We should multiply the expression by (9+√14) fraction.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers.
To rationalize the terms, we multiply both the denominator and denominator by the conjugate of the denominator.
The denominator is 9-√14 and its conjugate is; (9+√14).
(5-√7)/(9-√14) = (5-√7)(9+√14)/(9-√14)(9+√14)
= (5-√7)(9+√14)/(9²-14)
= (45 + 5√14 - 9√7 - √98)/(81-14)
= (45 + 5√14 - 9√7 - √98)/67
= (45 + 5√14 - 9√7 - 7√2)67
This is the rationalized expression.
The denominator is (9-√14) and its conjugate is (9+√14).
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Recursive formula for
-4,3,10,17
Answer:
Recursive:
Step-by-step explanation:
Common difference ( d ): 17 - 10 = 7
Recursive Arithmetic:
[tex]a_n = a_{n-1} + d[/tex]
[tex]a_n = a_{n-1} + 7[/tex]
[tex]a_1 = -4[/tex]
Hopefully this helped!
8
Which of the following is a composite number between 80 and 100?
OA. 81
OB. 89
OC. 83
OD. 97
Answer:
OA. 81
Step-by-step explanation:
A composite number is a positive integer that can be formed by multiplying two smaller positive integers.
81 = 9 x 9
81 = 3 x 27
Classify the triangle by its angle measures.
Answer:
d) Acute
Step-by-step explanation:
if all three angle measures are less than 90 degrees, the triangle is acute
What is the value of y in the diagram?
y
x
X-20
Answer:
x+x-20 = 180-90
2x-20 = 90
2x. =90+20
2x. =110
x. =55
y+55. =90
y. =90-55
y. =35
help please i need it
Answer:
Around 140
Step-by-step explanation:
It's over 90 degree angle
What is the answer?
It says i should put it in the order and which one comes first
Answer:
B. -11
Step-by-step explanation:
ascending order means least to greatest.
-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7,...
3, -1, [tex]\sqrt{5}[/tex], 13, -11
-11 is the least number because it is the greatest negative number
PLS HELP ILL MARK AS BRAINLIST AND FOLLOW U
Answer:
[tex]31\:\text{square units}[/tex]
Step-by-step explanation:
We can break the composite figure into two triangles and two trapezoids. The area of a triangle is given by [tex]A=\frac{1}{2}bh[/tex] and the area of a trapezoid is given by [tex]A=\frac{b_1+b_2}{2}\cdot h[/tex] (average of the bases multiplied by the height).
Area of first triangle (larger triangle to the figure's left): [tex]\frac{1}{2}\cdot 4\cdot 4=8[/tex]
Area of second triangle (smaller triangle to the figure's right ): [tex]\frac{1}{2}\cdot 2\cdot 5=5[/tex]
Area of first trapezoid (smaller trapezoid directly underneath second triangle and adjacent to both triangles): [tex]4\cdot 2 =8[/tex]
Area of first triangle (larger triangle to the figure's left): [tex]5\cdot 2=10[/tex]
Thus, the area of the entire figure is:
[tex]8+5+8+10=\boxed{31\:\mathrm{units^2}}[/tex]
5x+3y=25 and 3x+4y=26 solve by substitution!
[tex]5x + 3y = 25 \\ 5x = 25 - 3y \\ x = \frac{25 - 3y}{5} \\ x = \frac{25}{5} - \frac{3y}{5} \\ x = 5 - \frac{3y}{5} \\ 3x + 4y = 26 \\ 3 (5 - \frac{3y}{5} ) + 4y = 26 \\ 15 + \frac{11y}{5} = 26 \\ \frac{11y}{5} = 26 - 15 \\ \frac{11y}{5} = 11 \\ \frac{5}{11} \times \frac{11y}{5} = 11 \times \frac{5}{11} \\ y = 5 \\ x = 5 - \frac{3y}{5} \\ x = 5 - \frac{3(5)}{5} \\ x = 2[/tex]
(x,y)—> (2,5)
What is the y-intercept of the line shown?
69
5-
4
3-
2-
1-
0
-4
-3
- 2
0
1
2
3
4
5
3
4
What is the solution to the system of equations below?
2 x + y = 7 3 x + 2 y = 16
Answer:
2x+y=7; 3x+2y=16
X = -2
Y = 11
What are the solutions to the quadratic equation
6x2 + 24X = 0?
Answer:
[tex]x = 0 \: \text{or} \: x = - 4.[/tex]
Step-by-step explanation:
[tex]6 {x}^{2} + 24x = 0 \\ \text{then} \: 6x(x + 4) = 0 \\ \text{hence} \: x = 0 \: \text{or} \: x + 4 = 0 \\\text{therefore} \: x = 0 \: \text{or} \: x = - 4.[/tex]
Amy buys eight apples that each weigh 150 grams. She notices that they are on sale for $3.00 per kilogram, how much will the apples cost? Prove your thinking.
Answer:
$3.60
Step-by-step explanation:
8 apples × 150 grams
1200 grams
1 kilogram = 1000 grams
x. = 1200 grams
X = 1.2 kg
1kg = $3.00
1.2kg =$3.6
The cost of 8 apples that have weight 1.2 kilograms is,
⇒ $3.60
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Amy buys eight apples that each weigh 150 grams.
And, She notices that they are on sale for $3.00 per kilogram.
Now,
Total weight of the apples is,
⇒ 8 × 150 grams
⇒ 1200 grams
⇒ 1.2 kilograms
Since, She notices that they are on sale for $3.00 per kilogram.
Hence, The cost of 8 apples that have weight 1.2 kilograms is,
⇒ $3.00 × 1.2
⇒ $3.60
Thus, The cost of 8 apples that have weight 1.2 kilograms is,
⇒ $3.60
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f(x)=x². What is g(x)?
A. g(x) = 2x²
B. g(x) = (½x)²
C. g(x) = (4x)²
D. g(x) = (2x)²
Answer:
g(x) = (2x)²
Step-by-step explanation:
One leg of a right triangle is 24. What is the length of the other leg if the hypotenuse is 25?
Answer:
Hello! answer: 7
Step-by-step explanation:
24 × 24 = 576
7 × 7 = 49
576 + 49 = 625
√625 = 25
therefore the missing leg is 7
what is the missing side-
Answer:
did u try looking it up lol?
Step-by-step explanation:
JK is J(-3 9) and K(5 -1), if LM is perpendicular to JK, what is the slope of LM?
Answer: 4/5
Step-by-step explanation:
Overnight the temperature in Chicago was -7F but by noon it had risen to 9 degrees F. What was the temperature in Chicago that afternoon?
Answer:
2 °F
Step-by-step explanation:
Overnight temperature = -7 °F
Total Noon temperature = 9 °F
What was the temperature in Chicago that afternoon?
Temperature in Chicago that afternoon = Total Noon temperature + Overnight temperature
= 9 °F + (-7 °F)
= 9 °F - 7 °F
= 2 °F
Temperature in Chicago that afternoon = 2 °F
If $36.25 in tax is added to the price of an item, what was the original price in dollars of the item?
$400
$500
$483.33
$600
Look at the picture
Its d because 16/12=1.33 same with 20/15 and 40/30 so its 24x1.33 which is 32 there for d is correct
is each pair of lines parallel perpendicular or neither
Answer:
perpendicular, parallel, neither, parallel
G
100%
Calculate the area of the parallelogram, in mề.
40 m
15 m
25 m
10 m
30 m
A. 250 m2
B. 450 m2
OC. 600 m²
OD. 900 m²
O E. 1000 m
Answer:
C. 600 m²
Step-by-step explanation:
A parallelogram is a quadrilateral (has four sides and four angles) with two pairs of parallel sides. Opposite sides and angles of a parallelogram are equal to each other. Also, the diagonals are equal.
The area of a parallelogram is the product of its base and its height. It is given by the formula:
Area = base * height
We can see that for this parallelogram, the height = 15 m, the base = 40 m, hence:
Area = base * height = 40 m * 15 m = 600 m²
If the ray ML makes an angle measuring 2 radians with the ray MN, and the length of the arc intercepted by the angle is 72 inches, what is the radius of the window?
Answer:
36 inches
Step-by-step explanation:
From the diagram attached,
Applying
s = 2πr∅/360
Where s = lenght of the arc, r = radius of the window, ∅ = angle formed in degree, π = pie.
make r the subject of the equation
r = 360s/2π∅................... Equation 2
From the question,
Given: s = 72 inches, ∅ = 2 radians = 114.6°
Constant: 3.14
Substitute these values into equation 2
r = (360×72)/(114.6×3.14×2)
r = 25920/719.688
r = 36 inches
Jina has scored 79, 85, 89 and 68 on her previous four tests. What score does she need on her next test so that her mean is 80?
Answer:
79
Step-by-step explanation:
79, 85, 89, 68 have a mean of 80.25 according to calculator.net. the number itself Is close to the number you want, in this case 80, i input 80, but it gave me a score of 80.2, so i tried again with 81, it gave me a score of 80.4, so the third attempt was successful with 79 being the input and 80 the output
calculator.net is approved on my school computer so there is a chance it is on yours as well.
Find the center and radius of a circle with the equation x² + y2 +6x–8y +16= 0.
a. (-3, 4);r=3
b. (3,-4);r=3
c. (-3, 4);r=9
d. (3,-4);r=9
30 POINTS I WILL GIVE U BRAINLIEST AND THANKS AND 5 STARS please help this is very important this is a big part of my grade
Answer:
[tex]1.\:2^x=64, x=\boxed{6},\\2.\:x=\left(\frac{2}{3}\right)^3,x=\boxed{\frac{8}{125}}\\3.\:3\cdot (3^4)=3^x, x=\boxed{5}\\4.\:\frac{16}{25}=x^2,x=\boxed{\frac{4}{5}},[/tex]
Step-by-step explanation:
[tex]1.\\\\2^x=64,\\\log 2^x=\log64,\\x\log 2=\log 64,\\x=\frac{\log 64}{\log 2}=\boxed{6}[/tex]
[tex]2.\\x=\left(\frac{2}{5}\right)^3=\frac{2^3}{5^3}=\boxed{\frac{8}{125}}[/tex]
3. This problem incorporates an exponent property.
Exponent property used: [tex]a^b\cdot a^c=a^{(b+c)}[/tex], yielding an answer of [tex]\boxed{5}[/tex]
[tex]4.\\\\\frac{16}{25}=x^2,\\x=\sqrt{\frac{16}{25}}=\frac{\sqrt{16}}{\sqrt{25}}=\boxed{\frac{4}{5}}[/tex]
Answer:
1. 6
2. 8/25
3. 5
4. 4/5
Step-by-step explanation:
Help me with this please
Answer:
F'
Your answer is correct
Step-by-step explanation:
The image most of the time we will put ' prime on it to let the other know that this is the image
SOMEONE PLEASE HELP ME! I promise i will mark brainlest, but i need the right answer for this. help is much appreciated <3
Answer:
I say A or B but in favor A
Step-by-step explanation:
permudahkan. 1. 3/4m (4m+16n) +m/n.
3/4m(4m+16n) + m/n open the bracket of equation,
3/4m(4m+16n) + m/n = 3+ 12n/m + m/n
now multiply and devide by mn on RHS,
3/4m(4m+16n) + m/n = (3mn+12n²+m²)/mn
In this diagram, radius AD = 5 mm, radius BD = 12 mm and chord
CD = 8 mm. Find the exact length of AB, in surd form.
Answer:
The exact length of AB is [tex]3 + 4\sqrt{10}[/tex] milimeters.
Step-by-step explanation:
Both triangles ACD and BCD are isosceles and triangles AEC, ADE, BDE and BCE are right-angled, where E is the point where line segments AB and CD meet each other. We can determine the exact length of AB by means of two horizontal right triangles (i.e. AEC, BCE) and the Pythagorean Theorem:
[tex]AB = \sqrt{AC^{2}-CE^{2}}+\sqrt{CB^{2}-CE^{2}}[/tex]
If we know that [tex]AD = AC[/tex], [tex]BC = BD[/tex], [tex]AC = 5\,mm[/tex], [tex]BC = 12\,mm[/tex] and [tex]CE = 4\,mm[/tex], then the exact length of AB is:
[tex]AB = \sqrt{(5\,mm)^{2}-(4\,mm)^{2}}+\sqrt{(12\,mm)^{2}-(4\,mm)^{2}}[/tex]
[tex]AB = 3 + 4\sqrt{10}\,[mm][/tex]
The diagram shows a campground in the shape of a right triangle. You walk along a path from the camp office
at point c to your campsite at point D on a path that bisects the right angle C. Determine how far you are from
the picnic area at Point A to the nearest tenth of a meter.