Answer:
[tex]x = -1, -3[/tex]
Solve by FactoringTo solve by factoring, we will split up the equation using our factoring rules.
In this particular instance, we will factor out common variables.
We need to ensure that we get two numbers that add to equal 4 and two numbers that multiply to equal 3.
[tex]x^2 + 4x + 3 = 0[/tex]
[tex](x+3)(x+1)=0[/tex]
Set each factor equal to zero and solve.
Root 1
[tex]x+3=0[/tex]
[tex]x=-3[/tex]
Root 2
[tex]x+1=0[/tex]
[tex]x=-1[/tex]
The final answer is [tex]\boxed{x = -1, -3}[/tex].
As requested in the question, we must now check with the quadratic formula.
What is the quadratic formula?To solve this quadratic equation, we will utilize the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
The parent formula for a quadratic equation is [tex]ax^2+bx+c=0[/tex].
We will define our variables:
a: 1b: 4c: 3Now, we will plug these into the equation and solve the equation.
Solve[tex]\displaystyle x=\frac{-4\pm\sqrt{4^2-4(1)(3)}}{2(1)}[/tex]
[tex]\displaystyle x=\frac{-4\pm\sqrt{16-12}}{2}[/tex]
[tex]\displaystyle x=\frac{-4\pm\sqrt{4}}{2}[/tex]
[tex]\displaystyle x=\frac{-4\pm2}{2}[/tex]
Root 1
[tex]\displaystyle x=\frac{-4+2}{2}[/tex]
[tex]\displaystyle x=\frac{-2}{2}[/tex]
[tex]\boxed{x=-1}[/tex]
Root 2
[tex]\displaystyle x=\frac{-4-2}{2}[/tex]
[tex]\displaystyle x=\frac{-6}{2}[/tex]
[tex]\boxed{x=-3}[/tex]
Final AnswerThe final answer is [tex]\boxed{x = -1, -3}[/tex].
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Given the equation, we can start by rewriting:
x^2 + 4x + 3 = 0
Now, let’s write in factored form:
(x + 1) (x + 3) = 0
since x is the only variable and there are 2 numbers, we can make 2 equations:
x + 1 = 0
x + 3 = 0
This forms:
(X + 1) (x + 3) = 0
Now, we can solve:
? + 1 = 0
? + 3 = 0
-1 + 1 = 0 and -3 + 3 = 0
x = -1 AND -3
five sixths divided by 5
[tex]\cfrac{5}{6}\div 5\implies \cfrac{5}{6}\div \cfrac{5}{1}\implies \cfrac{5}{6}\cdot \cfrac{1}{5}\implies \cfrac{1}{6}\cdot \cfrac{5}{5}\implies \cfrac{1}{6}\cdot 1\implies \cfrac{1}{6}[/tex]
Name three planes that intersect at point P
Name the intersection of plane PQO and plane NMP
Name three lines that intersect at point S
I points PM & Q collinear are they coplanar
There are points P, M & Q collinear are not collinear because they didn't lie in the same line but they are coplanar.
What are the collinear points and the coplanar?Collinear points are defined as points that are along a straight line represented by a collinear. Because a straight line may be drawn continuously between any two points, they are always collinear. There can be a collinear relationship from three or more points, although it is not necessary.
We have given a line and a planar surface with points O, M, N, Q, P, S, and T.
Here three planes that intersect at point P which are PMN plane, PQM plane and QST plane.
Here three planes that intersect at point S which are STN plane, MNS plane and QST plane.
Here points P, M & Q collinear are not collinear because they didn't lie in the same line but they are coplanar.
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Um yea anyone want to answer this for me
Find a₁ for each arithmetic series. S₈ =440 and d=6
An arithmetic sequence (AP) is a progression in which the difference (called the tolerance) between two consecutive terms in the passage/progression is constant.
Therefore, the expression for the nth term is,
an = a₁ + (n − 1) d
and in general
an = am + (n - m) d.
where d is the difference.
For an arithmetic series with initial term a₁ and difference between terms of d
an = a₁ + (n − 1) d
We are given some of the values,
d = 6 and
S8 = 440
So, we will put the values in the formula and calculate the desired value,
a1 = 440 = a1 + ( 8 - 1 ) * 6 = a1 + 42
a1 = 440 - 42 = 398.
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33 is 22% of what
number?
Answer:
150
Step-by-step explanation:
[tex]33 = 0.22(x)\\\\\\frac{33}{0.22} =\frac{0.22(x)}{0.22} \\\\\large\boxed{x=150}[/tex]
Can you help me in identifying m?
The length of the side m are obtained using the theorem of Pythagoras and proportional triangles to give;
a) m ≈ 28.4
b) m ≈ 12.09
c) m ≈ 9.38
Which theorem can be applied to find the value of m?a) The given triangle, is a right triangle.
The length of the legs of the triangle are; 33 and 56.
According to Pythagorean theorem, the length of the hypotenuse side, l, is therefore;
l = √(33² + 56²) = 65
From the formula for the area of a triangle, we have;
Area of a triangle, A, equals half the base length multiplied by the height.
A = 0.5 × Base length × Height
For the right triangle, we have;
A = 0.5 × Leg 1 × Leg 2
Which gives;
A = 0.5 × 33 × 56 = 924
However;
A = 0.5 × l × m
Where;
l = The hypotenuse = The base length = 65
m = The height of the triangle
Which gives;
A = 0.5 × 65 × m = 924
m = 924/(0.5 × 65) ≈ 28.4
m ≈ 28.4b) The side m is parallel the 14 units long side.
The proportion the side m divides a side of the triangle = 3 and 19
Given that the triangle formed by m is proportional to the larger triangle, we have;
m/14 = 19/(19+3)
m = 14 × 19/(19+3) ≈ 12.09c) From the proportionality of similar triangles, we have;
m/16 = 17/(14+15)
m = 16×17/(14+15) ≈ 9.38Learn more about the proportionality of similar triangles here:
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Which expressions are equivalent to-2y-8+4y?
Answer:
The expression that is equivalent to -2y-8+4y is 2y-8.
Worth 60 POINTTSS!!! PLEASE HELPP MEEE i need explanation on how u got it tho
Answer:
1.-150 250-400 is -150
2. 6570 6288+282=6570
3.123 because 102+21 is 123
Step-by-step explanation:
can i have the brainlieast award?
Evaluate the formula V = Bh/3 for each pair of values.
B = 118 m^2 , h = 66 m
Answer:
i just need a points thnkyuuuu
Given parallelogram LMNO with diagonals intersecting at point P. If MP = 2x + 5 and OP = 3x − 4, find OP.
−9
9
23
31
Given parallelogram LMNO with diagonals intersecting at point P, OP is equal to 23.
A parallelogram is a two-dimensional figure with two pairs of parallel sides. A parallelogram's pair of opposite sides are of equal length and its opposite angles are of equal measure.
The diagonals of a parallelogram bisect each other, divides each other into two equal lengths.
If the diagonals of parallelogram LMNO intersects at point P, then MP is equal to OP. If MP = 2x + 5 and OP = 3x − 4, solve for x.
MP = OP
2x + 5 = 3x − 4
5 + 4 = 3x - 2x
x = 9
Substitute the value of x to solve for OP.
OP = 3x − 4
OP = 3(9) - 4
OP = 27 - 4
OP = 23
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Someone please help I’ll give brainles u gotta put the steps
Answer:
All answers in explanation
Step-by-step explanation:
Step 1: Unknown
Unknown is the number of refills purchased
Step 2 Key Information
Cost of souvenir cup, price per refill and total money spent
Step 3: Strategy (equation)
Define a variable x that represents the number of refills bought
The souvenir cup cost $14.25
Each refill costs $1.25
So x refills will cost 1.25x
Total cost = 14.25 + 1.25x
We are told she spent $23
So the equation is
14.25 + 1.25x = 23
Step 4: Solution
Equation is
14.25 + 1.25x = 23
a) Isolate the x term by subtracting 14.25 on both sides
14.25 - 14.25 + 1.25x = 23 - 14.25
1.25x = 8.75
b) Divide both sides by 1.25:
1.25x/1.25 = 8.75/1.25
x = 7
Solution is 7 refills
Step 5: Check your answer
Plug x = 7 back into the left side of the equation and check if it works out to 23
14.25 + 1.25 (7) = 14.25 + 8.75 = 23
So our answer is correct
Find the distance between each pair of parallel lines with the given equations.
y=x-11 y=x-7
The distance between each pair of parallel lines with the given equations y = x-11 and y = x-7 is 4 units.
We can find the points passing through the lines
Hence,
The points passing through the line y = x - 11 are:-
Let x = 11
y = 11 - 11 = 0
(11,0)
and;
Let x = 12
y = 12 -11 = 1
(12,1)
The points passing through the line y = x - 7 are:-
Let x = 7
y = 7 - 7 = 0
(7,0)
and;
Let x = 8
y = 8 -7 = 1
(8,1)
Hence, using distance formula, the distance between the parallel lines will be:-
[tex]\sqrt{(1-1)^2+(12-8)^2} =\sqrt{0+16}=\sqrt{16} =4 units[/tex]
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PLEASE HELP I DONT UNDERSTAND
Answer:
x = 16
Step-by-step explanation:
16 and x have the same length.
Write each number as a percent.
1.23
.
Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100.
The number 1.23 as a percentage is 123 %.
What is a percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The percent sign, %, is frequently used to indicate it. There is no unit of measurement for a percentage. It is a dimensionless number (pure number).
Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.
Let the number be 1.23
To find percentage multiply it by 100, we get
So, 1.23 × 100 = 123 %
Therefore, the number 1.23 as a percentage is 123 %.
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The length of an animal's stride is the distance between two consecutive tracks. The average stride length of a duck is about 5 inches. Write a glide reflection that can be used to predict the location of the next track for the following animal tracks.
duck
The glide reflection ( x + 2.5 , y ) is that is reflected in the line that separates the left prints from the right prints.
A glide translation is what?
A glide reflection is made up of a translation and a reflection in which the translation and the reflection are parallel to each other or the direction of the translation. A gliding reflection has opposite isometry and is -commutative.Now, let's assume that the initial position is (x , y) .
Since, the average stride length of a turkey is about 11 inches; also since the turkey has two legs, therefore, the average stride length between the two legs is as shown below:
average = 5/2 = 2.5
Thus, the glide reflection is ( x + 2.5 , y )
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How far apart are the foci of an ellipse with a major axis of 32ft and minor axis of 14ft ?
The foci are placed 4 feet apart from the ellipse's center. Then the distance between the foci of the ellipse will be separated by 8 feet.
What is an ellipse?Ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called foci adds up to a constant. It is taken from the cone by cutting it at an angle.
A major axis of 32 ft and a minor axis of 14 ft.
The major axis 2a of the ellipse will be
2a = 10 feet
a = 5 feet
The minor axis 2b of the ellipse will be
2b = 14
b = 7 feet
We must utilize the following connection to get the foci's coordinate:
b² = a² - c²
3² = 5² - c²
c² = 25 - 9
c² = 16
c = ± 4
As a result, the foci are placed 4 feet apart from the ellipse's center. As a result, the foci are separated by 4 + 4 = 8 feet.
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Use synthetic division to divide the polynomials.
Answer:
11
8z² + 9z + 12 + -------
z - 1
Step-by-step explanation:
x - c = x - 1
change the sign of -1 to +1
8z³ + z² + 3z -1
1 | 8 1 3 -1
↓ 8 9 12
-------------------------
8 9 12 11
8z² + 9z + 12 remainder of 11
I hope this helps!
This graph shows the amount of medicine in a patient after receiving an injection.
How much medicine was in the patient after `4` hours?
729 mg
144 mg
2/3 mg
4 mg
Answer:
144 mg
Step-by-step explanation:
Ariane feeds her kitten kkk grams of food 222 times in the morning and 222 times in the evening. She feeds her dog ddd grams of food 111 time in the morning and 111 time in the evening.
Which expressions can we use to describe how many grams of food Ariane feeds her animals per day?
Step-by-step explanation:
in the morning, 222k + 111d
in the evening, 222k + 111d
grams, g = 444k + 222d
Compute the BMI 75 kg 6'1"
round 0.6666 to 3 sf
Answer:
0.66 with a bar
Step-by-step explanation:
A squirrel can run a short distance at a rate of 4 3/4 miles in 15 minutes. A fox can run a short distance at a rate of 21 miles in half an hour. Which is faster, and how much faster in miles per hour?
35 mph= .58 of a mile per minute
21 miles in 30 minutes= .7 of a mile per minute
if you multiply by 60 to see the distance in the same amount of time:
rabbit: 35 mph
fox: 42
So the fox would run a greater distance in the time given. Hope this helps!
Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition. (Lesson 5-3)
measures less than m∠5
The exterior angle (∠ 5) is larger than either remote interior angle (∠ 7 and ∠ 8).
Exterior Angle Inequality Theorem
According to the exterior angle inequality theorem, the measure of any exterior angle of a triangle is greater than the measure of either of the opposite interior angles. The adjacent interior angle and the exterior angle are supplementary. A triangle's exterior angles add up to 360º.
A triangle's exterior angle is always greater than its two remote interior angles.
By the Exterior Angle Inequality Theorem, the exterior angle (∠ 5) is larger than either remote interior angle (∠ 7 and ∠ 8).
m ∠ 7 < m ∠ 5 and m ∠ 8 < m ∠ 5 .
Therefore, the correct answer is ∠ 7 and ∠ 8.
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Find the missing term of each arithmetic sequence.... 5, .. , 21,...
The missing terms of an arithmetic progression (AP) are -3, 5, 13, 21, 29.
What is meant by arithmetic progression (AP)?An arithmetic progression (AP) is a pattern in which each successive term has the same distinctions.
Each term in an arithmetic progression (except the first) is deduced by adding a specific range to the term preceding the first.The following arithmetic progression concepts are most often used to solve various AP problems for the initial term 'a' of an AP together with the common difference 'd.'The most common difference AP is 'd': d = a2 - a1 = a3 - a2 = a4 - a3 =...... = a - an-1. nth term of an AP: an = a + (n - 1) dThe sum of an AP's n terms is; Sn = n/2(2a+(n-1)d) = n/2(a + l), where l is the final term of the AP.The arithmetic sequence.... 5, .. , 21,...
There are total 5 terms in the series.
Let the initial term be 'a₁'.
Let the second term be 'a₂' = 5.
Let the third term be 'a₃'.
Let the fourth term is be 'a₄' = 21.
And final, the fifth term be 'a₅'.
The common difference of the AP are same. so,
d = a₃ - a₂ ........(equation 1)
d = a₄ - a₃ .......(equation 2)
Thus, equate the two formed equation;
a₃ - a₂ = a₄ - a₃
Substituting the values;
a₃ - 5 = 21 - a₃
Simplify the above equation;
a₃ = 26/2
a₃ = 13.
Put the value in equation 1 and find the common difference.
d = a₃ - a₂
d = 13 - 5 = 8
So, the first term will be;
d = a₂ - a₁
a₁ = a₂ - d
a₁ = 5 - 8
a₁ = -3
Now, the fifth term will be;
a₅ = a₄ + d
a₅ = 21 + 8
a₅ = 29.
Therefore, the arithmetic sequence of the AP formed as -3, 5, 13, 21, 29.
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Find the 17 th term of each sequence. a₁₆=18, d=5
The 17 th term of the Arithmetic Progression (AP) is found to be a₁₇ = 26.
What is the AP sequence for arithmetic progression?In Arithmetic Progression (AP), the difference between the two numerical orders is a constant value. Arithmetic Sequence is another name for it.
We'd come across a few important words in AP, denoted as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)The AP may also be characterized in concepts of common distinctions, as shown below.
The following is the formula for determining an AP's n-th term: an = a + (n − 1) × dThe arithmetic progression sum is as follows: Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, as per the given data in the question;
16th term; a₁₆ = 18
Common difference; d = 5
Then, the 17th term would be calculated as;
Use the common difference formula;
d = a₁₇ - a₁₆
a₁₇ = a₁₆ + d
a₁₇ = 21 + 5
a₁₇ = 26
Therefore, the value of the 17th term of a AP is found as 26.
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What is the sum of the 9th square number and the 1st square number?
Answer:
sum is 82
Step-by-step explanation:
[tex]\sf \textsf{The 9th square number is }9^2 = 81[/tex]
[tex]\sf \textsf{The 1st square number is }1^2 = 1.[/tex]
In order to find the sum of these two square numbers, simply add them together:
[tex]\sf Sum = 81 + 1 = 82[/tex]
The sum of the 9th square number and the 1st square number is 82.
Draw a tessellation using the following shape(s).
octagon and square
The network of equilateral triangles, squares, and hexagons is used in just three regular tessellations.
What does tessellation of a form mean?
A flat surface is tessellated when one or more geometric forms, known as tiles, are used to tile the surface without any gaps or overlaps.Tessellations in mathematics can be expanded to greater dimensions and a wide range of geometries.A tiling is referred to as "non-periodic" if it doesn't have a repeating pattern.Only regular triangles, squares, and hexagons can tessellate on their own.
If you use more than one sort of form, you can create additional tessellations of regular shapes.
The network of equilateral triangles, squares, and hexagons is used in just three regular tessellations.
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help pleasee
In a right triangle, the sides are 1 cm and √3 cm. Calculate the measures of acute angles
Answer:
This will be a 30°-60°-90° triangle because the hypotenuse is 2 cm, which is twice the length of the shorter leg.
She bought 0.85 pounds of ground beef for $5.60 per pound and 1 can of tomatoes for $1.79. if she had a coupon for $1.50 off, how much did she spend all together on the ingredients?
Answer:
$5.05
Step-by-step explanation:
.85($5.60) + $1.79 - $1.50
$4.76 + $1.79 - $1.50 = $5.05
which multiplication expression is equal to 2/3 ÷ 1/2?
Answer:
2/3*2/1
this is the answer
Answer:
2/3 × 2/1
Hope this helps :)
Explanation below.
Step-by-step explanation:
To find the multiplication expression, use the Keep, Change, Flip (KCF) method.
