Answer:
x = 1/3 or -2
Step-by-step explanation:
2x^2 + 7x - 2 = - x^2 + 2x
3x^2 + 5x - 2 = 0 (use factoring)
(3x − 1)(x + 2) = 0
3x - 1 = 0 OR x + 2 = 0
3x = 1 x = - 2
x = 1/3
Can you mark as brainliest? Hope it helps by the way!
Answer:
{-2, 1/3)
Step-by-step explanation:
Combine like terms in 2x2 + 7x - 2 =- x2 + 2x: We get:
3x^2 + 5x - 2 = 0
Use synthetic division from this point on. If the remainder in synthetic division is zero, the divisor is a root of the polynomial. Setting up this division for the possible root 3, we get:
3 / 3 5 -2
15 60
----------------------
3 20 58 The non-zero remainder tells us that 3 is NOT a
solution.
Try C: x = -2. Is this a solution?
-2 / 3 5 -2
-6 2
----------------------
3 -1 0 The zero remainder tells us that -2 is a solution (C)
The other factor is (3x - 1). If we set this equal to zero and solve for x, we get:
3x = 1, or x = 1/3. Thus B: 1/3 is the second solution.
On a coordinate plane, 2 quadrilaterals are shown. Quadrilateral Q R S T has points (negative 1, 0), (5, 0), (3.5, negative 6) and (negative 2.5, negative 6). Quadrilateral Q prime R prime S prime T prime has points (negative 1, 2), (1, 2), (0.5, 0), and (negative 1.5, 0). Quadrilateral QRST is dilated and translated to form similar figure Q'R'S'T'. What is the scale factor for the dilation?
Answer:
[tex]\dfrac{1}{3}[/tex].
Step-by-step explanation:
In quadrilateral QRST, Q(-1,0), R(5,0), S(3.5,-6), T(-2.5,-6).
In quadrilateral Q'R'S'T', Q'(-1,2), R'(1,2), S'(0.5,0), T'(-1.5,0).
Distance formula:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using distance formula , we get
[tex]QR=\sqrt{(5-(-1))^2+(0-0)^2}=\sqrt{6^2}=6[/tex]
[tex]Q'R'=\sqrt{(1-(-1))^2+(2-2)^2}=\sqrt{2^2}=2[/tex]
Now,
[tex]\text{Scale factor}=\dfrac{Q'R'}{QR}[/tex]
[tex]\text{Scale factor}=\dfrac{2}{6}[/tex]
[tex]\text{Scale factor}=\dfrac{1}{3}[/tex]
Therefore the scale factor is [tex]\dfrac{1}{3}[/tex].
The given transformation of quadrilateral QRST to quadrilateral Q'R'S'T'
are a dilation and a translation, therefore, QRST is similar to Q'R'S'T'.
[tex]\mathrm{The \ scale \ factor \ of \ the \ dilation\ between \ QRST \ and \ Q'R'S'T' \ is} \ \dfrac{1}{3}[/tex]
Reasons:
The vertices of the quadrilateral are;
Quadrilateral QRST
Q(-1, 0)
R(5, 0)
S(3.5, -6)
T(-1, 2)
Quadrilateral Q'R'S'T'
Q'(-1, 2)
R'(1, 2)
S'(0.5, 0)
T'(-1.5, 0)
The given transformation that gives quadrilateral Q'R'S'T' from quadrilateral QRST are a dilation and a translation.
Required:
The scale factor of the dilation
Solution:
[tex]\mathrm{The \ scale \ factor \ of \ the \ dilation} = \dfrac{\mathrm{Length \ of \ \overline{Q'R'} }}{\mathrm{Length \ of \ \overline{QR}} }[/tex]
Length of [tex]\overline{Q'R'}} }[/tex] = 1 - (-1) = 2
Length of [tex]\overline{QR}} }[/tex] = 5 - (-1) = 6
Therefore;
[tex]\mathrm{The \ scale \ factor \ of \ the \ dilation} = \dfrac{2}{6} = \dfrac{1}{3}[/tex]
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A lottery ticket costs $5. You pick 3 two-digit numbers (anything from 00 to 99) in order. If you match the first number only, you win $200. If you match the first two numbers and not the third, you win $5000. If you match all three numbers, you win $100,000. In two or more complete sentences, explain whether or not the game is fair. In your explanation, include all necessary calculations.
Answer:
00 to 99 are 100 numbers.
If you match the first number only, you win $200. The Probability for this is 1/100.
If you match the first two numbers and not the third, you win $5000. The Probability for this is 1/50.
If you match all three numbers, you win $100,000. The Probability for this is 3/100.
And, If you are a customer, You will think is fair for you.
But if you are the lottery tickets company, you will think is not fair for you.
It depends who you are.
the game isn't fair because 100,000/3=3333 1/3, so each number should be worth $3333.3333...... dollars but you can't really give 1/3 dollars so the game is impossible to be fair. Also, if you match the first two numbers you apparently get $5000. That's also not fair because each number is worth $50 dollars more than if you get the first number matched. So, the game isn't fair but it will be pretty much impossible to be fair.
Help me do my ‘mymaths’ homework I’ll give brainliest to the best answer thanks.
Step-by-step explanation:
you make x the subject of formula for all the questions.
a(x+b)=cfirstly you divide both sides of the equation by a, this way the a will cancel it self out of the equation
x+b= c/a
then you take '+b' to the other side of the equation over the = sign, this makes +b sign to change it then becomes -b
x=c/a -b
2. 7(x-a)=b
you divide both sides of the equation by 7.
x-a=b/7
then you take -a to the other side of the equation it becomes +a
x=b/7+a
NOTE: always eliminate the number/letter beside the bracket first. it unlocks the bracket. the number or letter is joined to a bracket by multiplication so we divide to eliminate it
by what rational no. should -7/85 be multiplied to obtain 1/17?
Answer:
-1/10115
Step-by-step explanation:
Let x be the rational number.
-7/85 × x = 1/17
x = 1/17 ÷ -7/85
x = 1/(17 × -7 × 85)
x = 1/(-10115)
x = -1/10115
The rational number is -1/10115.
Answer:
- 5/7
Step-by-step explanation:
-7/85*x= 1/17
x= 1/17 ÷ (-7/85)
x= - 1/17 × 85/7
x= - 5/7
The average body temperature of a lemming is 98.6 degrees Fahrenheit. The
temperature is considered abnormal if it is more than 1.5 degrees above or below that.
Write the absolute value inequality that represents this.
Answer:
|x-98.6|>1.5
Step-by-step explanation:
THE IMAGE DOWN BELOW MATH PLEASE HELP ME WITH THIS ALEGEBRA IM CRYING YALL
Answer:
25%
Step-by-step explanation:
Let's call the factor by which production increased x.
[tex]x\cdot 84=105 \\\\\\x=\dfrac{105}{84}=1.25[/tex]
To find the percent increase, you need to subtract 1 from this value, because that represents the initial amount of robots produced. 1.25-1=0.25. Now, to find the percentage:
[tex]0.25=\dfrac{25}{100}=25\%[/tex]
Hope this helps!
Answer:
25%solution,
[tex]percent \: increase = \\ [/tex]
[tex] (\frac{105 - 84}{84}) \times 100 \: percent \\ = \frac{21}{84} \times 100 \: percent \\ = 25 \: percent[/tex]
Hope this helps..
Good luck on your assignment.
Find an equivalent function to f(x) = 5(3)^3x. (5 points)
Answer:
[tex]B. f(x) = 5(27)^x[/tex]
Step-by-step explanation:
Well lets graph it first,
Look at the image below ↓
By looking at the image we can tell that answer choice [tex]B. f(x) = 5(27)^x[/tex].
Thus,
answer choice B is correct.
Hope this helps :)
Answer:
The correct result would be f(x) = 5(27)x.
Step-by-step explanation:
If you would like to find an equivalent function to f(x) = 5(3)^(3x), you can do this using the following steps:
f(x) = 5(3)^(3x) = 5(3^(3x)) = 5(27)^x = 5(27)x
hope this helped :)
In a triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= square root 2 .
Answer:
AC=2.06cm
Step-by-step explanation:
AC^2=AD^2+CD^2
AC^2=1.5^2+1.4142^2
AC^2=2.25+2=4.25
....
[tex] \sqrt{ac {}^{2} } [/tex]
=
[tex] \sqrt{4.25 = } 2.06[/tex]
Answer:
AC=2.06 cm
Step-by-step explanation:
(11a - 2b +7c) - (3a - 9b + 5c)
Work Shown:
(11a - 2b + 7c) - (3a - 9b + 5c)
11a - 2b + 7c - 3a + 9b - 5c ... see note below
(11a-3a) + (-2b+9b) + (7c-5c)
8a + 7b + 2c
note: don't forget to distribute the negative through to every term inside the parenthesis
━━━━━━━☆☆━━━━━━━
▹ Answer
8a + 7b + 2c
▹ Step-by-Step Explanation
(11a - 2b + 7c) - (3a - 9b + 5c)
Remove the parentheses
11a - 2b + 7c - (3a - 9b + 5c)
Collect like terms
8a - 2b + 7c + 9b - 5c
Final Answer
8a + 7b + 2c
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Which of the following list of ordered pairs is a function?
simplify(2a+1/3)²-(2a-1/3)²
Answer:
hope this helps you :) have a good day
Coach kunal stacks all of the tennis balls in a square pyramid. The number of tennis balls, P(n), in n layers of the square pyramid is given by P(n) = P(n - 1) + n^2. Which could not be the number of tennis balls Coach Kunal has? A. 30 B. 5 C. 14 D. 9
Answer:9
Step-by-step explanation:
Answer is D. 9 I took the quiz
I WILL MARK BRAINLIEST WHAT DOES THIS MEAN????
Answer:
The answers are: 1 and 1.
Step-by-step explanation:
I believe they are how combinations are written. In other words:
[tex]_{n}C_{r}=(\frac{n}{r})=n!/(r!(n-r)!)[/tex] (Ignore the fraction bar, I can't really format it properly).
Anyways, simply find the combination of each:
[tex](\frac{9}{0})=9!/(0!(9-0)!)=9!/9!=1[/tex]
[tex](\frac{9}{9} )=9!/(9!(9-9)!)=9!/9!(0!)=9!/9!=1[/tex]
Note that 0! equals 1.
Answer:
Ahh
Step-by-step explanation:
Hhs
ur welcome brainliest person
ERRE
A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the translation?
O(x,y) - (x + 5, y-3)
(x,y) - (x + 5, y + 3)
O (x, y) - (x-3, y + 5)
O(x, y) - (x + 3, y + 5)
"translated 5 units up" means y becomes y+5. We just add 5 to whatever the y coordinate is to shift the point 5 units up.
To shift 3 units left, we subtract 3 from whatever the x coordinate value is. So we go from x to x-3.
Put this together and the translation rule is [tex](x,y) \to (x-3, y+5)[/tex]
Answer: Choice CLines L and M are parallel.
3/4
2 5
16
38° 7
-L
<-M
:
Find : m_1
Enter the number that
belongs in the green box.
[? ? ]
Enter
The angles of a quadrilateral are in the ratio of 2:6:9:13
Find all the angles of the quadrilateral
Answer:
24° , 72° , 108° , 156°Step-by-step explanation:
Let the angles be 2x , 6x , 9x , 13x
We know that the sum of quadrilateral is 360°
Now,
[tex]2x + 6x + 9x + 13x = 360[/tex]
Calculate the sum
[tex]30x = 360[/tex]
Divide both sides of the equation by 30
[tex] \frac{30x}{30} = \frac{360}{30} [/tex]
Calculate
[tex]x = 12[/tex]
Replacing the value,
2x = 2 * 12 = 24°
6x = 6 * 12 = 72°
9x = 9 * 12 = 108°
13x = 13 * 12 = 156°
So, the angles are 24° , 72° , 108° , 156°
Hope this helps...
Good luck on your assignment...
Answer:
Below in bold.
Step-by-step explanation:
2+6+9+13 = 30.
Now there are 360 degrees in a a quadrilateral.
So the value of the shortest angle = 2/30 * 360
= 1/15 * 360
= 24 degrees.
In the same way the value of the other 3 angles is:
6/30 * 360, 9/30 * 360 and 13/30 * 360
= 72, 108 and 156 degrees.
P(2, 2), Q(1, -3), R(-4, 2), S(-3, 7) Using the information above, answer the following questions. Find the length of RS Find the length of SP Find the length of PQ Find the length of RQ Use this information to determine if the quadrilateral a parallelogram.
Answer:
Yes the Quadrilateral is a Parallelogram.
Step-by-step explanation:
A parallelogram can be defined as a quadrilateral i.e a geometric shape with four sides that has opposite sides parallel and equal in length.
From the question, we are given the following points
P(2, 2), Q(1, -3), R(-4, 2), S(-3, 7)
Given points: (x1, y1) and (x2, y2)
The formula would be
√(x2 - x1)² +(y2 - y1)²
a) P(2, 2), Q(1, -3)
Length PQ = √(1 - 2)² +(-3 - 2)² = √-1² + -5² = √26
b) R(-4, 2), S(-3, 7)
Length RS = √(-3 - (-4))² + (7 - 2) ² = √ 1² + 5² = √26
c) R(-4, 2), Q(1, -3)
Length RQ = √(1 - (-4))² + (-3 - 2)² = √5² + 5² = √(25 + 25) = √50
d) S(-3, 7), P(2, 2)
Length SP = √(2 - (-3))² + (2 - 7)² = √5² +(-5)² = √(25 + 25) = √50
From the above solution, we can see that
Length PQ = Length RS
Length RQ = Length SP
This means the opposite sides are parallel and equal in length, hence it is a Parallelogram.
Help me ASAP for this question
In two or more complete sentences write and solve an equation for the situation and explain how you will
solve the equation.
Diane has $500 to spend on gifts. How many gifts can she purchase if she spends $20 on each gift
Answer:
25 gifts
Step-by-step explanation:
if you divide $500 from $20 you will get 25 so basically she can get 25 gifts with the $500
A fruit salad is to contain 1 green fruit, 2 different yellow fruits, and 3 different red fruits. Determine the number of possible fruit salads that can be made from 2 different green fruits, 5 different yellow fruits, and 9 different red fruits.
Answer:
90
Step-by-step explanation:
A river drops 12 ft vertically over a horizontal distance of 1500 ft.
What is the slope of the river?
Answer:
Slope = rise / run
= -12 / 1500 (It's -12 and not 12 because a drop means it's decreasing)
= -0.008
Please answer please correct
Answer:
BDA is the answer
Step-by-step explanation:
Because its 90 degrees
Answer:
Angle CDA or ADC
(both work as an answer)
Step-by-step explanation:
A complementary angle is one that has a sum of 90 degrees. In the picture, you can see that the two adjacent angles add up to 90. The second angle would be CDA or ADC, in other words, the answer
Convert: 3 ½ mi = ____ ft.
Answer:
3.5 mi = 18480 ft
Step-by-step explanation:
There are 5,280 feet for every one mile. Because there are 3.5 mile, you would multiply 5,280 x 3.5, getting 18480 feet.
Answer:
18480 feet
Step-by-step explanation:
1 mile is equal to 5280 feet. so then 3 1/2 miles is equal to 18480 feet.
Hope this helps!
the subject of the formula below is y, y=x-8, rearrange the formule to make x the subject
Answer:
x = y + 8
Step-by-step explanation:
y = x - 8 and we need to make x the subject
→ Add 8 to both sides to isolate x
y + 8 = x
→ Switch it around
x = y + 8
Answer:
Given,
y=x-8
Since,we want to make X subject so,
Or,y+8=X[side change]
Or,X=y+8.
Step-by-step explanation:
UI
A bag contains 4 red marbles, 6
white marbles, and 5 blue marbles.
If a marble is selected from the
bag, what is the probability that the
marble is not red?
Answer:
the probability that the marble is NOT red is 1 - 4/15, or 11/15
Step-by-step explanation:
Find the probability that the marble IS red: 4/(4 + 6 + 5) = 4/15
Then the probability that the marble is NOT red is 1 - 4/15, or 11/15
the probability that the marble selected from the bag is not red is 11/15 or approximately 0.7333.
To calculate the probability that a marble selected from the bag is not red, we need to determine the total number of marbles that are not red and divide it by the total number of marbles in the bag.
The bag contains 4 red marbles, 6 white marbles, and 5 blue marbles.
The total number of marbles that are not red is the sum of the white and blue marbles, which is 6 + 5 = 11.
The total number of marbles in the bag is the sum of all three colors, which is 4 + 6 + 5 = 15.
Therefore, the probability that the marble selected is not red is:
Probability = Number of marbles not red / Total number of marbles
Probability = 11 / 15
The probability is 11/15, which can also be expressed as approximately 0.7333 or 73.33% (rounded to two decimal places).
So, the probability that the marble selected from the bag is not red is 11/15 or approximately 0.7333.
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#SPJ2
Complete the solution of the equation. Find the
value of y when x equals -14.
-2x + 5y = 8
Answer:
y = -4
Step-by-step explanation:
-2x + 5y = 8
Let x=-14
-2(-14) +5y = 8
28 +5y = 8
Subtract 28 from each side
28-28 +5y = 8-28
5y = -20
Divide by 5
5y/5 = -20/5
y = -4
Solve the proportion for “y”. 5/7=30/y
Answer:
y = 42
Step-by-step explanation:
5/7=30/y
Cross multiply.
5y = 7 × 30
5y = 210
Divide 5 into both sides.
y = 210/5
y = 42
Answer:
y = 42
Step-by-step explanation:
5/7=30/y
Use cross products
5y = 7*30
5y = 210
Divide by 5
5y/5 = 210/5
y =42
When
4a- a x 3a + 7a
is simplified it is equivalent to
Answer:
30a
Step-by-step explanation:
4a-a x 3a +7a
3a x 10a
30a
The given expression is:
[tex]4a- a\times 3a + 7a[/tex]By applying multiplication, we get
→ [tex]4a - 3a^2+7a[/tex]
By applying addition, we get
→ [tex]-3a^2+11a[/tex]
By taking "a" as common, we get
→ [tex]a (-3a+11)[/tex]
Thus the answer above is right.
Learn more about simplification will be:
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PLEASE HELP QUICKLY! Line k is the perpendicular bisector of (line)PQ. If line k intersects (line)PQ at point R, which of the following statements must be true? check all that apply A. Line k bisects PQ B. PR is congruent to QR C. Line k intersects PQ at a 90 angle D. Point R is the midpoint of line k E. Line k is parallel to PQ
Answer:
A. Line k bisects PQ
B. PR is congruent to QR
C. Line k intersects PQ at a 90 angle
Step-by-step explanation:
A perpendicular bisector of a line is a segment that cuts right in the middle a line, and that segment forms a 90º degree angle with the line. This means that the point where the segment cuts the line would be exactly the half, making both resultant segments on the line congruent. So the options that are correct are ABC.
Answer:
In the diagram below, is the perpendicular bisector of PQ. Which of the following statements must be true?
Check all that apply.
A. PQ is the perpendicular bisector of
√B. mPTR = 90
√C. PT = QT
D. RT = ST
√E.↔rs⊥pq↔
√F. T is the midpoint of PQ
Step-by-step explanation:
Solve the following equation using the methods learned in this section.
3a2 = 54
The answer is a = 3√2. The explanation and steps of how I got the answer is in the image below.
A number increased by its product with 7 equals 48. Find the number.
• 6
• 8
• 10
• 41
Answer:
x = 6
Step-by-step explanation:
x + 7x = 48
8x = 48
Answer:
6
Step-by-step explanation:
x+7x=48
8x=48
x= 48/8
x=6
The first choice