Answer:
[tex]x=\frac{-b\pm \sqrt{b^{2}-4ac } }{2a}[/tex]
Step-by-step explanation:
If a quadratic equation is in the form of ax²+ bx + c = 0
Then the roots of this quadratic equation can be obtained by,
1). Factoring the expression.
2). By quadratic formula.
If we use the method to get the value of x or roots of the equation,
x = [tex]\frac{-b\pm \sqrt{b^{2}-4ac } }{2a}[/tex]
where a, b and c are the coefficients used in the quadratic equation.
What's the perimeter of rectangle DEFG, shown? A) 17 B) 28 C) 40 D) 34
Answer:
[tex]\huge\boxed{Perimeter = 34\ units}[/tex]
Step-by-step explanation:
DE = 10 units
GF = 10 units
DG = 7 units
EF = 7 units
Perimeter of rectangle = Sum of all sides
P = DE + GF + DG + EF
P = 10 + 10 + 7 + 7
Perimeter = 34 units
Answer:
D) 34 units
Step-by-step explanation:
Coordinates:
D: (-5,4)
E: (5,4)
F: (5, -3)
G: (-5,-3)
Distance between points D and E = Distance between points F and G = 10
Distance between points E and F = Distance between points G and D = 7
Formula for perimeter of your rectangle:
2(x) + 2(y) =
2(10) + 2(7) =
20 + 14 = 34 units
That's your answer!
Hope that helps and maybe earns a brainliest!
Have a terrific day! > <
U
Find the distance between (-5,-6) and (-3,-8 WILL GIVEBRANLIEST TO FIRST PERSON WHO AWNSES WITH EXPLANATION
Answer:
d = √8
d ≈ 2.82843
Step-by-step explanation:
Distance Formula: [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Simply plug in our coordinates into the distance formula:
[tex]d = \sqrt{(-3 + 5)^2+(-8 + 6)^2}[/tex]
[tex]d = \sqrt{(2)^2+(-2)^2}[/tex]
[tex]d = \sqrt{4+4}[/tex]
[tex]d = \sqrt{8}[/tex]
To find the decimal, simply evaluate the square root:
√8 = 2.82843
Answer:
[tex] \boxed{2 \sqrt{2} \: \: units}[/tex]Step-by-step explanation:
Let the points be A and B
A ( - 5 , - 6 ) ⇒ ( x₁ , y₁ )
B ( -3 , - 8 )⇒( x₂ , y₂ )
Now, let's find the distance between these two points:
AB = [tex] \mathsf{ \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }[/tex]
Plug the values
⇒[tex] \mathsf{ \sqrt{( - 3 - ( - 5) )^{2} + {( - 8 - ( - 6))}^{2} } }[/tex]
When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression
⇒[tex] \mathsf{ \sqrt{ {( - 3 + 5)}^{2} + {( - 8 + 6)}^{2} } }[/tex]
Calculate
⇒[tex] \mathsf{ \sqrt{ {(2)}^{2} + {( - 2)}^{2} } }[/tex]
Evaluate the power
⇒[tex] \mathsf{ \sqrt{4 + 4} }[/tex]
Add the numbers
⇒[tex] \mathsf{\sqrt{8} }[/tex]
Simplify the radical expression
⇒[tex] \mathsf{ \sqrt{2 \times 2 \times 2}} [/tex]
⇒[tex] \mathsf{2 \sqrt{2} }[/tex] units
Hope I helped!
Best regards!
Using the function f(x)=-x^2+8x-13 find f(4)
Answer:
f(4) = 3
Step-by-step explanation:
f(x) = -[tex]x^{2}[/tex] + 8x - 13
To find f(4), substitute 4 for all instances of x:
f(4) = -(4[tex])^{2}[/tex] + 8(4) - 13
Simplify the exponent:
f(4) = -16 + 8(4) - 13
Multiply:
f(4) = -16 + 32 - 13
Combine terms:
f(4) = 3
Answer:
3
Step-by-step explanation:
You plug in 4.
f(4)= -(4)^2+8(4)-13
f(4)= -16+32-13
f(4)= 16-13
f(4)=3
What is - 15 +6f = 5
Answer:
f = 10/3
Step-by-step explanation:
-15 + 6f = 5
-15 + 15 + 6f = 5 + 15
6f = 20
6f/6 = 20/6
f = 20/6 = 10/3 = 3.333...
Answer:
10/3
Step-by-step explanation:
-15+6f=5
6f=5-(-15)
6f=5+15
6f=20
f=20/6
simplify
f=10/3
Which scatterplot shows the strongest negative linear association? On a graph, points are grouped closely together and increase. On a graph, points are grouped closely together to form a line and increase. On a graph, points are grouped closely together and decrease. On a graph, points are grouped closely together to form a line and decrease.
On a graph, points are grouped closely together to form a line and decrease.
====================================
Explanation:
Negative association is where the points decrease as you move from left to right. In other words, you move downhill as you move from left to right. There could be random upward bumps here and there, but overall the general trend is down.
Linear association is when the points are close to the same straight line, known as the regression line.
When points have strong negative linear association, we combine the two ideas mentioned above. The points are close to the same straight line and this line has a negative slope. The correlation coefficient r is close to r = -1.
Choice C is a close answer, but choice D is the better answer due to the "to form a line". If all points are on the same straight line, then r = -1 exactly and we have the strongest possible negative correlation.
The strongest negative linear association is depicted by the graph where points are grouped closely together to form a line and decrease.
Linear associations are deduced from a graph when the points are grouped closely together to form a line. Then we have a strong linear association. Negative association are deduced from a graph when the slope of the line decreasesTherefore, a graph with closely grouped points which forms a line and decreases infers a strong negative linear association.
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What is the range of possible sizes for side x?
8.0
2.5
Please helpp!!
Triangle inequality theorem:
In any triangle, the length of any side must be:
less than the sum of the lengths of the other two sides.greater than the difference of the lengths of the other two sides.For the problem you have:
x must be greater than 8.0 - 2.5 and less than 8.0 + 2.5
5.5 < x < 10.5
Answer:
5.5<x<10.5
Step-by-step explanation:
Kitty buys hot chocolate sachets. There are 14 hot chocolate sachets in a small box. A small box costs £3.49. Kitty uses 3 hot chocolate sachets each day. Work out the how much Kitty spends on hot chocolate sachets in a four-week period.
Answer:
24.43
Step-by-step explanation:
first find the price of One sachets
next Find the no. of sachets consumed for four weeks..
and at last the product of the price of one sachet and no. of sachets consumed will give the answer...
Mathematical operation are above...
If you transform x2 + y2 = 25 into 4x2 + 4y2 = 25, which option below describes the effect of this transformation on the radius? A. It multiplies the radius by 2. B.It multiplies the radius by 4. C.It divides the radius by 4. D.It divides the radius by 2.
Answer:
C. It divides the radius by 4.
Step-by-step explanation:
We have x2 + y2 = 25.
If all terms were multiplied by 4, we would have 4x2 + 4y2 = 100. But, the radius is 25 units. 100 / 25 = 4. So, the radius was divided by 4.
Hope this helps!
GUYS PLEASE HELP WILL MARK BRAINLIEST
Answer:
14 yards²
Step-by-step explanation:
To find the area of this complex shape, we can break it down into two parts.
I've broken it down into the left shape (with side lengths of 2, 2, 4 and 4) and the right shape (with side lengths of 2, 2, 2 and 3).
Looking at the shape on the left, the width is 4 yards and the length is 2 yards. Multiplying these numbers will get the area for that shape.
[tex]2\cdot4=8[/tex] yards².
Now in the right shape, the length is 3 and the width is 2, so:
[tex]3\cdot2=6[/tex] yards².
Now we can add both of these to get the total area of the figure.
[tex]6+8=14[/tex] yards².
Hope this helped!
Answer:
14 yds^2
Step-by-step explanation:
We can split this into two rectangles
There is a vertical rectangle on the left, 4 yds by 2 yds
The area is 4*2 = 8 yd^2
There is a horizontal rectangle on the right 3 yds by 2 yds
The area is 3*2 = 6 yd ^2
Add the areas together
8+6 = 14
Calculate the area of the circle to the nearest hundredth of a square unit. Approximate as 3.14. a. 124.63 cm 2 b. 124.6 cm 2 c. 39.56 cm 2 d.19.78 cm 2
Answer:
[tex]124.63[/tex]
Step-by-step explanation:
[tex]a = \pi \times r {}^{2} = \pi \times (6.3) {}^{2} = \pi \times 39.69[/tex]
[tex]\pi \times 39.6 = 3.14 \times 39.69 = 124.63[/tex]
Hope this helps ;) ❤️❤️❤️
The area of circle will be;
⇒ 124.63 cm²
What is Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The radius of circle = 6.3 cm
Now,
Since, The radius of circle = 6.3 cm
We know that;
Area of circle = π r²
Hence, We get;
⇒ Area of circle = 3.14 × 6.3²
= 3.14 × 39.69
= 124.63 cm²
Thus, The area of circle will be;
⇒ 124.63 cm²
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Find the area of the ACTUAL gym
Step-by-step explanation:
The three main types of exercise are cardiovascular exercise, strength training and stretching. All three types of exercise are important for physical fitness. Cardiovascular aerobic exercise is repetitive, rhythmic exercise that increases your heart rate and requires you to use more oxygen.
Answer:
6.67
Step-by-step explanation:
write the fraction for each of the following do number 3 and 4 thanks
Answer:
7
Step-by-step explanation:
22% of $900 = twenty two percent of $900 =
━━━━━━━☆☆━━━━━━━
▹ Answer
$198
▹ Step-by-Step Explanation
[tex]\frac{22}{100} * 900\\\\\frac{22}{1} * 9 = \frac{198}{1} \\\\= 198[/tex]
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
198
Step-by-step explanation:
22% of 900
22% * 900
Change to decimal form
.22 * 900
198
PLS PLEASE HELP!!!!!!
Evaluate 18 + 4 ÷ 2 − 8. (5 points) 2 8 12 3
18 + 4 ÷ 2 − 8
Following PEDMAS, divide first:
18 + 2 -8
Now add and subtract to get the final answer:
18+2 = 20
20-8 = 12
The answer is 12
Answer:
12
Step-by-step explanation:
solve the following problem (1+5^2)-16(1/2)^3
Answer:
24
Step-by-step explanation:
Using PEMDAS, we know to solve exponents before everything else.
So:
[tex](1+5^2)-16(\frac{1}{2})^3 = (1+25) - 16(\frac{1}{8} )\\\\26 - 2\\24[/tex]
Hope this helped!
Answer:
24
Step-by-step explanation:
(1+5^2)-16(1/2)^3
simplify
(1+25)-16(1/8)
simplify
26-2
simplify
24
A building casts a 33-m shadow when the sun is at an angle of 27° the vertical. How tall is the building to the
nearest meter? How far is it from the top of the building to the tip of the shadow?
Answer:
1. EF = 65m
2. DF = 73m
Step-by-step explanation:
1. EF = height of the building = h = 33 / tan 27 = 65m
2. DF = sqrt (65² + 33²) = 73m
The building is 64.76 meters long and 73 meters far from the top of the building to the tip of the shadow.
From the triangle DEF, we find the value of EF by using tan function.
tan function is a ratio of opposite side and adjacent side.
tan(27)= 33/FE
0.5095 = 33/FE
Apply cross multiplication:
FE=33/0.5095
FE=64.76
Now DF is the hypotenuse, we find it by using pythagoras theorem.
DF²=DE²+EF²
DF²=33²+64.76²
DF²=1089+4193.85
DF²=5282.85
Take square root on both sides:
DF=72.68
In a triangle the the sum of three angles is 180 degrees.
∠D + 27 +90 =180
∠D + 117 =180
Subtract 117 from both sides:
∠D =63 degrees.
Hence, the building is 64.76 meters long and 73 meters far from the top of the building to the tip of the shadow.
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Round 18.049 to the nearest tenth.
Answer:
18.0
Step-by-step explanation:
Note the tenth place value (underlined and bolded): 18.049
Look at the number to the direct right of the tenth place value (or the hundredth place value in this case). It is a 4.
Note the rules of rounding. If the number:
1) is 5 or greater, round up.
2) is 4 or less, round down.
In this case, it is 4, so you will round down.
18.049 rounded to the nearest tenth is 18.0
~
Answer:
18.0
Step-by-step explanation:
first time i put 18 and it was wrong so
In trapezoid ABCD, AB ∥ CD , m∠A=90°, AD=8 in, DC=9 in, CB=10 in, and ∠B is acute. Find DB.
Answer:
the length of DB is 17 in
Step-by-step explanation:
Consider the sketch attached.
We will draw an imaginary line from point C to met line AB at point E.
A right-angled triangle will now be formed between points CBE.
The dimensions of the right-angled triangle will be:
CB = 10 in
CE= 8 in
EB = unknown
We will now proceed to find out the length of side EB using the Pythagoras' theorem.
[tex]EB =\sqrt{CB^2 -CE^2} \\EB =\sqrt{10^2 -8^2} \\EB = 6 in[/tex]
From the shape, we can find out that another right-angled triangle is made between points DAB.
The dimensions of the triangle are:
DA= 8in
AB = 9 in + 6 in = 15 in
DB = unknown.
We will now proceed to find out the length of side DB using the Pythagoras' theorem.
[tex]DB =\sqrt{AD^2 +AB^2} \\DB =\sqrt{8^2 +15^2} \\DB = 17 in[/tex]
Therefore, the length of DB is 17 in
help meplz i want help i bad
Answer:
.00002
Step-by-step explanation:
2 * 10 ^-5
Move the decimal 5 places to the left since the exponent is negative
2.
We will need to add zeros on the left Add 4 zeros since we can move it one place already
.00002
Answer:
(D) 0.00002
Step-by-step explanation:
Let's first forget about the 2 in the expression and focus on [tex]10^{-5}[/tex].
If we have 10 to a positive number, that many times the decimal place will move to the right. It's the opposite for 10 to the power of a negative number.
The decimal place will move 5 places to the LEFT.
So:
[tex]0000010\\\\0.00001[/tex]
Now we remember the two, and multiply this by two to get 0.00002.
Hope this helped!
f(x) = [tex]\sqrt{x+7} -\sqrt{x^2+2x-15}[/tex] find the domain
Answer:
x >= -7 ................(1a)
x >= 3 ...............(2a1)
Step-by-step explanation:
f(x) = [tex]\sqrt{x+7}-\sqrt{x^2+2x-15}[/tex] .............(0)
find the domain.
To find the (real) domain, we need to ensure that each term remains a real number.
which means the following conditions must be met
x+7 >= 0 .....................(1)
AND
x^2+2x-15 >= 0 ..........(2)
To satisfy (1), x >= -7 .....................(1a) by transposition of (1)
To satisfy (2), we need first to find the roots of (2)
factor (2)
(x+5)(x-3) >= 0
This implis
(x+5) >= 0 AND (x-3) >= 0.....................(2a)
OR
(x+5) <= 0 AND (x-3) <= 0 ...................(2b)
(2a) is satisfied with x >= 3 ...............(2a1)
(2b) is satisfied with x <= -5 ................(2b1)
Combine the conditions (1a), (2a1), and (2b1),
x >= -7 ................(1a)
AND
(
x >= 3 ...............(2a1)
OR
x <= -5 ................(2b1)
)
which expands to
(1a) and (2a1) OR (1a) and (2b1)
( x >= -7 and x >= 3 ) OR ( x >= -7 and x <= -5 )
Simplifying, we have
x >= 3 OR ( -7 <= x <= -5 )
Referring to attached figure, the domain is indicated in dark (purple), the red-brown and white regions satisfiy only one of the two conditions.
Plssss answer this guys fastt Pleaseeee
Pleaseeeeeeeeeeeeeeeeeee
And when u make pls do it all and not half thanks u so much if u dooo
Answer:
You cant get someone to do all of this try doing a few or getting help from someone older that's what I did
Explanation:
I asked help for one problem and the explanation and now I understand how they did it so the other problems I can do now
It's better to make an effort and try doing some of them instead of asking someone to do all of it
Because when the test comes it won't be that easy so next time just try putting a few so that way you can try understanding it and you can apply it to similar problems.
I hope you can find this some what help to you in the future. Also this is a suggestion from my experience so you don't have to do it I'm just trying to help out.
PLS HELP ME WITH THIS QUESTION, ANYTHING REALLY HELPSS!!!!
Answer:
x = 75
Step-by-step explanation:
FGE is a straight line so it equals 180 degrees
FGA + AGC + CGE = FGE
x + 90 + 15 = 180
Combine like terms
x+ 105 = 180
Subtract 105 from each side
x = 180-105
x = 75
Answer:
x = 75º
Step-by-step explanation:
The Vertical Angle Theorem shows that:
∠CGE ≅ ∠DGF
So:
∠DGF = 15º
∠AGD = 90º
90º - 15º = 75º
x = 75º
Change 06:00 to 12 hour clock time using a.m. and p.m.
I will mark you as brainlist
Answer:
06:00 a.m.
Step-by-step explanation:
That very simble, from 0:00 to 11:59 you use am, from 12:00 to 23:59 you use p.m :)
The ratio of boys to girls in the ninth grade is 7 to 9. there are 218 girls set up a proportion to model this information
Answer:
24.2
Step-by-step explanation:
A fortnight is 1/26 of a year. What part of a year is 8 fortnights?
Answer:
Isn’t it just 8/26
Step-by-step explanation:
Since 1 is 1/26 so 8 is just 8/26?
The part of a year is 8 fortnights is ( 8 / 26 ).
What is multiplication?Multiplication is the process of determining the product of two or more numbers in mathematics.
It is given that a fortnight is 1/26 of a year. The part of the year for 8 fortnights is calculated as:-
⇒ 8 x ( 1 / 26 )
⇒( 8 / 26 )
Therefore, the part of a year is 8 fortnights is ( 8 / 26 ).
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Can you solve this???
BAE + HEG = 180°
124 + 2x+6 = 180°
2x+6 = 56
x = 50/2
x = 25°
Reason:
Given
HEG = EAD since they are corresponding angles
EAD + EAB = 180° since they are supplementary angles.
xx
Find the area and perimeter of the shaded region.
Answer:
Area: [tex]50\pi -100[/tex]
Perimeter: 20[tex]\pi[/tex]
Step-by-step explanation:
If we take half of one of these "pedals" we can see that it is simply 1/4 of a circle with radius 5, subtracted by a triangle. Let's calculate this half-pedal.
[tex]1/4(25 \pi) - 1/2(5* 5)[/tex]
That means 4 pedals is equal to:
[tex]8(1/4(25\pi) - 1/2 (25))[/tex]
[tex]50\pi - 100[/tex]
So.. The area of the shaded region is [tex]50\pi -100[/tex]
Perimeter is even simpler. the half-pedal is just 1/4 of the circumference of the circle. The circumference is just [tex]10\pi[/tex], which means our half pedal is:
[tex]1/4(10\pi )[/tex]
Multiplying by 8, our perimeter is just 20[tex]\pi[/tex].
(will give brainliest) find the value of x
Answer:
x = 180 - [(180 - 3x) + (180 - 2x)]
Step-by-step explanation:
Start off by finding the angles of the triangle
Angle F = 180 - 3x
The angle across from I (which I will call I) = 180 - 2x
Angle G = 180 - (F + I)
Now that we know what G is, we know what x is because the Alternate Exterior Angles Theorem states that if a pair of parallel lines are cut by a transversal, then the alternate exterior angles are congruent. So pretty much X = G
Therefore x = 180 - (F + I) or otherwise said as:
x = 180 - [(180 - 3x) + (180 - 2x)]
I hope this is helpful :)
Three-fourths of the water leaked out of a full aquarium tank. and 15 gallons of
water was left. After the leak was fixed, 10 gallons of water was added to the
aquarium tank.
4) How many gallons of water can the aquarium tank hold when it is full?
5) How full was the aquarium tank after the 10 gallons of water was added?
6) How much more water would have to be added to fill the aquarium tank?
Answer: 4) 60 gallons 5) 25 gallons 6) 35 gallons
Step-by-step explanation:
If three-fourths of the water in the tank leaked out of the full aquarium tank then one-fourths will be left.
so if the leftover was 15 gallons then 1/4 of a number has to equal 15 gallons.
We could represent that by the equation.
1/4 * x = 15
0.25x = 15
x= 60
4) which means the aquarium tank can hold 60 gallons of water when it is full.
5) If 15 gallons of water was left after the leaking and then they added 10 more gallons of water then 15 + 10 = 25 which means the aquarium was 25 gallon full.
6) If they are 25 gallons in the water now and we need to add some amount of water to get to 60 gallons of water then we will subtract 25 from 60 find how much water needs to be added.
So 60 -25 = 35 which means 35 gallons needs to be added.
Explanation/Answer would be appreciated please
Answer: The solution for the system is (2, -7)
Step-by-step explanation:
Ok, here we have linear relationships.
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
In this case, we have two lines:
ya, that passes through:
(-8, -5) and (-3, -6)
Then the slope is:
a = (-6 - (-5))/(-3 - (-8)) = (-6 + 5)/(-3 + 8) = -1/5
now, knowing one of the points like (-3, - 6) we can find the value of b.
y(x) = (-1/5)*x + b
y(-3) = -6 = (-1/5)*-3 + b
-6 = 3/5 + b
b = -6 - 3/5 = -33/5
then the first line is:
ya = (-1/5)*x -33/5
For the second line, we know that it passes through the points:
(-8, -15) and (-3, -11)
Then the slope is:
a = (-11 - (-15))/(-3 -(-8)) = (-11 + 15)/(-3 + 8) = 4/5
The our line is:
y(x) = (4/5)*x + b
and for b, we do the same as above, using one of the points, for example (-3, -11)
y(-3) = -11 = (4/5)*-3 + b
b = -11 + 12/5 = -(55 + 12)/5 = -43/5
then:
yb = (4/5)*x - 43/5.
Ok, our system of equations is:
ya = (-1/5)*x -33/5
yb = (4/5)*x - 43/5.
To solve this, we suppose ya = yb
then:
(-1/5)*x + -33/5 = (4/5)*x - 43/5.
-33/5 + 43/5 = (4/5)*x + (1/5)*x
10/5 = 2 = (4/5 + 1/5)*x = x
2 = x
now we evaluate x = 2 in one of the lines:
ya = (-1/5)*2 -33/5 = -2/5 - 33/5 = -35/5 = -7
Then the lines intersect at the point (2, - 7), which is the solution for the system.