equation.
M=y^2-y^1/x^2-x^1
1. What is the slope of all horizontal lines? What is the slope of all vertical lines?
The slope of all horizontal lines is 0. The slope of all vertical lines is undefined.
B. Lesson Content
3. Copy and paste the 3-step procedure for finding the slope using the formula.
4. Use Example 3 as your model for the following: In the 2000 census, the population was 8000; in the 2010 census, the population was 7500. Find the rate of growth for the town. Show the 3-step procedure, as well as the final answer in words.
A(200(x1), 8000(y1)) and B(2010(x2), 7500(y2))
M=(y2-y1)(x1-x2)=7500-8000/2010-2000
M=-50=50 people per year decrease
C. Write the slope-intercept (y = mx + b) form of the equation from the information given. Show your steps as done in the lesson content to earn credit.
Answer:
Step-by-step explanation:
Slope is m
in this case slope is -50
b is the y-int,
in this case the y-int is 8000
so your equation: y = -50x + 8000
Evaluate 7(-4) - |-6| + |4|
Answer:
-30
Step-by-step explanation:
7x-4=-28-6=-34+4=-30
Pls mark as brainliest!!!!!
Answer:
The answer for this is -30.
Step-by-step explanation:
Basically, you start out with solving the equation from left to right (as always). First, you multiply 7* -4, and you get -28. Then you have -28 - |-6| + |4|. Now, |-6| is equal to 6, since it's the absolute value of -6. |4| is equal to 4 for the same reason as well. That leaves you with -28 - 6 + 4. Now you just solve left to right. -28 - 6 is -34, so then you have -34 + 4, which is equal to -30.
Hope that helped!
Yesterday, Jack drove 31 1/2 miles. He used 1 1/4 gallons of gasoline. What is the unit rate for miles per gallon.?
Answer:
25.2 miles per gallon
Step-by-step explanation:
the easiest way to solve would be to set this up as fractions
Rectangles P, Q, R, and S are scaled copies of one another. For each pair, decide if the scale factor from one to the other is greater than 1, equal to 1, or less than 1. Four rectangles, labeled P, Q, R and S. Each rectangle is a scaled copy of one another. Ranked in order from least to greatest, the area of the rectangles are as follows: the area of P is equal to S, which are less than the area of Q, which is less than the area of R. From P to Q from P to R from Q to S from Q to R from S to P from R to P from P to S
I attached a diagram that will aid the understanding of the question.
Firstly, I would love to review what a scale factor is before going into the question.
If you have two shapes that are similar, that is they have corresponding angles, then the scale factor of one to the other is simply the ratio of any two corresponding lengths in the two similar geometric figures.
Looking at these figures in the question, we see that R is an enlargement of the other rectangles while Q is an enlargement of P and S. With this information we can answer the questions:
1. From P to Q, the scale factor greater than one because Q is bigger than P.
2. From P to R, the scale factor is greater than one for the same reason.
3. From Q to S, the scale factor is less than one because S is smaller than Q.
4. From Q to R, the scale factor is greater than one because R is bigger than Q.
5. From S to P, the scale factor is equal to one because they are equal.
6. From R to P, the scale factor is less than one because p is smaller than R.
7. From P to S, the scale factor is equal to one because they are equal.
Please help meeeeeeee
What is the length of BC?
O 11
O 23
O 40
O 60
Plz help
Answer:
BC = 40
Step-by-step explanation:
Answer:
X=23
BC = 40
Step-by-step explanation:
What is 5+5 I will give brainliest
Answer:
5+5=10
tep-by-step explanation:
Psychological fact: people with bad handwriting tend to be smarter
Yes, they jolt things down causing bad handwriting
Solve for x.
-18x + 21 > -15 OR 20x – 13 >27
Answer:
C
Step-by-step explanation:
-18x + 21 > -15 /// x = 2
20x – 13 >27 /// x = 2
The solution of inequality -18x + 21 > -15 OR 20x – 13 > 27 is x ∈ (- ∞, ∞), so option E is correct.
What is inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. It is most frequently used to compare the sizes of two numbers on the number line.
Given:
-18x + 21 > -15 or 20x – 13 >27
Solve the first inequality as shown below,
-18x + 21 > -15
-18x + 21 - 21 > -15 - 21 (Subtract 21 from both sides)
-18x > -36
-18x / -18 > -36 / -18 (Divide by -18 into both sides, the inequality sign changes as the value will become positive)
x < 2
Similarly, solve the second inequality,
20x – 13 > 27
20x > 40
x > 2
Thus, the solution will be x < 2 ∪ x > 2 or x ∈ (- ∞, ∞)
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Which of the following is equivalent to -(7/4) ?
A. 7/-4
B. -7/-4
C. 4/-7
D. 7/4
Answer:
A
Step-by-step explanation:
-(7/4) equals -7/4 or negative seven forths. Its doesn't matter where the negative sign is as long there's only 1 of them and that its still 7/4.
So through process of elimination, we take out B because theres 2 negative, which make a positive, our answer is negative
C is wrong because its 4/7, not 7/4
D is wrong because it's positive, leaving us with A
what is 6 plus6^2÷3
It's easy I'm just not I'm my head rn can someone help?
This is a career explorations question, not math btw!!
Event planners may be responsible for which of the following? Select all that apply.
A: a sporting arena's fan night
B: a birthday party
C: a wedding
D: a Black Friday sale
Which of the following are solutions to the equation below?
Check all that apply.
x2 - 10x+ 25 = 17
I A. X = 17-5
B. x = --58-5
c. x= - - _17-5
D. x= 177 +5
E. x = 18 +5
F. x= -17 +5
Answer:
The answer is letter F po
Step-by-step explanation:
Use the formula
(b2)2 in order to create a new term. Solve for x
by using this term to complete the square.
Exact Form:x=±√17+5
(ANSWER ASAP PLZZ) WILL MARK BRAINEST IF CORRECT)Jason and 4 friends went bowling. Three friends rented shoes for $2 each. The total cost to rent the shoes and the lane fees was $42. What was the cost of the lane fees for each person?
Answer: 30/4
Step-by-step explanation:
An ostrich is being chased by a cheetah,
The ostrich is running at 44 feet per
second and the cheetah at 110 feet per
second. If the two started at the same
place and the ostrich got a 60-second
head start, how many seconds will it be
before the cheetah catches it?
Answer:
40 seconds
Step-by-step explanation:
(ostrich speed * seconds) + head start = (cheetah speed * seconds)
44x + (44 * 60) = 110x
44x + 2640 = 110x
2640 = 66x
x = 40
No. of seconds before cheetah catches ostrich = 40 seconds
What is speed?Speed tells us how slow or fast an object moves. It describes the distance travelled divided by the time taken to cover the distance.
Speed is directly Proportional to Distance and Inversely proportional to Time.
Speed = Distance/Time
Given,
Speed of ostrich = 44 feet per second
Speed of cheetah = 110 feet per second
Starting point is same
Ostrich got 60 second head start
Distance travelled by ostrich in 60 second = 44 × 60 = 2640 feet
let S be the number of seconds that it will take the cheetah to catch the ostrich
Distance covered by cheetah = 110S
Distance that the ostrich will cover before being caught is 2640 + 44S
According to the question
110S = 2640 + 44S
110S - 44S =2650
66S = 2640
S = 2640/66
S = 40 seconds.
Hence, It will be 40 seconds before cheetah catches the ostrich.
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Can someone please help me with my homework !
Answer:
Nah ;)
Step-by-step explanation:
6. A person can order a new car with a choice of 11 possible
colors, with or without air conditioning, with or without
heated seats, with or without anti-lock brakes, with or
without power windows, and with or without a CD player. In
how many different ways can a new car be ordered in terms
of these options?
A) 352
B) 704
C) 22
D) 176
A 32-ounce package of a snack mix is 24 percent pretzel. How many ounces are pretzels? A. 0.706 B. 0.768 C. 7.06 or D. 7.68
Answer:
D.7.68
Step-by-step explanation:
100%= 32 ounces
24%= 24% x 32ounces = 768 ounces
100% 100
= 7.68 ounces
I could rlly use sum help - Brainliest!!!!!
Factor completely 4x^4− 20x^3 + 12x^2
Factor completely x^2 − 4x − 12
Which of the following is a factor of x^2 − 6x − 27
Which is a factor of 3x^2 − 33x + 84
Factor completely 81x^2 − 100
Which is a factor of 3x^2y^2 + 6x^2 + 12y^2 + 24
Which of the following is a factor of 15x^2 − 14x − 8
Which is a factor of 12x^2 − 46x − 8
Which of the following is a factor of 2xy + 8y − 8x − 32
What is the factored form of 3x^2 + 5x − 12
Answer: The answers are 4x^2(x^2+5x+3), (x–6) (x+2), (x–9), 3(x–7)(x–4), (9x–10) (9x+10), 3(y^2+2)(x^2+4), (5x+2), 2(x–4)(6x+1), 2(x + 4)(y - 4), and the factored form is (3x–4)(x–3).
Step-by-step explanation: To solve all the factoring equations, factor using the AC method or factoring the polynomials, the 3 steps are Grouping: using the sum-product pattern, common factor from the two pairs, and
rewrite the expression in factored form.
Evaluate the expression w² - v + 1 for w = -2 and v = -8.
Answer:
13
Step-by-step explanation:
-2(-2) - (-8) + 1
4 + 8 + 1 = 13
Answer:
13
Step-by-step explanation:
cause i did it and it was right
please help I will mark brainiest
Answer:
dark blue {-3,3}
Step-by-step explanation:
Answer:
I think it's none of the above-
Step-by-step explanation:
a car travels along the highway to yuma at steady speed. when it begins, it is 400 miles from yuma. After 7 hours, it is 59 miles from yuma. which function describes the cars distance from yuma?
The car's position can be described with the linear function below:
y = (-48.7 mi/h)*x + 400 mi
Which function describes the car's distance from Yuma?
We know that the car is initially at a distance of 400 miles from Yuma. We also know that the car moves at a constant rate (steady speed) then its position will be described by a linear equation:
y = a*x + b
Where y is the distance, a is the slope and b is the y-intercept.
Knowing the initial distance, we can write:
y = a*x + 400mi
And we know that after 7 hours, the car is at 59 mi, then we can write:
59 mi = a*7h + 400mi
59mi - 400mi = a*7h
-341 mi = a*7h
-341mi/7h = a
-48.7mi/h = a
Then the equation that describes the distance from Yuma is:
y = (-48.7 mi/h)*x + 400 mi
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Answer:
y=-50x+400
Step-by-step explanation:
Took the text
A newborn baby what weighs 3⁷ kilograms. An adult blue whale weighs 81 times the newborn. How many kilograms does the adult bluewhale weigh? Write your answer as a power of 3.
Answer:
2187
Step-by-step explanation: 27 times 81 equals 2187
What equation represents a line that passes through (2,-1/2) and has a slope of 3.
Express 4/10 as a decimal number, and identify another decimal number that is equal to it. 4/10 expressed as a decimal number is ___, which is equal to ___
Answer:
Step-by-step explanation:
Decimal number in mathematics is one in which the whole number and the fractional part is separated by a decimal point
If we divide 4 by 10 it will give us a a decimal number which was done below
4/10
=0.4
And also if we divide 40 by 100 we will still have a decimal of 0.4
0.4=40/100
Express 4/10 as a decimal number, and identify another decimal number that is equal to it. 4/10 expressed as a decimal number is 0.4 which is equal to _40/100__