Answer:
[tex](x,y) = (\frac{28}{5},\frac{2}{5})[/tex]
Step-by-step explanation:
Given
A = (4,-2)
B = (12,-10)
Ration = 1/4
Required
Determine the coordinate of point at 1 million buys
The formula to use is as follows:
[tex](x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
Where m and n are the ratios
i.e.
[tex]\frac{m}{n} = \frac{1}{4}[/tex]
Convert to ratios
[tex]m:n = 1:4[/tex]
Considering A(4,-2) and B(12,10); we have
[tex](x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
[tex](x,y) = (\frac{1 * 12 + 4 * 4}{4+1},\frac{1*10 + 4*-2}{4+1})[/tex]
[tex](x,y) = (\frac{12 + 16}{5},\frac{10 -8}{5})[/tex]
[tex](x,y) = (\frac{28}{5},\frac{2}{5})[/tex]
Hence, the coordinate of the point is [tex](x,y) = (\frac{28}{5},\frac{2}{5})[/tex]
The total combined volume of a glass, a jar, and a pitcher is 54 liters. If the jar has the same volume as 3 glasses and the pitcher has the same volume as 5 glasses, what is the volume of the glass?
Answer:
6 liters.
Step-by-step explanation:
So we have a glass, a jar, and a pitcher and together, they hold 54 liters.
We are told that the jar has the same volume as 3 glasses and the pitcher has the same volume as 5 glasses. In other words, let g denote glasses, j denote jars, and p denote pitchers:
[tex]g+j+p=54[/tex]
Since jar is the same as 3 glasses, this means that j=3g. And since the pitcher is the same as 5 glasses, this means that p=5g. Substitute:
[tex]g+(3g)+(5g)=54[/tex]
Combine like terms:
[tex]9g=54[/tex]
Divide both sides by 9. The left cancels:
[tex](9g)/9=54/9\\g=6[/tex]
Therefore, the volume of the glass is 6 liters.
Answer:
[tex]\Large \boxed{\sf 6 \ liters}[/tex]
Step-by-step explanation:
Let the volume of the glass be x.
Let the volume of the jar be y.
Let the volume of the pitcher be z.
[tex]\sf y = 3x \\\\z = 5x[/tex]
[tex]\sf x + y + z = 54[/tex]
Substitution method.
[tex]\sf x+3x+5x=54[/tex]
Combining like terms.
[tex]\sf 9x = 54[/tex]
Dividing both sides by 9.
[tex]\sf x = 6[/tex]
The volume of the glass is 6 liters.
Alexia ran three laps around her neighborhood. Each lap is 1 and StartFraction 3 over 8 EndFraction miles. Which is the best estimate of the number of miles that Alexia ran?
Answer:
4 and 1/8
Step-by-step explanation:
1 and 3/8 is equivalent to 11/8 which is one lap. If she ran 3 laps, you would multiply 11/8 by 3 which would get you 33/8- which is equivalent to 4 and 1/8.
Answer:
The answer is not -1/2
Step-by-step explanation:
I got the answer from the person above and the answer is not -1/2 so do not believe them.
12. The sum of four consecutive numbers in A.P. is 32 and the ratio of the product of the first and last terms to the product of two middle terms is 7:15. Find the number.
Answer:
2, 6, 10, 14
or
14, 10, 6, 2.
Step-by-step explanation:
Let the four consecutive numbers in A.P. be a - 3d, a - d, a + d, a + 3d
According to the first condition:
a - 3d + a - d + a + d + a + 3d =32
4a = 32
a = 32/4
a = 8
According to the second condition:
[tex] \frac{(a - 3d)(a + 3d)}{(a - d)(a + d)} = \frac{7}{15} \\ \\ \frac{ {a}^{2} - (3d)^{2} }{ {a}^{2} - {d}^{2} } = \frac{7}{15} \\ \\ \frac{ {a}^{2} - 9d^{2} }{ {a}^{2} - {d}^{2} } = \frac{7}{15} \\ \\ \frac{ {8}^{2} - 9d^{2} }{ {8}^{2} - {d}^{2} } = \frac{7}{15} \\ \\ \frac{ 64 - 9d^{2} }{ 64 - {d}^{2} } = \frac{7}{15} \\ \\ 15(64 - 9 {d}^{2} ) = 7(64 - {d}^{2} ) \\ \\ 960 - 135 {d}^{2} = 448 - 7 {d}^{2} \\ \\ 960 - 448 = 135 {d}^{2} - 7 {d}^{2} \\ \\ 512 = 128 {d}^{2} \\ \\ {d}^{2} = \frac{512}{128} \\ \\ {d}^{2} = 4 \\ \\ d = \pm 2 \\ \\ when \: d = 2 \\ a - 3d = 8 - 3 \times 2 = 8 - 6 = 2 \\ a - d = 8 - 2 = 6 \\ a + d = 8 + 2 = 10 \\ a + 3d = 8 + 3 \times 2 = 8 + 6 = 14 \\\\ when \: d = - 2 \\ a - 3d = 8 - 3 \times ( -2 ) = 8 + 6 = 14 \\ a - d = 8 -( - 2 )= 8 + 2 = 10 \\ a + d = 8 + ( - 2 )= 8 - 2 = 6\\ a + 3d = 8 + 3 \times ( - 2 )= 8 - 6 = 2 \\[/tex]
Thus the four consecutive numbers of the A. P. are 2, 6, 10, 14 or 14, 10, 6, 2.
How many positive four-digit integer palindromes have 12 as the sum of the digits of the number?
One more than the product of a number, x, and 7 is 5 less than that number, x. Rewrite this as an equation then solve for x.
Answer:
(7x+1)=x-5
Step-by-step explanation:
please tell me this asap..
y/2 - 1/5 = 2 - y/3
Answer:
y=2 16/25
in other words, two and sixteen twenty-fifths
Step-by-step explanation:
y/2-1/5=2-y/3
Move the variables to one side and constants to the other
y/2+y/3=2+1/5
Multiply y/2 by 3/3 and y/3 by 2/2 so that they have a common denominator
3y/6+2y/6=2 1/5
5y/6=11/5
Cross multiply
66=25y
y=66/25
y=2 16/25
HOPE THIS HELPS!!!
Can someone help me, I need to find the function of a graph
Step-by-step explanation:
f(x)=y
(x,y)
(x,f(x))
then,
f(-4)=1
f(0)=2
f(4)=3
Solve the equation below for x. 3.25x = 8.125 A. x = 0.025 B. x = 0.25 C. x = 2.5 D. x = 25
Answer:
C
Step-by-step explanation:
Answer: C
Step-by-step explanation: Because its just easy ;/
Please help me!! This a mathematical question. I will be so happy if someone helps me♂️
Answer:
The answer is the fourth one.
[tex]\frac{1}{r^7} +\frac{1}{s^12}[/tex]
Step-by-step explanation:
Find the vertex of the parabola y = 2x2 + 10x + 8
Step-by-step explanation:
2x*2+10x + 8
=4x+10x+8
=14x+8
inverse of 14x+8
x-8/14
=14
Answer:
y vertex=2(-5/2)^2+10(-5/2)+8=-9/2
vertex=(-5/2, -9/2)
Pls help me and show working
Answer:
4x + 10 > 3x + 14
x > 4
Step-by-step explanation:
Use the given values for length and width in the formula for perimeter of a rectangle. You will be able to find the perimeter of rectangles A and B.
A = 2(l + w)
A = 2(x + 5 + x)
A = 2(2x + 5)
A = 4x + 10
B = 2(l + w)
B = 2(x + 7 + x/2)
B = 2(3x/2 + 7)
B = 3x + 14
The perimeter of rectangle A is larger than that of rectangle B.
A > B
4x + 10 > 3x + 14
(4x + 10) - 3x > (3x + 14) - 3x
x + 10 > 14
(x + 10) - 10 > 14 - 10
x > 4
In 2003, a remote controlled model airplane became the first ever to fly nonstop across the Atlantic Ocean. The map shows the airplane's position at three different points during its flight. Point A represents Cape Spear, Newfoundland, point B represents the approximate position after 1 day, and point C represents Mannin Bay, Ireland. The airplane left from Cape Spear and landed in Mannin Bay. Find the total distance the model airplane flew. It flew miles. The model airplane's flight lasted nearly 38 hours. Estimate the airplane's average speed to the nearest mile per hour. The average speed was about miles per hour.
Answer: it flew 1883 miles and average speed was about 50 miles per hour
Step-by-step explanation: to get 1883 you just add up 1282+601
If a line with slope = 2 passes through the points (4,-8) and (x,2), find x
Answer:
x = 9
Step-by-step explanation:
Calculate the slope m using the slope formula then equate to 2
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, - 8) and (x₂, y₂ ) = (x, 2 )
m = [tex]\frac{2+8}{x-4}[/tex] = [tex]\frac{10}{x-4}[/tex] = 2 ( multiply both sides by x - 4 )
2(x - 4) = 10 ( divide both sides by 2 )
x - 4 = 5 ( add 4 to both sides )
x = 9
Which of the following is not true? Bonus number 7
Answer:
the first one i think
Step-by-step explanation:
i can't see the pic clearly make it better, and i will solve for u
Help me please I don't understand the question
Answer:
y = - 2x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (1,1) ← 2 points on the line
m = [tex]\frac{1-3}{1-0}[/tex] = - 2
The line crosses the y- axis at (0, 3) ⇒ c = 3
y = - 2x + 3 ← equation of line
What is the slope of the equation y – 3 = –4(x – 5)?e of the equation y – 3 = –4(x – 5)?
Answer:
The slope of the equation y-3=-4(x-5) is -4.
Step-by-step explanation:
This equation is written in point-slope form: y-y₁=m(x-x₁), where "m" is the slope or the equations. In the equation y-3=-4(x-5), the -4 stands in the "m", or slope, spot, so the sope of this equation is -4.
Slope of the equation is equals to -4.
What is slope?
" Slope is defined as the ratio of the change in y-coordinates to the x-coordinates. It is also known as inclined plane."
General equation of line
y = m x + c ____(1)
'm' = slope of the line
'c' = y - intercept
According to the question,
Given equation,
[tex]y-3 = -4(x-5)[/tex]
Open the brackets of the equation we get,
[tex]y-3 = -4x+20[/tex]
Add 3 both the sides of the equation we get,
[tex]y = -4x+23[/tex] ______(2)
Compare equation (1) and (2) to get the slope we have,
Slope 'm' = -4
y-intercept = 23
Hence, slope of the equation is equals to -4.
Learn more about slope here
https://brainly.com/question/3605446
#SPJ2
Olivia counted the number of ladybugs on each plant in her garden, then made the graph below.
If ten ladybug fly from the lettuce to the alfalfa, which 2 kinds of plants will have the same number of ladybugs?
Choose 2 answers:
A) Roses
B) Lettuce
C) Alfalfa
D) Grape vines
Answer:
A) Roses , C) Alfalfa
Step-by-step explanation:
Each ladybug symbol = 5 ladybugs
Roses: 35 ladybugs
Lettuce: 15 ladybugs
Alfalfa: 25 ladybugs
Grape vines: 10 ladybugs
10 ladybugs go from lettuce to alfalfa. You end up with:
Roses: 35 ladybugs
Lettuce: 5 ladybugs
Alfalfa: 35 ladybugs
Grape vines: 10 ladybugs
Roses and alfalfa end up with 35 ladybugs each.
Answer: A) Roses , C) Alfalfa
A resting heart rate for men on a chart say 62-65 beats per minute puts men in the good category of scott counted 238 heart beats in 3 1/2 minutes does his heart rate fall into the good category
Solve. -1/2+(3/4x4/9)=
Answer:
-1/6
Step-by-step explanation:
- 1/2 + 3/4 x 4/9 = -1/2 + 3(4) / 4(9) = -1/2 + 12 / 36 = -1/ 2 + 1 / 3 = -3/6 + 2/6 = -1/6
The solution for the given expression [tex]-\frac{1}{2} +(\frac{3}{4} \times \frac{4}{9} )[/tex] after simplifying the expression is [tex]-\frac{1}{6}[/tex].
Given an expression:
[tex]-\frac{1}{2} +(\frac{3}{4} \times \frac{4}{9} )[/tex]
It is required to find the value of the expression after simplifying the expression.
Since there is more than one operation used in this expression, the rule of BODMAS has to be used.
The expression in brackets has to be solved first, which is [tex]\frac{3}{4} \times \frac{4}{9}[/tex].
Here, the numerator of the first fraction and the denominator of the second fraction is 4. So, it can be canceled.
So, this can be simplified as:
[tex]\frac{3}{4} \times \frac{4}{9} =\frac{3}{9}[/tex]
[tex]=\frac{1}{3}[/tex]
The whole expression thus is [tex]-\frac{1}{2} +\frac{1}{3}[/tex].
Make the denominators equal.
[tex]-\frac{1}{2} +\frac{1}{3} =-\frac{3}{6} +\frac{2}{6}[/tex]
[tex]=-\frac{1}{6}[/tex]
Hence, the value is [tex]-\frac{1}{6}[/tex].
Learn more about Fractions here :
https://brainly.com/question/10354322
#SPJ6
3xy + 5x + 2 + 3y +x + 4
Answer:
= 3xy + ( 5x + x) + 3y + ( 4 +2 )
= 3xy + 6x + 3y + 6
Suzi can type around 50 words per minute she has less than a week to taper final research paper is the paper has to at least be 20 pages long and each Page has about 380 words how many hours should Susie Santa side to taper assignment show your work to receive full credit round your answer to the nearest tenths place
Answer:
2.5 hours
Step-by-step explanation:
(380/50) x 20
7.6 x 20
152
The final answer wold be 152 minutes or 2.5 hours
It costs $10 to initially get in to a county fair, then $2 for every ride that somebody wants to go on. What would be the slope and the y-intercept
in this situation?
Select 2 that apply
Da
Lь
d
Y-Intercept = 10
Y-Intercept = 5
Y-Intercept = 2
Y-Intercept = 20
Slope = 5
Slope = 20
Slope = 2
Slope = 10
Le
h
Answer:
y intercept is 10 and slope is 2
Step-by-step explanation:
Solve 4(2x − 1) − 3 = 9(x − 4)
Answer:
x = 29
Step by step explantion:
Answer:
x = 29
Step-by-step explanation:
Distribute/ Multiply:
8x - 4 - 3 = 9x - 36
Rearrange the equation:
8x - 9x = -36 + 4 + 3
Combine like terms:
-1x = -29
Divide:
x = 29
If you could help solve this and show your work I would really appreciate it
Answer:
D
Step-by-step explanation:
The difference between 63y and 35y is 28y. 28/2=14, 28/4=7, 28/7=4, 28/9=not whole number so I'm not doing the math, and to make sure we are right, 28/14=2
Answer:
9Step-by-step explanation:
[tex]63y-35y\\=28y[/tex]
[tex]\frac{28y}{2} = 14y\\\\\frac{28y}{4} = 7y\\\\\frac{28y}{7} =4y\\\\\frac{28y}{14} = 2y\\\\\frac{28y}{9} =3.1111y[/tex]
Evaluate 6+x6+x6, plus, x when x=3?
Answer:
42
Step-by-step explanation:
x=3
6+x6+x6
6+(3)6+(3)6
6=6
(3)6=18
(3)6=18
6+18+18
24+18
42
Hope this helps ;) ❤❤❤
Answer:
1467Step-by-step explanation:
[tex]6+x^6+x^6+x\\\\6+(3)^6+(3)^6+3\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:exponents}\:\left(3\right)^6\::\quad 729\\=6+729+\left(3\right)^6+3\\\\\mathrm{Calculate\:exponents}\:\left(3\right)^6\::\quad 729\\=6+729+729+3\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:6+729+729+3\::\quad 1467[/tex]
What is 196 classified as
Answer:
it is so unclear to say . If any more information is given, then only it can be answered. I don't think 196 is so special to be classified.
a^2+b^2=9 , a+b=? with the method
Answer:
3
Step-by-step explanation:
a^2+b^2=9
(a+b)^2=9
finding the square root on both sides of the equation
a+b=3
What percent is 16 hr of 2 days
Answer: 33.33%
Step-by-step explanation:
1 day=24 hrs, 2 days=48hrs
16hrs/2days × 100%
=16hrs/48hrs × 100%
=0.333... × 100%
=33.33% (rounded)
Step-by-step explanation:
[tex] \frac{16}{100} \times 48(2day) = 7.68\%[/tex]
The quadratic function g(x) has a vertex at (-5, 0) and y-intercept of (0, -5). What is g(1)?
Answer:
g(1)=7 1/5
Step-by-step explanation:
vertex (-5,0) , y intercept(0,5)
the quadratic equation is in the form of a parabola: y=ax²+bx+c
y=a(x-h)²+k find a and b and c
5=a(0-(-5))²+0
5=a(5)²+0
5=25a ⇒ a=5/25 ⇒ a=1/5
-b/2a=h
-b=2ah ⇒=-b=2(1/5)(-5) ⇒ -b=-2⇒ b=2
y=c=5 ( when x=0, y intercept)
y=1/5x² + 2x + 5
g(1)=1/5(1)²+2(1)+5
g(1)=1/5+2+5
g(1)=7 1/5
A quadratic function has a degree of 2, and it is represented as: [tex]y = ax^2 + bx + c[/tex]. The value of g(1) is -7.2
Given that:
[tex](h,k) = (-5,0)[/tex] --- the vertex
[tex](x,y) = (0,-5)[/tex] --- the y-intercept
The quadratic function in vertex form is:
[tex]y = a(x - h)^2 + k[/tex]
Where:
[tex](h,k) = (-5,0)[/tex] --- the vertex
So, we have:
[tex]y = a(x - -5)^2 + 0[/tex]
[tex]y = a(x +5)^2[/tex]
Substitute [tex](x,y) = (0,-5)[/tex] to calculate the value of a
[tex]-5 = a(0 +5)^2[/tex]
[tex]-5 = a(5)^2[/tex]
[tex]-5 = a \times 25[/tex]
Divide both sides by 25
[tex]a = -\frac 15[/tex]
So, the quadratic equation is:
[tex]y = a(x +5)^2[/tex]
[tex]y = -\frac 15(x +5)^2[/tex]
Rewrite as a function
[tex]g(x) = -\frac 15(x +5)^2\\[/tex]
To calculate g(1), we simply substitute 1 for x
[tex]g(1) = -\frac 15(1 +5)^2[/tex]
[tex]g(1) = -\frac 15(6)^2[/tex]
[tex]g(1) = -\frac 15 \times 36[/tex]
[tex]g(1) = -7.2[/tex]
Hence:
The value of g(1) is -7.2
Read more about quadratic functions at:
https://brainly.com/question/4119784
write each expression using exponents 4 x p x 4 x p
Answer:
[tex]4 * p * 4 * p = 4^2p^2[/tex]
Step-by-step explanation:
Given
[tex]4 * p * 4 * p[/tex]
Required
Write as exponents
[tex]4 * p * 4 * p[/tex]
Rearrange to collect Like Terms
[tex]4 * 4 *p * p[/tex]
Group both items
[tex](4 * 4) *(p * p)[/tex]
Apply law of indices
[tex](4^{1+1})(p^{1+1})[/tex]
[tex](4^2)(p^2)[/tex]
Remove bracket
[tex]4^2p^2[/tex]
Hence:
[tex]4 * p * 4 * p = 4^2p^2[/tex]