Answer:
[tex]6g -86h[/tex]
Step-by-step explanation:
[tex]10( 7g-9h) -4h - 8(-h + 8g)[/tex]
1) First, distribute the 10 and the -8 to the terms in the parentheses next to them. Remember, don't distribute to the -4h since it is not in the parentheses.
[tex]10( 7g - 9h) -4h - 8(-h + 8g)\\70g - 90h-4h+8h-64g\\[/tex]
2) Next, combine like terms. (Any terms that have the same variables must be added together by their coefficients.)
[tex]70g - 90h-4h+8h-64g\\\\70g-64g-90h-4h+8h\\6g-86h[/tex]
There are no more like terms to combine, so [tex]6g -86h[/tex] is the answer.
Perform the operation and get
your answer in the form a + bi.
(5 – 2i)(5 + 2i)
[?] + [ ]i
Answer:
Step-by-step explanation:
(5-2i) ( 5+2i) = (5^2) - ((2i)^2) = 25 - 4i^2
= 25 - 4(-1) = 25 +4 = 29 + 0i
The Solution is 29 + 0i.
What are complex numbers?The sum of a real number and an imaginary number is called a complex number. A complex number is usually represented by z and has the form a + ib. Here, both a and b are real numbers. The real part, denoted by Re(z), is represented by the value "a," and the imaginary part, represented by "b," is represented by Im(z). Also known as an imaginary number, ib.
Given Expression (5 – 2i)(5 + 2i)
we know a² - b² = (a - b)(a + b)
(5 – 2i)(5 + 2i) = 5² - (2i)²
= 25 - 4i²
and i² = -1
= 25 - 4(-1)
= 25 + 4 = 29
since the solution has 0i
so the equation is 29 + 0i
where a = 29 and b = 0
Hence, equation is 29 + 0i.
Learn more about complex numbers;
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A car travels 104 kilometers in 2 hours. What is its speed?
Answer:
52 kilometers per hour
:)
Which of the following best describes the equation y= -2/7x +12
A. Linear
B. Both linear and nonlinear
C. Nonlinear
D. Neither linear or nonlinear
A point (–7, –6) is rotated counterclockwise about the origin to map onto (–6, 7). The angle of rotation is
Question 18 options:
A)
180°.
B)
90°.
C)
270°.
D)
360°.
Answer:
C
Step-by-step explanation:
took the quiz and got it right
Help plssssssssssssssssss
Answer:
131.2 ft
Step-by-step explanation:
12.8*10.25=131.2
A person invests $1000 in a bank. The bank pays 6% interest compounded monthly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches $3300
Answer:
20 years approx
Step-by-step explanation:
Step one:
given data
Principal= $1000
rate= 6%
Final amount A= $3300
Required
Time t
Step two:
the expression for the compound interest is given data
A= P(1+r)^t
t = ln(A/P) / r
substitute
t= ln(3300/1000)/0.06
t= ln3.3/0.06
t= 1.193/0.06
t=19.88 years
t= 20 years approx
Find the length of the radius of the circle.
A)
2 inches
B
B)
3 inches
)
6 inches
D)
8.5 inches
Answer:
C) 6 inches
Step-by-step explanation:
(√72)² = x² + x²
72 = 2x²
72/2 = x²
36 = x²
√36 = √x²
6 = x
x = 6 inches
Answer:
By Pythagoras theorem, we get
[tex] {x}^{2} + {x}^{2} = {( \sqrt{72}) }^{2} \\ 2 {x}^{2} = 72 \\ {x}^{2} = 36 \\ \boxed{x = 6}[/tex]
C) 6 inches is the right answer.Please and thank you
Answer:
is this free points. cuz why you said please and thank you?
Step-by-step explanation:
On a piece of paper, use a protractor and a ruler to construct triangle ABCABC with ABAB = 3 in., ACAC = 3 in., and m∠Am∠A = 90°90° . What is the measure of m∠Cm∠C?
A:60°
B:30°
C:90°
D:45°
The graphs below have the same shape. What is the equation of the blue graph?
Please answer quickly
Answer:
I answered the first two Q but i dont know the third one sorryy
Step-by-step explanation: i put the answers as pics
30 points ans brainliest
plz i really need this awnser asap
Tom, Brad, Angela, and Mona went to a theater. In how many different ways can they sit on four adjacent seats in a line in the theater?
Answer:
16
Step-by-step explanation:
4x4 = 16
Question (in need of help)
This is an right angle ∆ and the side lengths containing a right angle are 9 and 11.
By Pythagoras theoram,
[tex] {p}^{2} + {b}^{2} = {h}^{2} [/tex]
where p is the perpendicular, b is the base and h is the hypotenuse.
Plugging the values,
[tex] {9}^{2} + {11}^{2} = {h}^{2} [/tex]
Then,
[tex]h = \sqrt{ {9}^{2} + {11}^{2} } [/tex]
[tex]h = 14.12(approx.)[/tex]
Hence:-The x of the right angled ∆ = 14.12
Answer:
the top angle is 11 and the angle on the left is 9 so the X will be rounded to the nearest hundreth since it's the biggest angle so 11×9=109 so yea I THINK its 100 since it's rounding
Solve the following system of equations using the elimination method. 5x + y = 9 –10x + 7y = 18 Question 6 options: A) (2,–6) B) (–7,3) C) (3,–4) D) (1,4)
Answer:
Step-by-step explanation:
5x + y = 9
-10x + 7y = 18
10x + 2y = 18
-10x + 7y = 18
9y = 36
y = 4
5x + 4 = 9
5x = 5
x = 1
(1,4)
answer is D
A bamboo plant grows about 3.9 feet each day find the growth in 9 weeks
Answer:
The answer is 245.7
Step-by-step explanation:
7 days in a week. 9 weeks. 9 x 7 = 63.
63 x 3.9 = 245.7
I need help i my math homework
Answer:
Domain: (-7, 4]
General Formulas and Concepts:
Algebra I
Domain is the set of x-values that can be inputted into function f(x)Step-by-step explanation:
According to the graph, the line's x-values span from -7 to 4. Since -7 is an open dot, it is exclusive in the domain. Since 4 is a closed dot, it is inclusive in the domain:
(-7, 4] or -7 < x ≤ 4
When the polynomial mx3 - 3x2 + nx + 2 is divided by x + 3, the remainder is -1. When it is divided by x - 2, the remainder is -4. What are the values of m and n?
Answer:
m = -2 and n = 10
Step-by-step explanation:
If the polynomial mx^3 - 3x^2 + nx + 2 is divided by x + 3, the remainder is -1. Then;
x+ 3 = 0
x = -3
Substitute x =-3 into the polynomial and equate to -1
-1 = m(-3)³-3(-3)²+n(-3) + 2
-1 = -27m - 27 - 3n + 2
27m + 3n = -25 + 1
27m + 3n = -24 ... 1
Similarly, if it is divided by x - 2, the remainder is -4, then;
-4 = m(2)³-3(2)²+n(2) + 2
-4 = 8m - 12- 2n + 2
8m -2n = -4 + 10
8m + 2n = 6 ... 2
Solve 1 and 2 simultaneously
27m + 3n = -24 ... 1 * 2
8m + 2n = 6 ... 2 * 3
______________________
54m + 6n = -48
24m + 6n = 12
54m - 24m = -48 - 12
30m = -60
m = -60/30
m = -2
Get n by substituting m = -2 into 1
From 1: 27m + 3n = -24
27(-2) + 3n = -24
-54 + 3n = -24
3n = -24 +54
3n = 30
n = 30/3
n = 10
Hence m = -2 and n = 10
Write an equivalent equation by combining like terms.
5x - 7y + 2x + 10y + 4
Answer:
7x+3y+4Step-by-step explanation:
Mrs. Jones has a recipe for cooking roast beef. It takes half an hour for one pound of beef in an oven heated to 325° Fahrenheit to cook. How long should it take to cook a roast that weighs 5 34 pounds?
_______________________________
1lbs = 30min
= 5.34lbs × 30mins= 160.2mins= 160.2mins ÷ 60mins= 2.67hrsIt Should Take Mrs. Jones 3hrs & 7mins________________________________
I will give brainiest to whoever answers correctly !!
Answer:
Step-by-step explanation:
The principal amount is
P=3000.
The time for which money is borrowed is ,
[tex]t=9 months[/tex]
The interest rate is ,
[tex]R=3\frac{1}{2}[/tex]
Determine the time in terms of year by division of time by 12.
[tex]t=\frac{9}{12} years\\= \frac{3}{4} years\\[/tex]
The formula for the interest is ,
[tex]I=\frac{P.r.t}{100}[/tex]
Substitute the known calues in the formula to obtain the value of interest.
[tex]I=\frac{3000.\frac{3}{4} .3\frac{1}{2} }{100} \\=\frac{3000.3.7}{2.4.100} \\=78.75\\[/tex]
So interest paid by the woman is $78.75
(b)
Determine the amount paid by the woman .
[tex]A=P+I\\=3000+78.75\\=3078.75[/tex]
So woman repay $3078.75 to the bank.
PLEASE MARK ME AS BRAINLIEST
Let sugar be the explanatory variable and calories be the response variable; which scenario best describes ŷ = 57 + 2.5x?
Select one:
a. The amount of calories in fruit juice increases by 57 for every one gram of sugar. The calorie amount estimated by this model is 2.5 if there are zero grams of sugar.
b. The amount of sugar in fruit juice increases by 2.5 grams for every one calorie. The sugar amount estimated by this model is 57 grams if there are zero calories.
c. The amount of sugar in fruit juice increases by 57 grams for every one calorie. The sugar amount estimated by this model is 2.5 grams if there are zero calories.
d. The amount of calories in fruit juice increases by 2.5 when there are zero grams of sugar. The calorie amount estimated by this model is 57 if there is one gram of sugar.
e. The amount of calories in fruit juice increases by 2.5 for every one gram of sugar. The calorie amount estimated by this model is 57 if there are zero grams of sugar.
Answer: Choice E)
The amount of calories in fruit juice increases by 2.5 for every one gram of sugar. The calorie amount estimated by this model is 57 if there are zero grams of sugar.
=============================================================
Explanation:
x = amount of sugar (in grams)
y = number of calories in the juice
ŷ = estimate of y, so its the estimate of calories in the juice
The regression equation rearranges to ŷ = 2.5x + 57
This is in the form y = mx+b where m = 2.5 is the slope and b = 57 is the y intercept.
The slope tells us what the rate of change is. Specifically, it tells us how much the amount of calories (y) is going up each time the amount of sugar (x) goes up. Each time x goes up by 1, y goes up by 2.5
The y intercept 57 is the starting or initial amount of calories. If you have 0 grams of sugar, the lowest amount of sugar possible, then you start off with 57 calories. We can see this by plugging x = 0 into ŷ = 2.5x + 57 (you should get ŷ = 57). Visually, the y intercept is where the line crosses the y axis.
All of these facts point to choice E as the final answer.
Answer:
e.
Step-by-step explanation:
calories is y or response variable and sugar is the explanatory variable, x.
if x(sugar) is 1
y = 57 + 2.5(1) = 59.5, a 2.5 increase.
if it is 2
y = 57 + 2.5(2) = 62, another 2.5 increase.
if zero grams of sugar x = 0
y = 57 + 2.5(0) = 57 calories.
find the value
any help
simplify -5 + 3d + 6 - 4d
-5+3d+6-4d
anwers is 12/-30
The larger of two numbers is eight more than five times the smaller number the sum of two numbers is 80 find the two numbers
Answer:
y=68
x=12
Step-by-step explanation:
Variables= x and y
Lets make y the larger variable.
x+y=80
y=5x+8
substitution
x+5x+8=80
6x+8=80
x=12
plug 12 back in to find y
5(12)+8=68
y=68
x=12
Please help me. My other question I need help on. 2- g(x)=x^2-4 is what is g(-3) 3- F(x)=3x+7 what is f(2) please help me please please
Answer:
[tex]g(-3) = 5[/tex]
[tex]f(2) = 13[/tex]
[tex](f + g)(x) = x^2 +2x- 1[/tex]
Step-by-step explanation:
Solving (a):
[tex]g(x) = x^2 - 4[/tex]
Required
Determine g(-3)
[tex]g(x) = x^2 - 4[/tex]
Substitute -3 for x
[tex]g(-3) = (-3)^2 - 4[/tex]
[tex]g(-3) = 9- 4[/tex]
[tex]g(-3) = 5[/tex]
Solving (b):
[tex]f(x) = 3x + 7[/tex]
Required
Determine f(2)
[tex]f(x) = 3x + 7[/tex]
Substitute 2 for x
[tex]f(2) = 3*2 + 7[/tex]
[tex]f(2) = 6 + 7[/tex]
[tex]f(2) = 13[/tex]
Solving (c):
[tex]f(x) = 2x + 3[/tex]
[tex]g(x) = x^2 - 4[/tex]
Required
[tex](f + g)(x)[/tex]
In functions:
[tex](f + g)(x) = f(x) + g(x)[/tex]
So, we have:
[tex](f + g)(x) = 2x + 3 + x^2 - 4[/tex]
Collect Like Terms
[tex](f + g)(x) = x^2 +2x- 4+3[/tex]
[tex](f + g)(x) = x^2 +2x- 1[/tex]
For the line 3x + 4y = 36, what is the slope?
Tina plans to make wooden frames to put her two triangular art pieces in.
How much wood would she need fortriangle DFG?
Enter your answer in the box.
in.
Answer: 54 in.
Step-by-step explanation: So, the problem does something a little sneaky, and that is they ask for the TOTAL amount of wood needed for triangle DFG. And to find that, we simply have to multiply side AC by 3 to get side DG. We do this because triangle ABC is 3 times as small as triangle DFG. Then, add your side DG that you just got, (21) to side FG and FD to get the total amount of wood needed, 54 in.
The length of wood needed for triangle DFG is 54 inches
Start by calculating the side length DG in triangle DFG
The side lengths of DFG are three times the corresponding side length of ABC
So, we have:
[tex]DG = 3 \times AC[/tex]
[tex]DG = 3 \times 7\ in[/tex]
[tex]DG = 21\ in[/tex]
The perimeter of triangle DFG is then calculated as:
[tex]P = DF + FG + DG[/tex]
This gives
[tex]P = 15 + 18 + 21[/tex]
[tex]P = 54[/tex]
Hence, the length of wood needed is 54 inches
Read more about perimeter at:
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Denise doesn't describe tabletop with an area of 36 x 16 squared white boy squared units running expression to represent one side length of the table top
Step-by-step explanation:
Side length = √Area = √(36x¹⁶y⁴)
= √[(6x⁸y²)²] = 6x⁸y².
Hence the expression for side length is 6x⁸y².
The length of the side of the table top will be 6x⁴y².
Based on the information given, it was stated that the area of the table top was given in the question.
It should be noted that the area of a square is gotten by squaring the sides. Therefore, the length of the side of the square will be 6x⁴y².
Learn more about squares on:
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A natural number is____a rational number.
A. Never
B. Sometimes
C. Always
Answer:
Always
Step-by-step explanation:
We know that,
As every natural number n be represented in a rational form: n/1, any natural number can be represented in the form p/q, where q≠0. Hence, all natural numbers are rational numbers.