Answer:
The perimeter of rectangle is [tex]18\ cm[/tex]
Step-by-step explanation:
Let
x-----> the length of the rectangle
y----> the width of the rectangle
we know that
[tex]x=y+5[/tex] ----> equation A
[tex]120=xy+2x^{2}+2y^{2}[/tex] ---> equation B (area of the constructed figure)
substitute the equation A in equation B
[tex]120=(y+5)y+2(y+5)^{2}+2y^{2}\\ 120=(y+5)y+2(y+5)^{2}+2y^{2}\\ 120=y^{2}+5y+2(y^{2}+10y+25)+2y^{2}\\ 120=y^{2}+5y+2y^{2}+20y+50+2y^{2}\\120=5y^{2}+25y+50\\5y^{2}+25y-70=0[/tex]
using a graphing calculator -----> solve the quadratic equation
The solution is
[tex]y=2\ cm[/tex]
Find the value of x
[tex]x=y+5 ----> x=2+5=7\ cm[/tex]
Find the perimeter of rectangle
[tex]P=2(x+y)=2(7+2)=18\ cm[/tex]
Answer:
Perimeter of rectangle = 38 cm
Step-by-step explanation:
It is given that, Length of a rectangle is 5 cm longer than the width.
Let 'x' be the width then length = x + 5
Area of of rectangle = x(x + 5)
One side of square = ( x+ 5)/4
Area of all squares = [(x +5)/4]² * 4 = (x + 5)²/4
To find the value of x
Total area = 120 cm²
Area of of rectangle + Area of all squares = 120
x(x + 5) + (x + 5)²/4 = 120
x² + 5x + (x² + 10x + 25)/4 = 120
4x² + 20x + x² + 10x + 25 = 120 * 4
x² + 6x + 5 = 24 * 4
x² + 6x - 96 =0
x = 7
To find the perimeter of rectangle
width = x = 7
Length = x + 5 = 7 + 5 = 12
Perimeter = 2(length + width) = 2(7 + 12) = 38 cm
simplify the fraction, 32/100÷ 4/4
[tex]\bf \cfrac{32}{100}\div \cfrac{4}{4}\implies \cfrac{32}{100}\div 1\implies \cfrac{32}{100}\implies \cfrac{\underline{2\cdot 2}\cdot 2\cdot 2\cdot 2}{\underline{2\cdot 2}\cdot 5\cdot 5}\implies \cfrac{2\cdot 2\cdot 2}{5\cdot 5}\implies \cfrac{8}{25}[/tex]
Answer:
8/25
Step-by-step explanation:
you divide 32/100 by 4/4=8/25 because 8x4=32 and 4x25=100
Solve the following equation using the quadratic formula x^2-8x+97=0
Answer:
x=4±9i
Step-by-step explanation:
Solve the equation for x by finding a, b, and c of the quadratic then use the qaudratic formula
Answer:
[tex]x=4-9i[/tex] or [tex]x=4+9i[/tex]
Step-by-step explanation:
The given equation is
[tex]x^2-8x+97=0[/tex]
By comparing to [tex]ax^2+bx+c=0[/tex], we have a=1,b=-8 and c= 97.
The quadratic formula is;
[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
We substitute the values to obtain;
[tex]x=\frac{--8\pm\sqrt{(-8)^2-4(1)(97)} }{2(1)}[/tex]
[tex]x=\frac{8\pm\sqrt{-324} }{2}[/tex]
[tex]x=\frac{8\pm18i }{2}[/tex]
[tex]x=4\pm9i[/tex]
Therefore [tex]x=4-9i[/tex] or [tex]x=4+9i[/tex]
Use f(x) = 1 2 x and f -1(x) = 2x to solve the problems. In general, f−1(f(x)) = f(f−1(x)) =
ANSWER
[tex]{f}^{ - 1}( f(x)) = f( {f}^{ - 1} ( x)) = x[/tex]
EXPLANATION
The given functions are;
[tex]f(x) = \frac{1}{2} x[/tex]
[tex] {f}^{ - 1} (x) = 2x[/tex]
[tex]f( {f}^{ - 1} (x)) = f(2x)[/tex]
[tex]f( {f}^{ - 1} (x)) = \frac{1}{2} \times 2x = x[/tex]
Also,
[tex] {f}^{ - 1}( f(x)) = {f}^{ - 1} ( \frac{1}{2} x)[/tex]
[tex]{f}^{ - 1}( f(x)) = 2 \times \frac{1}{2} x = x[/tex]
In general,
[tex]{f}^{ - 1}( f(x)) = f( {f}^{ - 1} ( x)) = x[/tex]
The area of a circle is 615.44 in2. What is the diameter of the circle? Use 3.14 for π.
Answer:
[tex]\large\boxed{C=87.92\ in}[/tex]
Step-by-step explanation:
The formula of an area of a circle:
[tex]A=\pi r^2[/tex]
r - radius
We have A = 615.44 in². Substitute:
[tex]615.44=\pi r^2[/tex]
[tex]\pi\approx3.14[/tex]
[tex]3.14r^2=615.44[/tex] divide both sides by 3.14
[tex]r^2=196\to r=\sqrt{196}\\\\r=14\ in[/tex]
The formula of a circumference of the circle:
[tex]C=2\pi r[/tex]
Substitute:
[tex]C=2\pi\cdot14=28\pi\approx28\cdot3.14=87.92\ in[/tex]
Each packet of jelly-child sweets contains 100 sweets. The cycling tour has 9425 jelly-child sweets remaining. How many unopened packets do they have?
Answer:
There was 94 unopened packets.
Step-by-step explanation:
Divide 9425 by 100.
9425 / 100 = 94.25
That means there was 94 unopened packets.
25.............::.....
Answer: Option a.
Step-by-step explanation:
1. Multiply the numerator and the denominator of the expression shown in the image, by the conjugate of the denominator ( [tex]\sqrt{x}-\sqrt{7}[/tex]), as you can see below:
[tex]\frac{(\sqrt{x})(\sqrt{x}-\sqrt{7})}{(\sqrt{x}+\sqrt{7})(\sqrt{x}-\sqrt{7})}[/tex]
2. By definition, you know that:
[tex](a+b)(a-b)=a^2-b^2[/tex]
3. Therefore, you obtain the following result:
[tex]\frac{(\sqrt{x})^2-\sqrt{7x}}{(\sqrt{x})^2-(\sqrt{7})^2}=\frac{x-\sqrt{7x}}{x-7}[/tex]
Then, the answer is option a.
The answer is:
a. [tex]\frac{x-\sqrt{7x}}{x-7}[/tex]
Why?Rationalizing involves eliminating or the roots of both numerator and denominators, there are severals ways to do it but one of the most common methods is using the conjugate term.
We must remember that:
[tex](a-b)(a+b)=a^{2}-b^{2}[/tex]
So, for the given expression:
[tex]\frac{\sqrt{x}}{\sqrt{x}+\sqrt{7}}[/tex]
The conjugate is:
[tex]\sqrt{x}-\sqrt{7}[/tex]
The, we need to multiply both numerator and denominator (in order to not affect the expression) by the conjugate expression in order to eliminate the radicals in the denominator:
[tex]\frac{\sqrt{x}}{\sqrt{x}+\sqrt{7}}*\frac{\sqrt{x}-\sqrt{7}}{\sqrt{x}-\sqrt{7}}=\frac{(\sqrt{x})*(\sqrt{x}-\sqrt{7})}{(\sqrt{x}+\sqrt{7})*(\sqrt{x}-\sqrt{7})}[/tex]
[tex]\frac{(\sqrt{x})*(\sqrt{x}-\sqrt{7})}{(\sqrt{x}+\sqrt{7})*(\sqrt{x}-\sqrt{7})}=\frac{(\sqrt{x})^{2}-(\sqrt{x})*(\sqrt{7})}{(\sqrt{x})^{2}-(\sqrt{7})^{2}}[/tex]
[tex]\frac{(\sqrt{x})^{2}-(\sqrt{x})*(\sqrt{7})}{(\sqrt{x})^{2}-(\sqrt{7})^{2}}=\frac{x-\sqrt{7x}}{x-7}[/tex]
Have a nice day!
Sorry about the bad quality :(
Answer:
Yes, y varies directly with x, and the equation is [tex]y=1.6x[/tex].
Step-by-step explanation:
To check where there is a direct relationship between x and y, we need to check whether all the x,y pairs we have fit some rule:
[tex]y=k\times x[/tex].
For the first pair (x=4, y=6.4),
[tex]6.4=k\times 4[/tex]
Therefore [tex]k = 1.6[/tex].
For the second pair (x=7, y=11.2),
[tex]11.2=k\times 7[/tex]
Therefore [tex]k = 1.6[/tex].
For the third pair (x=10, y=16),
[tex]16=k\times 10[/tex]
Therefore [tex]k = 1.6[/tex].
For the second pair (x=13, y=20.8),
[tex]20.8=k\times 13[/tex]
Therefore [tex]k = 1.6[/tex].
So x does directly vary with y, and we have found out that [tex]k=1.6[/tex].
Answer: [tex]\bold{\dfrac{y}{x}=1.6\quad \text{which is also equivalent to}\quad y=1.6x}[/tex]
Step-by-step explanation:
[tex]\begin {array}{c|c||l}x&y&\dfrac{y}{x}=k\\--&--&-----\\4&6.4&\dfrac{6.4}{4}=1.6\\\\11.2&7&\dfrac{11.2}{7}=1.6\\\\10&16&\dfrac{16}{10}=1.6\\\\13&20.8&\dfrac{20.8}{13}=1.6\\\end{array}\\[/tex]
Since the k-value is the same for every value in the table, we can conclude that y varies directly with x and the constant of variation k = 1.6
Choose the correct correspondence
AB <->
Options
1.Side AC
2.Side BD
3.Side CD
Answer:
AC
Step-by-step explanation:
Looking at triangles ABD and ACD, they appear to be congruent. This means they have corresponding or matching parts which are equal and form each triangle.
The segment AB is the shortest segment of triangle ABD. It matches to the shortest segment in ACD. This segment is AC.
Answer:
AB <--> AC
Step-by-step explanation:
Hello! Segment AB is congruent to segment AC in ABD and ACD.
Thus, they are in correspondence to one another.
Hope this helps!
d ÷ 4/5 = 5/7, what is D in fraction form
Answer:
d=4/7
Step-by-step explanation:
d=5/7*4/5
John had 84 dollars, and his brother Fred owed 12 dollars to his friend. John gave his brother some money. Fred paid his debt and now both of them has the same amount left. How much money did John give Fred? PLZZZZ HELP!!!!!
Answer:
John gave Fred $48
Step-by-step explanation:
Let
x be the amount of dollars John gave fred
y1 be the amount of dollars Fred has at the end
y2 be the amount of dollars John has at the end
Fred has
y1 = - $12 + x
John has
y2 = $84 - x
y1 = y2
- $12 + x = $84 - x
2*x = $96
x = $48
Which of the following is a not a rational number?
1.3
3.1415...
5.25
0.66
Answer:
Step-by-step explanation:
3.14159 is irrational because it's a repeating decimal; it cannot be expressed as the ratio of two integers. All the others can be expressed in that way.
Answer:
B. would be your answer
which of the following terms refers to the level of detail of a measurement, such as the number of decimal places to which an amount is measured?
a. accuracy
b measurement
c estimation
d precision
Answer:
Option D.
Step-by-step explanation:
Precision refers to the the level of measurement and exactness of a measurement. The mean diference between 'precision' and 'exactness' is that if a measuring device gives consisten measurements it's considered precise, but it's not necessarily accurate.
For example, a measurement of 2.365m is more precise than a measurement of 2.3m, given that 2.365m has more significant figures and was made with an instrument that has higher precision. This doesn't mean that the measurement is accurate, the real value could be 3m for example! ✅
The sum of two numbers is 47 and the difference is 9 what are the numbers ?
The numbers are 19 and 28.
Answer:
28 and 19
Step-by-step explanation:
let the 2 numbers be x and y, x > y, then
x + y = 47 → (1) ← sum of numbers
x - y = 9 → (2) ← difference of numbers
Adding the 2 equations to eliminate y
2x = 56 ( divide both sides by 2 )
x = 28
substitute x = 28 into (1) and solve for y
28 + y = 47 ( subtract 28 from both sides )
y = 47 - 28 = 19
The 2 numbers are 28 and 19
ABCD is a rectangle.
Use the diagram to answer the questions.
The length of AB is .
The length of BC is .
The length of AC is .
Answer:
i need more details
Step-by-step explanation:
factor completely x^2+4x-21
Answer:
(x + 7)(x - 3)
Step-by-step explanation:
To factor the quadratic
Consider the factors of the constant term (- 21) which sum to give the coefficient of the x- term (+ 4 )
The factors are + 7 and - 3 since
+ 7 × - 3 = - 21 and + 7 - 3 = + 4, hence
x² + 4x - 21 = (x + 7)(x - 3)
The quadratic equation x^2 + 4x - 21 is factored into (x - 3)(x + 7) where these two factors multiply to -21 and add up to 4.
Explanation:To completely factor the equation x^2 + 4x - 21, we look for two numbers that multiply to -21 (the c term) and add up to 4 (the b term). The numbers that satisfy these conditions are 7 and -3.
Therefore, the factored form of the equation x^2 + 4x - 21 is: (x - 3)(x + 7) as (x - 3) * (x + 7) gives x^2 + 4x - 21.
Learn more about Factorization here:https://brainly.com/question/33624529
#SPJ3
How do you make predictions using experimental probability
Answer:
How you make predictions is by finding the ratio of the number of times an event occurs to the total number of trials.
Step-by-step explanation:
Is 8in, 15in, 17in a right triangle
[tex] {8}^{2} + {15}^{2} = 64 + 225 = 289 \\ {17}^{2} = 289 \\ \Rightarrow {8}^{2} + {15}^{2} = {17}^{2} \\ \Rightarrow A \: right \: triangle[/tex]
Answer:Yes
Step-by-step explanation:
a^2 + b^2 = c^2
C is the hypotenuse which is the longest side, b is the second longest and a is the shortest one
WILL MARK BRAINEST!! : Using the slope formula, find the slope of the line through the given points.
(13,0) and (3,-2)
Answer:
1/5
Step-by-step explanation:
Multiply these two together in simplest from
Answer:
[tex]\frac{3x}{5(x+2)}[/tex]
Step-by-step explanation:
Multiply the fractions by multiplying the numerators.
[tex]\frac{6x^2}{x(x-3)} * \frac{(x-3)}{10(x+2)} \\\\\frac{6x^2(x-3)}{10x(x-3)(x+2)} \\\\ \frac{6x}{10(x+2)} \\\\\frac{3x}{5(x+2)}[/tex]
identify the sequence as arithmetic geometric or neither -8, -3, 6, 11, -22
Answer:
Neither
Step-by-step explanation:
Check if it's arithmetic:
-8, -3, 6, 11, -22
+5 +6 +5 -33
Nope
Check if geometric:
-8, -3, 6, 11, -22
*3/8 *-2 *11/6 *-2
Nope
So it's neither
Solve for T. B=RT-4/6
if the radius of a circle with center 0 is 15.5, and the measure of angle AOB is 90, what is the length of arc AB?
7.75
7.75π
10
10π
I'm stupid when it comes to math.
surprised I made it here.
The circumference of the circle is found using the formula C = 2 PI r
Circumference = 2 *PI * 15.5 = 31pi
The angle is 90 degrees, which is 1/4 of a complete circle ( 360 degrees).
The arc length would be 1/4 of the circumference:
Arc length = 31pi / 4 = 7.75PI
Evaluate the expression below when y = -3. 2y + 7 -4y − 10 A. -1 22 B. -13 2 C. 1 2 D. 1
Answer:
3
Step-by-step explanation:
We are given the following expression and we are to evaluate it when the value of [tex] y [/tex] is [tex] - 3 [/tex]:
[tex] 2 y + 7 - 4 y - 1 0 [/tex]
Given that [tex] y = 3 [/tex], we will substitute this value of [tex] y [/tex] in the given expression to get:
[tex] 2 y + 7 - 4 y - 1 0 [/tex]
[tex] - 2 y - 3 [/tex]
[tex] - 2 (-3) - 3 [/tex]
[tex] 3 [/tex]
Answer:
.5 or 1/2
Step-by-step explanation:
type the problem in you calculator
what is the answer to
(y + z)3
Answer: The answer to this question is 3y + 3z, You need to distribute into the parentheses.
Step-by-step explanation: Distribute the 4 outside the parentheses to each inside term. Then, move the coefficient in front of the term. Finally, rearrange to put the coefficient in front.
How do I solve x+1/x-1 >0
[tex] \frac{x + 1}{x - 1} > 0 \\ [/tex]
multiply both sides by the x-1 to get rid of the fraction.
[tex]x + 1 > 0 \\ because \: x - 1 \times 0 = 0[/tex]
subtract 1 from each side
x>-1
The solution is
x<−1
x>1
Step-by-step explanation:See the image
please answer fast!
Question 5 options:
A blender is shaped like a rectangular prism. The blender is 5½ in. wide, 6½ in. long, and 12 in. tall. What is the volume of the blender?
Answer:
I believe your answer is 429.
Step-by-step explanation:
5 1/2 x 6 1/2 x 12 = 429
Find the missing value to the nearest hundredth. sin ________ = 6/19
Answer:
The missing value is [tex]18.41\°[/tex]
Step-by-step explanation:
Let
x-----> the angle (missing value)
we know that
[tex]sin(x)=\frac{6}{19}[/tex]
therefore
[tex]x=arcsin(\frac{6}{19})=18.41\°[/tex]
The probability that z is greater than -1.8
Answer:
0.964
Step-by-step explanation:
It's easier to approach this problem if you find the prob. that z is less than -1.8 and then subtract your result from 1.00.
The prob. that z is less than -1.8 can be found using any calculator with probability and statistic functions.
The prob. that z is less than -1.8 = normcdf(-100,-8) = 0.036. Here "cdf" stands for "cumulative probability density function)," -100 is far to the left of z = -1.8, and the result (0.036) is the area under the standard normal probability density curve to the left of z = -1.8.
Finally, subtract this 0.036 from 1.000, obtaining 0.964. This is the probability that z is greater than -1.8.
What is the area of this triangle? Please help me.
Answer:
8 units²
Step-by-step explanation:
The area (A) of a triangle is calculated using the formula
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = LK = 7 - 3 = 4 units
and h = J → x- axis = 4 - 0 = 4, hence
A = [tex]\frac{1}{2}[/tex] × 4 × 4 = 8 units²
Given a right triangle with legs a, b and hypotenusec, solve for c if a =3 and b= 4 pls help
Answer:
c = 5
Step-by-step explanation:
This is the classic problem that the ancients (particularly the Egyptians) used extensively. When the Nile over flowed in spring, the land had to be reclaimed and surveyed in the early summer for planting. The 3-4-5 triangle was used to determine right angles for surveying purposes.
Formula
c^2 = a^2 + b^2
Givens
a = 3
b = 4
c = ?
Solution
c^2 = 3*3 + 4*4
c^2 = 9 + 16
c^2 = 25
Take the square root of both sides
To take the square root on your calculator, find the √ on the key pad. Some calculators give it a key and some have the symbol on the body of the calculator. If has its own key do it like this.
√
25
=
The answer should come up as five. If the √ is on the body of the calculator, then
2nd F
√
25
=
The same 5 will come up.
Answer
c = 5
The hypotenuse c of a right triangle with legs a = 3 and b = 4 can be found using the Pythagorean theorem, yielding c = 5
To solve for c, the hypotenuse of a right triangle when given the legs a and b, we utilize the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). This is expressed as a² + b² = c².
To solve for c when a = 3 and b = 4, we substitute these values into the theorem to get 3² + 4² = c², which simplifies to 9 + 16 = c². When we combine the values we get 25 = c². Finally, we take the square root of both sides to solve for c, resulting in c = 5.