Answer:
I)
[tex]2a + 2b = -10\text{ or } 2a + 2b = 10[/tex]
II)
[tex]2a - 2b = -2 \text{ or } 2a-2b= 2[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaytstyle a^2 + b^2 = 13 \text{ and } ab= 6[/tex]
I)
Recall the perfect square trinomial pattern:
[tex]\displaystyle (a+b)^2 = a^2 + 2ab + b^2[/tex]
Rewrite:
[tex]\displaystyle (a+b)^2 = (a^2 + b^2) + (2ab)[/tex]
Substitute:
[tex]\displaystyle (a+b)^2 = (13) + (12)[/tex]
Evaluate:
[tex]\displaystyle (a + b)^2 = 25[/tex]
Take the square root of both sides:
[tex]\displaystyle a + b = \pm\sqrt{25} = \pm5[/tex]
Hence:
[tex]\displaystyle 2a + 2b = \pm 10[/tex]
Therefore:
[tex]\displaystyle 2a + 2b = -10 \text{ or } 2a + 2b = 10[/tex]
II)
Likewise:
[tex]\displaystyle (a-b)^2 = a^2 - 2ab + b^2[/tex]
Substitute:
[tex]\displaystyle (a-b)^2 = (13) -(12)[/tex]
Solve:
[tex]\displaystyle \begin{aligned} (a-b)^2 &= 1 \\ a-b &= \pm \sqrt{1} \\ a-b &= \pm 1\\ 2a - 2b &= \pm 2\end{aligned}[/tex]
In conclusion:
[tex]2a - 2b = -2 \text{ or } 2a-2b= 2[/tex]
12 less than 10 times a number x
Step-by-step explanation:
10x-12 is the equation form
SOMEONE HELP ME PLEASE
Answer: D,E,F
Step-by-step explanation:
collinear means points on the same line
a=23 an= 5 n=10 find d
Answer:
d=-2
Step-by-step explanation:
a10=5, a10=a+(10-1)d
5=23+9d, d=-2
Answer:
d is -2
Step-by-step explanation:
From arithmetic progression:
[tex]{ \bf{a_{n} = a + (n - 1)d }}[/tex]
substitute:
[tex]{ \sf{5 = 23 + (10 - 1)d}} \\ { \sf{5 - 23 = 9d}} \\ { \sf{9d = - 18}} \\ { \sf{d = \frac{ - 18}{9} }} \\ \\ { \sf{d = - 2}}[/tex]
Pls Solve
4x+16=x+166
Answer:
50
Step-by-step explanation:
4x+16=x+166
-x -x
3x+16=166
-16 -16
3x=150
/3 /3
x=50
Answer :
• 50
Step-by-step explanation:
4x + 16 = x + 1664x - x = 166 - 16 (Subsituation )3x = 150x = 150 / 3x = 50 !What is one of the best ways to stop procrastinating and study More
Answer:
use the two minute rule. you tell yourself you will study for two minutes or ten minutes and then if you're in a flow you keep going. hope this helps :)
Fill in the blank to complete this trig
ratio.
y
sin a =
[?]
a
Х
N
A
00
С
Х
У
N
Answer:
Z/X
Step-by-step explanation:
cause sin is p/h and p=Z and h=X
[tex] \displaystyle \large \tt{ \sin a = \frac{opposite}{hypotenuse} }[/tex]
First, we have to focus on ∠a, at the angle a or ∠a, the opposite is z because ∠a is the opposite side of z.
The hypotenuse side is always x, even if we change from ∠a to ∠b (b = 90°-a)
So what we have now are:
opposite = z (Refer to the bold text)hypotenuse = x (hypotenuse is always the side that is opposed to a right angle.)Substitute the letter in the ratio:
[tex] \displaystyle \large \boxed{ \sin a = \frac{z}{x} }[/tex]
PLS HELP I WILL MARK THE CORRECT ANSWER BRAINLIEST !!!!!!! PLS HELP IMAGE INCLUDED!!!!!!
Help
When i
is written as a decimal, how many digits are in the smallest sequence of repeating
digits?
OA) 3
B) 2
OC) 1
D) 0
Trang can run up a hill at 3 m/s and down the hill at 7 m/s. It takes her 60 seconds in total to
run up and then down the hill. What distance does she cover going from the bottom to the
top of the hill?
Please step by step explanation:)
Answer:
d=126 (m)
Step-by-step explanation:
Let say:
d the distance from the bottom to the top
t1 the time used for running up
t2 the time for running down
[tex]\left\{\begin{array}{ccc}d&=&3*t_1\\d&=&7*t_2\\t_1+t_2&=&60\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}d&=&3*t_1\\t_2&=&\dfrac{3}{7} t_1\\t_1+\dfrac{3}{7} t_1&=&60\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}t_1&=&\dfrac{60*7}{10}=42 \\\\t_2&=&\dfrac{3*42}{7}=18\\\\d&=&3*42=126\\\end{array}\right.\\[/tex]
6 . The scale of a map is 1: 250 000. (a) The actual distance between two cities is 80 km. Calculate this distance on the map. Give your answer in centimeters. (b) On the map a large forest has an area of 6 cm?. Calculate the actual area of the forest. Give your answer in Square kilometres.
Answer:
The scale of a map is 1:250000.The actual distance between two cities is 80 km. Calculate this distance on the map. Give your answer in centimetre
Step-by-step explanation:
1 m = 100 cm
1 km = 1000 m = 100 000 cm
1:250 000 mean that 1 cm on the map represents an actual distance of 250 000 cm = 2.5 km
1:250 000 = 2.5 km / cm
80 km / 2.5 km / cm = 32 cm
OR
80 km = 8 000 000 cm
8 000 000 cm ∙ 1 / 250 000 = 8 000 000 cm / 250 000 = 32 cm
A bag contains green balls and red balls only A ball is taken at random from the bag The probability of taking a green ball is 0.38 Write down the probability of taking a red ball and a blue ball
Answer:
blue ball is zero, red ball is 1-0.38=0.62
Step-by-step explanation:
1. no blue balls
2. probabilities have to add to 100%
I need some help on 9 and 10
Answer:
Step-by-step explanation:
9
The angles are vertically opposite. Vertically opposite angles are equal.
12x - 5 = 10x + 1 Add 5 to both sides.
12x = 10x + 5 + 1 Combine
12x = 10x + 6 Subtract 10x from both sides.
12x - 10x = 6 Combine
2x = 6 Divide by 2
x = 6/2
x = 3
10
Adjacent angles to each other when sharing a side are supplementary
4x + 7 + 2x + 5 = 180 Combine like terms on the left
6x + 12 = 180 Subtract 12 from both sides
6x = 180 - 12 Combine
6x = 168 Divide by 6
x = 168 / 6
x = 28
Please help me I will mark brainliest :)
Answer:
X should equal 12.
Step-by-step explanation:
I say this because we know TED= 30° bc 50°-20° = 30
then u have to think about what × 2 + 6 equals 30
sure enough 12 × 2 = 24 and 24 + 6 = 30
that's why I say X equals 12
is 2/3 rational is 3.1415926535 rational
Answer:
yes 2/3 is rational.
Step-by-step explanation:
please mark me brain list
Cody stamped 460 envelopes in 30 minutes. How many envelopes per minute did Cody stamp?
Answer:
15 1/3 envelopes in 1 minutes
Step-by-step explanation:
Take the number of envelopes and divide by the number of minutes
460 envelopes / 30 minutes
15.333333.... envelopes per minute
15 1/3 envelopes in 1 minutes
Divide. Write your answer as a fraction in simplest form. − 7 1/0÷2/5=
Answer:
-71/4
Step-by-step explanation:
the diagrams below show the numbers in base two which are arranged in few rows
let x is equalbut if you quality I and Y is equal to 80 ft decide that young (a minus b is equal to young) a greatest loss - 1 (a intersection b) close
The difference of -13 and 8 multiplied by the square of 4
I need help asap plz.
Answer:
» [tex]❎ \: f( \frac{ - 1}{2} ) = - 2 [/tex]
when x is -½, f(x) is 5/4.
» [tex]{ \boxed{✔}} \: f(0) = \frac{3}{2} [/tex]
check second row.
» [tex] ❎ \: f(1) = - 1[/tex]
f(1) is 2
» [tex]❎ \: \: f(2) = 1[/tex]
f(2) is 5/2
» [tex]{ \boxed{✔}} \: f(4) = \frac{7}{2} [/tex]
Answer:
B. f(0) = 3/2 and E f(4) = 7/2Step-by-step explanation:
Given function:
f(x) = 1/2x + 3/2Find the following:
f(-1/2) = 1/2(-1/2) + 3/2 = -1/4 + 6/4 = 5/4, incorrectf(0) = 3/2, given in the table, correctf(1) = 2, given in the table, incorrectf(2) = 5/2, given in the table, incorrectf(4) = 1/2(4) + 3/2 = 2 + 3/2 = 7/2, correctCorrect choices:
f(0) = 3/2f(4) = 7/2Kevin buys eggs and potatoes at the store.
He pays a total of $25.98.
He pays a total of $6.46 for the eggs.
He buys 4 bags of potatoes that each cost the same amount.
How much does each bag of potatoes cost?
Determine the name of the polygon formed by the points below.
A(5,-1),B(0,5),C(4,5),D(-2,-1)
No spams.Answer should be well explained .Attach a diagram or graph of it .
Answer:
Given
Points A(5,-1),B(0,5),C(4,5),D(-2,-1)Plot the points and connect to get a trapezoid (attached).
Just consider this is going to be ACBD according to coordinates.
Step-by-step explanation:
Given points are A(5,-1), B(0,5), C(4,5) and D(-2,-1)
When the given points are plotted on a graph paper and are connected. Then the formed polygon is trapezoid.
1. Find the distance between the pair of points: (-8, -2) and (-4,5)
Hi, I'm happy to help!
To solve, this, we need to find the distance in x coordinates, y coordinates, then use the Pythagorean Theorem, let's solve!
First, we have to find the distance in x coordinate values. The first coordinate is -8, and the second is -4, which means there is an x distance of 4.
Next, we need to find the distance in y coordinate values. The first coordinate is -2, and the second is 5, meaning there is a y distance of 7.
From here, we use the Pythagorean Theorem. This states that a²+b²=c².
This applies to right triangles, which is what we have. The x distance is a, the y distance is b, and the overall distance is c. We need to find c to answer the question. Let's plug in our values:
4²+7²=c²
16+49=c²
65=c²
To find c, we need to find the square root of 65.
√65
8.0622577...
Rounding to the nearest tenth is 8.1.
The distance between the two points is about 8.1.
I hope this was helpful, keep learning! :D
Evaluate
15
r
−
1
r
15
−1start fraction, 15, divided by, r, end fraction, minus, 1 when
r
=
5
r=5r, equals, 5.
Answer:
do you have a photo that makes it easier?
A clothing company buys t-shirts for $10 and sells them for $100. What is the percentage mark up on
t-shirts? Make sure you show at least one step of working
Answer:
900%
Step-by-step explanation:
Starting price : 10
End price: 100
100-10 = 90
90/10 = 9 = 900%
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
can anyone solve this question
Answer:
12 in Mathematics and 16 in Science
Step-by-step explanation:
12+16=28
12+3=15 and 16-4=12
15*12=180
Answer:
He got 12 marks in mathematics and 16 in science.
Step-by-step explanation:
M + S = 28, (M + 3)(S - 4) = 180.
(M + 3)(S - 4) = MS - 4M + 3S - 12 = 180
MS - 4M + 3S - 12 = 180
MS - 4M + 3S = 192
M + S = 28
S = 28 - M
M(28 - M) - 4M + 3(28 - M) = 192
28M - [tex]M^{2}[/tex] - 4M + 84 - 3M = 192
-[tex]M^{2}[/tex] + 21M = 108
-[tex]M^{2}[/tex] + 21M - 108 = 0
(-M + 9)(M - 12) = 0
M = -9, 12
S = 37, 16
1st solution:
(-9 + 3)(37 - 4) = 180
-6 * 33 = 180
-198 = 180
2nd solution:
(12 + 3)(16 - 4) = 180
15 * 12 = 180
180 = 180
Therefore, M = 12 and S = 16.
use the diagram on the right. How many planes contain both the line and the point
a. FG and point P
b. EP and point G
Part (a)
Answer: 0-------------------
Explanation:
Point P is part of 3 planes or faces of this triangular prism:
plane PEF (the front slanted plane)plane PEH (the left triangular face)plane PHG (the back rectangular wall)Notice how each three letter sequence involves "P", though this isn't technically always necessary. I did so to emphasize how point P is involved with these planes.
Each of the three planes mentioned do not involve line FG
Plane PEF only deals with point FPlane PEH doesn't have any of F or G involvedplane PHG only involves GSo there are no planes that contain line FG and point P.
==================================================
Part (b)
Answer: 0-------------------
Explanation:
It's the same idea as part (a) earlier. The planes involving point G are
plane GQF (triangular face on the right)plane GFE (bottom rectangular floor)plane GHP (back rectangular wall)None of these planes have line EP going through them.
As an alternative, we could reverse things and focus on all of the planes connected to line EP. Those 2 planes are
plane PEH (triangular face on the left)plane PEF (front slanted rectangular face)None of these planes have point G located in them.
What is the degree of 5xpower2+6xpower2+7ypower2
Answer:
7
Step-by-step explanation:
Explanation:
6x5+5x4−3x2+x7
Multiply (-4) (-2) (-5)
-40
-8
8
40
Answer:
your answer is -40
I hope it's helps you
Answer:
-40
Step-by-step explanation:
-4*-2*-5
+8*-5
-40
-*-=+
-*+=-
If your gross monthly income will be $3,750, you need to determine the net pay for your monthly budget.
Your monthly net pay is
Answer:
The correct answer to the given question is $2,989.12. The monthly net pay is $2,989.12, when the gross monthly income is $3,750.
Thank You
Answer: correct answer is 2,989.12
Step-by-step explanation:
6.55743... is an irrational number because it is an
a terminating decimal
a repeating decimal
a non-terminating and non-repeating decimal
a non-repeating decimal
a non-terminating decimal
Answer:
#3. a non-terminating and non-repeating
Step-by-step explanation:
6.55743... never ends and it never repeats either
Answer:
Not terminating but doesn't repeat either
Step-by-step explanation: