Answer:
The solutions are:
[tex]x=\frac{7-\sqrt{17}}{2},\:x=\frac{7+\sqrt{17}}{2}[/tex]
Step-by-step explanation:
Given the quadratic equation
-x² + 7x = 8
Solving using the quadratic formula
[tex]-x^2+7x=8[/tex]
Subtract 8 from both sides
[tex]-x^2+7x-8=8-8[/tex]
Simplify
[tex]-x^2+7x-8=0[/tex]
For a quadratic function of the form ax² + bx + c = 0, the solutions are:
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
For a = -1, b = 7, c = -8
[tex]x_{1,\:2}=\frac{-7\pm \sqrt{7^2-4\left(-1\right)\left(-8\right)}}{2\left(-1\right)}[/tex]
[tex]x_{1,\:2}=\frac{-7\pm \:\sqrt{49-32}}{2\left(-1\right)}[/tex]
[tex]x_{1,\:2}=\frac{-7\pm \sqrt{17}}{2\left(-1\right)}[/tex]
Separate the solutions
[tex]x_1=\frac{-7+\sqrt{17}}{2\left(-1\right)},\:x_2=\frac{-7-\sqrt{17}}{2\left(-1\right)}v[/tex]
solving
[tex]x_1=\frac{-7+\sqrt{17}}{2\left(-1\right)}[/tex]
[tex]=\frac{-7+\sqrt{17}}{-2}[/tex]
Apply the fraction rule: [tex]\frac{-a}{-b}=\frac{a}{b}[/tex]
i.e. [tex]-7+\sqrt{17}=-\left(7-\sqrt{17}\right)[/tex]
so
[tex]=\frac{7-\sqrt{17}}{2}[/tex]
Similarly solving
[tex]x_2=\frac{-7-\sqrt{17}}{2\left(-1\right)}[/tex]
[tex]=\frac{-7-\sqrt{17}}{-2\cdot \:1}[/tex]
Apply the fraction rule: [tex]\frac{-a}{-b}=\frac{a}{b}[/tex]
i.e. [tex]-7-\sqrt{17}=-\left(7+ \sqrt{17}\right)[/tex]
[tex]=\frac{7+\sqrt{17}}{2}[/tex]
Therefore, the solutions are:
[tex]x=\frac{7-\sqrt{17}}{2},\:x=\frac{7+\sqrt{17}}{2}[/tex]
At a country music concert 48 people played guitars. That number is 6 times as many as the number of people who played banjos. How many people played banjos?
Answer:
8
Step-by-step explanation:
48 divided by 6 is 8
Answer:
8
Step-by-step explanation:
48/6=8
Please help!! BRAINLIEST to correct answer!!
Answer:
Let us use Pythagoras theorem Hence [tex] {4}^{2} + {b}^{2} = {10}^{2} [/tex][tex]16 + {b}^{2} = 100[/tex][tex] {b}^{2} = 84[/tex][tex]b = \sqrt{84} [/tex][tex]b = 9.16[/tex]So Option A6c – 7 + d + 4 – 6d combine like terms
Answer:
6c-5d-3
Step-by-step explanation:
6c-7+d+4-6d=6c-5d-3
Write the equation of a line with points (2, - 4) and (4, 2) in slope-intercept form
Answer:
y+4=3(x-2)
..
.
.
PLEASE HELP WILL GIVE BRAINLIEST!!!
Answer:
sas
i don't think so
0œ ßægœ5 kœ
really need help asap
A pair of fire towers uses technology to search for forest fires. Let the center of the forest be the origin on a coordinate grid. The first fire tower is located 5 km east and 8 km south of the center, and the second fire tower is located 7 km west and 4 km north of the center. The technology at the first tower can locate fires within a radius of 10 km and the second tower within a radius of 9 km. The system of inequalities represents this scenario.
StartLayout Enlarged left-brace first row (x minus 5) squared + (y + 8) squared less-than-or-equal-to 100 second row (x + 7) squared + (y minus 4) squared less-than-or-equal-to 81 EndLayout
At which location, from the origin, would a fire be detected by both towers?
2 km east and 3 km south
3 km east and 2 km north
2 km west and 1 km north
1 km west and 2 km south
Answer:
the answer is D 1km west and 2km south
Step-by-step explanation:
Just took the test 100%
please help me thank you
Answer:
the answer is A
Step-by-step explanation:
Answer:
your answer would be 84 simplify 2
Step-by-step explanation:
The area of a right triangle is 30 square inches and the length of one of the legs is 5 inches. What is the length of
the other leg?
Answer:
it might be 6 inches
Step-by-step explanation:
Answer:
It is 6 inches
Step-by-step explanation:
well 5x6= 30 which is what the right triangle equals 30=30
50 POINTS PLEASE HELP ASAP IF CORRECT WILL GIVE BRAINLYIST
Answer:
1: (5,-2) 16
2: (-2,2) √3
3: (-14,21) 2
4: (-7,10) √8
5: (2/3,17) √5
Step-by-step explanation:
I’ll give brainlist if u answer with evidence
Answer:
The answer is 17/36
Step-by-step explanation:
First you multiply 1/4 times 9/9 and you get 9/36. Then you multiply 2/9 times 4/4 and you would get 8/36 and 8/36 + 9/36=17/36.
chicken tenders or chicken nuggets
Answer:
i dont know which one to choose but chicken tenders
Answer:
Chicken tenders.
Step-by-step explanation:
Chicken nuggets are the gross consumption of organs including lungs and others mushed together and fried. In return kids run to it because (most) kids only eat gross stuff. This made the marketing campaign SKY ROCKET with kids everywhere trying to get a bite. FORCING their poor parents to get them that disgusting mush. And then dip it in ketchup. Which is NOT a fruit or veggie. (As the school system thinks they are a veggie.)
While chicken tenders are chopped off the chicken meat then rolled in bread crumbs. And then deep fried to make a crispy exterior with a delicious tender interior. Without getting mushed together with other things.
Also you never know what they put in that chicken nugget since its mushed together ♀️.
Solve for the roots in simplest form using the quadratic formula:
x^2 + 61 =-10x
9514 1404 393
Answer:
-5 ± 6i
Step-by-step explanation:
To use the quadratic formula, we need the equation in standard form. Adding 10x gives ...
x^2 +10x +61 = 0
Then a=1, b=10, c=61, and the solutions are ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-10\pm\sqrt{10^2-4(1)(61)}}{2(1)}\\\\=\dfrac{-10\pm\sqrt{-144}}{2}=\dfrac{-10\pm12i}{2}\\\\ \boxed{x=\{-5-6i,-6+6i\}}[/tex]
Larissa dives into a pool that is 8 feet deep. She touches the bottom of the pool with her hands 6 feet horizontally from the point at which she entered the water. What is the approximate angle of elevation from the point on the bottom of the pool where she touched to her entry point? 36.9° 41.4° 48.6° 53.1
The approximate angle of elevation from the point on the bottom is; D: 53.1°
What is the angle of elevation?We are told she dived into a pool that is 8 ft deep.
Now, she could touch the bottom with her hands 6 ft horizontally. Thus;
We can use trigonometric ratio to determine the approximate angle of elevation from the point on the bottom of the pool where she touched to her entry point.
If the angle of elevation is θ, then we have;
θ = tan⁻¹(8/6)
θ = 53.1°
Read more about angle of elevation at; https://brainly.com/question/15580615
M is the midpoint solve for x
Answer:
x = 3
Step-by-step explanation:
5x + 9 = 24
5x = 24 - 9
5x = 15
x = 3
Check:
5(3) + 9 = 24
SM = 24, MT = 24 ✔️
Answer:
Step-by-step explanation:
If M is the midpoint between points S and T, then both sides; SM and ST are equal. This means that 5x + 9 has to equal 24.
5x + 9= 24
5x +9 - 9= 24 - 9
5x= 15
5x / 5 = 15 / 5
x = 3
ANSWER: x = 3
I JUST NEED THE EQUATION!!!!!!!!!!!!!
Answer:
The equation is 24 - y = 45
I need help pleasee
Answer:
c is the answer
explination:
4*3 1/2=28/2
28/2 divided by 6 is equal to 7/3 or 2 1/3
PLS HELP ME ON THIS ASAP!!!!
Answer:
a = upward
vertex = -2,4
Step-by-step explanation:
i will answer the rest under comments
The expression 42 + 57 shows how much money Nate spent at the store. Which expression also shows how much money Nate spent ?
Answer: See explanation
Step-by-step explanation:
You didn't give the options but let me help out. We are informed that he expression 42 + 57 shows how much money Nate spent at the store. This means that she spent (42 + 57) = 99.
The expression that also shows how much money Nate spent would be a number that when you add will give you 99. This will be
• 66 + 33
• 22 + 77
• 40 + 59 etc
Proportional?
Non-proportional?
Answer:
Non-proportional
Step-by-step explanation:
Cross-Multiply
can someone answer my last question please- its due today
Answer:
you would solve D first.
0.545
Convert to fraction
Answer:
109/200
Step-by-step explanation:
write 2x + y= 9 in the form of y=mx + b
Step-by-step explanation:
2x+y=9 ( y=mx+b)
y=-2x+9
sorry...if its wrong
what is 28 divided by 5 5/6
One sixth of the candies in a bag of M&M's are
orange. If there are 15 orange candies, how many
M&M's are in the bag?
Answer:
90 candies
Step-by-step explanation:
15/ 1/6=90
90*1/6=15
Answer:
90
Step-by-step explanation:
Let x = number of M&M's in the bag
(1/6) * x = 15 [in word (story) problems, "of" usually means multiply]
x = 90 [multiply both sides by 6]
Giving brainliest !!!!!!
The equation is basically saying
distance/3
Therefore, to replace the word "distance" you would use d
The answer is ( B. d )
Simplify the expression. Write your answer as a power.
(-2.9) x (-2.9)^7
(The seven is the exponent btw)
Answer:
5002.46412961
Step-by-step explanation:
-3 |x-3|+3=6
Please hell!
Frank goes to the library to check out books each week. If he checks out x number of
books each week, which expression can be used to find how many books he checks out
in 6 weeks?
A. x + 6
B. X-6
X-6
C. 6 x
D. x divided by6
Answer:
c is your answer
Step-by-step explanation:
x is the books per week
2x in 2 weeks
3x in 3 weeks .....
Jeff traveled at an average speed of 65 miles per hour for 2.5 hours and then traveled at an average speed of 70 miles per hour for 1.5 hours. What was the total distance in miles that Jeff traveled during this time?
Answer:
267.5 miles
Step-by-step explanation:
We start with the formula for speed:
speed = distance/time
Now we solve it for distance:
distance = speed * time
65 mph for 2.5 hours + 70 mph for 1.5 hours
distance = 65 * 2.5 + 70 * 1.5
distance = 162.5 + 105
distance = 267.5
Answer: 267.5 miles
Answer:
what they said..
Step-by-step explanation:
what is 2 8/15+ 1 1/30
Answer:
3 17/30
Step-by-step explanation:
In order to do this problem, we have to get the two fractions to have the same denominator
So we change 2 8/15 into 2 16/30 (multiplying both the numerator by 2, if you don't know why this works then ask me) and then we just add. So 2 16/30 + 1 1/30 = 3 17/30