Answer:
A) x = 5 or x = 6
B) x = 0.298 or 6.702
C) x = 3
D) x = ±1
Step-by-step explanation:
A) Values of x for which;
x² − 11x + 31 = 1
x² - 11x + 30 = 0
Using quadratic formula, we have;
x = 5 and x = 6
B) Values of x for which;
x² − 5x − 3 = 2x − 5
x² − 5x - 2x - 3 + 5 = 0
x² - 7x + 2 = 0
Using quadratic formula, we have;
x = 0.298 or 6.702
C) Values of x for which;
7x + 1 = 3x² − 2x + 1
3x² - 2x - 7x + 1 - 1 = 0
3x² - 9x = 0
3x² = 9x
Divide both sides by 3x to get;
x = 3
D) Values of x for which;
−2x² + 5x + 6 = 4x² + 5x
Rearranging, we have;
4x² + 2x² + 5x - 5x - 6 = 0
6x² - 6 = 0
x² = 6/6
x² = 1
x = √1
x = ±1
The values of [tex]x[/tex] for the given situations would be as follows:
A). [tex]x = 5[/tex] or [tex]x = 6[/tex].
B). [tex]x = 0.298[/tex] or [tex]6.702[/tex]
C). [tex]x = 3[/tex]
D). [tex]x =[/tex] ±[tex]1[/tex]
Find the value of xa). [tex]x^2 - 11x + 31 = 1[/tex]
⇒ [tex]x^2 - 11x + 30 = 0[/tex]
by employing the quadratic equation, we have the values of [tex]x[/tex];
Considering
a = 1
b = -11
c = 30
⇒ {[tex]-(-11)[/tex] ± [tex]\sqrt{(-11)^2 -4 .1. 30 }[/tex]}[tex]/2.1[/tex]
Now,
[tex]x =[/tex] ([tex]11[/tex] ± [tex]1)/2[/tex]
Thus, the values for which the given trinomial would be equivalent to 1 would be:
∵ [tex]x = 5[/tex] and [tex]x = 6[/tex]
b). [tex]x^2 - 5x - 3 = 2x - 5[/tex]
⇒ [tex]x^2 - 5x - 2x - 3 + 5 = 0[/tex]
⇒ [tex]x^2 - 7x + 2 = 0[/tex]
by employing the quadratic equation, we have the values of [tex]x[/tex];
Therefore, the values of polynomials [tex]x^2 - 5x - 3 = 2x - 5[/tex] when:
∵ [tex]x = 0.298[/tex] or [tex]x = 6.702[/tex]
c). [tex]7x + 1 = 3x^2 - 2x + 1[/tex]
⇒ [tex]3x^2 - 2x - 7x + 1 - 1 = 0[/tex]
⇒ [tex]3x^2 - 9x = 0[/tex]
⇒ [tex]3x^2 = 9x[/tex]
by dividing both the sides by [tex]3x[/tex] to receive;
Hence, the binomial and trinomial [tex]7x + 1 = 3x^2 - 2x + 1[/tex] when:
∵ [tex]x = 3[/tex]
d). [tex]-2x^2 + 5x + 6 = 4x^2 + 5x[/tex]
by arranging them again, we get;
[tex]4x^2 + 2x^2 + 5x - 5x - 6 = 0[/tex]
⇒ [tex]6x^2 - 6 = 0[/tex]
⇒ [tex]x^2 = 6/6[/tex]
The trinomial and binomial [tex]-2x^2 + 5x + 6 = 4x^2 + 5x[/tex] would be when:
∵ [tex]x =[/tex] ±[tex]1[/tex]
Learn more about "Binomial" here:
brainly.com/question/3560614
help me pls!!!! :c rip
Answer:
p^⁴/5
Step-by-step explanation:
Step-by-step explanation:
p^4/5. I just know the answer
PLEASE HELP!!
How could writing a problem using an exponent be easier to understand than repeated multiplication?
Answer:
One reason, is because it clearer and easier to read.
Seeing two numbers (3^5) can let you know, in this example, 3x3x3x3x3 is harder to understand than 3^5.
3 is the number being multiplied, and 5 tells you how many times.
~Hope this helps~
do y’all know this one?
Step-by-step explanation:
For first triangle,
sin 45 = 3 / d
1 / root 2 = 3 / d
d = 3 root 2
For second triangle,
tan 60 = 7 / a
root 3 = 7 / a
a = 7 / root 3
Rick's cat weighs 7 pounds. His neighbor says her puppy weighs 103 ounces.
Does Rick's cat weigh more than the puppy?
1 pound = 16 ounces )
How much does Rick's cat weigh in ounces?
Answer:
1. Yes
2. 112 ounces
Step-by-step explanation:
To answer this question, we should first convert the amount of pounds Rick's cat weighs into ounces, so that both measurements are in the same unit. Since 1 pound is the same as 16 ounces, we can multiply 7 pounds by 16 ounces:
7 * 16 = 112
So, Rick's cat weighs 112 ounces, which is more than his neighbor's puppy, which only weighs 103 ounces. so for the first question, the answer is:
Yes, Rick's cat weighs more than the puppy.
And the second answer is:
Rick's cat weighs 112 ounces.
Hope this helps :)
Please answer for Brainliest.
Rotate the triangle 180 degrees around the origin
Three angles are complementary. One angle is double the smallest angle. The largest angle is
triple the smallest angle. Find the measures of
the three angles.
Answer:
Step-by-step explanation:
A+B+C = 90°
A ≤ B ≤ C
C = 3A
B = 2A
A+B+C = A + 2A + 3A = 6A = 90°
A = 15°
B = 2A = 30°
C = 3A = 45°
y = 6x - 13
5x - 2y = 5
Using the substitution method
Answer:
x=3, y=5
Step-by-step explanation:
Ben flipped a coin and got heads
7/15
of the time. If he flipped the coin 45 more times, how many times would you expect Ben to flip tails?
7
28
35
24
Answer:
28
Step-by-step explanation:
4x + 5y = 22
7x - 3y = -32
Answer:
x = -2
y = 6
Step-by-step explanation:
i multiplied the 1st equation by 3 and the 2nd by 5 to get the y-terms to zero out
12x + 15y = 66
+ 35x - 15y = -160
47x = -94
x = -94/47
x = -2
substitute -2 for 'x' to solve for 'y':
4(-2) + 5y = 22
-8 + 5y = 22
5y = 30
y = 6
what is the distance between (-1, 2) and (5, -2)on a graph put into a decimal form.
Given:
The two points are (-1,2) and (5,-2).
To find:
The distance between the given points.
Solution:
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using the distance formula, the distance between the given points is
[tex]d=\sqrt{(5-(-1))^2+(-2-2)^2}[/tex]
[tex]d=\sqrt{(5+1)^2+(-4)^2}[/tex]
[tex]d=\sqrt{(6)^2+16}[/tex]
[tex]d=\sqrt{36+16}[/tex]
On further simplification, we get
[tex]d=\sqrt{52}[/tex]
[tex]d=7.2111[/tex]
[tex]d\approx 7.21[/tex]
Therefore, the the distance between the given points is about 7.21 units.
ANSWER THESE 2 QUESTIONS FOR 100 FLIPPING POINTS :DDDD
Answer:
43.5 cm² and 112 cm²
Step-by-step explanation:
Here the instructions aren't given what to do. So I am finding the area of the ∆s .
Area of first ∆ :-
A = 1/2 * b * h A = 1/2 * 14.5 cm * 6cmA = 3 × 14.5 cm²A = 43.5 cm²Area of second ∆ :-
A = 1/2 * ( sum of || sides) * h A = 1/2 * ( 9 cm + 19cm) * 8cm A = 4cm * 28cmA = 112 cm²Answer:
[tex] \displaystyle 3) \boxed{ \rm {43.5 \: cm}^{2} }[/tex]
[tex] \displaystyle 4)\rm \boxed{112 {cm}^{2} }[/tex]
Step-by-step explanation:
Question-1:we are given a triangle and we want to figure out the area of it Since we are given the base and the height we can consider the following formula
[tex] \displaystyle \frac{1}{2} bh[/tex]
from the triangle we can assume base and height as 14.5 and 8 respectively Thus substitute:
[tex] \displaystyle \frac{1}{2} (14.5cm)(6cm)[/tex]
reduce fraction:
[tex] \displaystyle (14.5cm)(3cm)[/tex]
simplify multiplication:
[tex] \displaystyle \boxed{ \rm {43.5 \: cm}^{2} }[/tex]
Question-2:our given shape is trapezoid
therefore recall that,
[tex] \displaystyle A _{ \text{trapezoid}} = \frac{a + b}{2} h[/tex]
from the shape we define that
[tex]a = 9[/tex][tex]b = 19[/tex][tex]h = 8[/tex]now substitute:
[tex] \displaystyle \rm A _{ \text{trapezoid}} = \frac{9cm + 19cm}{2} (8cm)[/tex]
reduce fraction:
[tex] \displaystyle \rm A _{ \text{trapezoid}} = (9cm + 19cm)(4cm)[/tex]
simplify addition:
[tex] \displaystyle \rm A _{ \text{trapezoid}} = (28cm)(4cm)[/tex]
simplify multiplication:
[tex] \displaystyle \rm A _{ \text{trapezoid}} = \boxed{112 {cm}^{2} }[/tex]
Which expression is equivalent to
3x +10- x + 12?
A. 26x
B. 4x + 22
C.2x + 22
D. 24x
Answer:
2x + 22
Step-by-step explanation:
3x - (1)x = 2x
10 + 12 = 22
therefore 2x + 22 is your answer
Answer:
C
Step-by-step explanation:
subtract : 3x - x = 2x
Add : 10 + 12 = 22
Answer: 2x + 22
GIVING BRAINLIEST! The triangles below are similar. How tall is the tree? Please show process.
Answer:
18m tall?
Step-by-step explanation:
Answer:
20 m
Step-by-step explanation:
The scale factor between the two triangles is 1/10 because of how 3/30 is 1/10.
Therefore we can calculate the height of the tree by multiplying the height of the smaller triangle by 10 to find the height of the tree.
2*10 = 20m
What is the graph of the solution set of b - 42 -1?
Answer:Your answer would be F
Step-by-step explanation:
y= 2? + 16x + 64
1. Identify a, b, and c
b=
C=
ask a tutor for help with that my dude I don't know sorry
9) 8.081 +
+ 0.6 = 10.201
10)
- 3.328 = 0.96
Two rovers are exploring a planet. The system of equations below shows each rovers elevation y at time x.
brainliest for ripromano please anybody else dont answer
Answer:
ahhh you didnt have to !!
Step-by-step explanation:
thank you so much, ill do the same!! check my page for a question w free brainliest
8. Solve for x. Round to the nearest tenth. (4pts)
55°
7
x=
Answer: I think 2
Step-by-step explanation:
Because
A box of cereal contains 510 grams of cereal. To make a bowl of cereal, n grams of cereal is removed from the box. What equation models the relationship between the quantity of cereal removed, n, and the quantity of the cereal remaining in the box, b?
Answer:
its 34
Step-by-step explanation: i
someone please answerrrrrr
Given 6, 8, and 11 as the three sides of a triangle, classify it as one of the following acute, right or obtuse. Please help and thank you
9514 1404 393
Answer:
obtuse
Step-by-step explanation:
You may remember that side lengths of 3, 4, 5 make a right triangle. Doubling those lengths to 6, 8, 10 will still give a right triangle.
The given triangle has a longest side (11) longer than would be appropriate for a right triangle (10), so the largest angle is larger than 90°.
The triangle is obtuse.
__
Comparison of a triangle to a right triangle with two sides the same is one of several ways the triangle can be classified. You can use the Law of Cosines to find the largest angle, or you can use a triangle solver (as we have below).
In case you don't recall that 3-4-5 makes a right triangle, you can use the Pythagorean theorem to find the longest side of a right triangle with the given shorter sides:
hypotenuse = √(6² +8²) = √100 = 10
Your long side is longer, so your largest angle is larger than 90°.
Law of Cosines:
angle = arccos((6² +8² -11²)/(2·6·8)) = arccos(-21/96) ≈ 102.6°
PLEASE FAST ANSWER ME PLEASEEE
During the election for class president, 30% of the students voted for Ruby, and 70% of the students voted for Ellie. 500 students voted in total. How many MORE students voted for Ellie than for Ruby?
Answer:
150,350
Step-by-step explanation:
FOR RUBY:
500x30/100=150
FOR ELLIE:
500x70/100=350
Answer:
200.
Step-by-step explanation:
100%->500
1%->500÷100=5
Ruby->30%->30×5=150
Ellie->70%->70×5=350
diff->350-150=200(ans)
A metalworker has a metal alloy that is 25% copper and another alloy that is 70% copper. How many kilograms of each alloy should the metalworker combine to create 100 kg of a 61% copper alloy?
Answer:
The metal worker should use 10 kgs of 25% copper alloy and 40kgs of 70% copper alloy to make it
Step-by-step explanation:
Answer:
The metalworker should use 10 kgs of 25% copper and 40 kgs of 70% alloy to make it.
I can’t do this plz help
Write an equation where the variable is divided by a number, and a solution is -4/5
Answer:
x/-5
Step-by-step explanation:
Just divide by 5 and the denominator will be 5 meaning x would have to be 4.
Make sure your 5 is negative so the whole equation also ends up negative. x/-5=-4/5
What is the value of each expression?
7/8 + 4/8
Answer:
7/8 + 4/8 = 1 3/8.
Step-by-step explanation:
In words the answer is 1 and 3/8.
What do studies tell about people's way of life in traditional societies??
(Note: Please don't give me silly answer)
Step-by-step explanation:
buffet or tells about the beliefs values behaviour and material object that constitute a people's way of life
Answer:
In sociology, traditional society refers to a society characterized by an orientation to the past, not the future, with a predominant role for custom and habit. Such societies are marked by a lack of distinction between family and business, with the division of labor influenced primarily by age, gender, and status.
Step-by-step explanation:
Hope it is helpful.....
someone pls help:>>
Explanation:
Imagine that you cross out the top-most square for each step of each diagram. The squares not crossed out have the following counts: 1, 4, 9
This is the sequence of perfect squares. So the rule will have us take the number n, and square it to get n^2. Then we add on the squares we crossed out earlier. This explains the "plus 1" at the end to get the answer of n^2+1
Answer:
[tex] {n}^{2} + 1 \\ \: respresents \: the \: following \: \\ function[/tex]
i hope it helped.