Answer:
Let A (2a, 4a)
B(2a, 6a)
C (2a + sqrt (3a), 5a)
Side AC:
[tex]\sqrt{(2a+\sqrt{3a}-2a)^2+(5a-4a)^2 }=\sqrt{3a+a^2}[/tex]
Side BC:
[tex]\sqrt{(2a+\sqrt{3a}-2a)^2+(5a-6a)^2 }=\sqrt{3a+a^2}[/tex]
Hence AC = BC
It is an isoceles triangle.
Side AB:
[tex]\sqrt{(2a-2a)^2+(6a-4a)^2 }=\sqrt{2a^2}=2a[/tex]
It proves that the triangle is NOT an equilateral triangle.
Average Weight Animal At Birth (g) Adult Female(g) Adult Male (g) Hamster 2 120 110 Guinea pig 65 800 1,030 Rat 7 265 470 On average, a hamster at birth weighs 2 3 the weight of a gerbil at birth. Enter and solve an equation to find the average weight of a gerbil at birth. Let g represent your variable. The equation is . The average weight of a gerbil at birth is g.
Answer:
The answer is below
Step-by-step explanation:
An equation is a mathematical statement that shows the equality between two expressions.
From the table, the average weight of the hamster at birth is 2 grams. The average weight of gerbil at birth is 2/3 of that of hamster. Let g represents the weight of the gerbil at birth, hence the weight can be gotten by solving the equation:
2/3 of hamster weight at birth = Average weight of gerbil at birth
2/3 × 2 grams = g
g = 2/3 × 2 grams = 4/3 grams = 1.33 grams
The average weight of gerbil at birth = 1.33 grams
Max drove 460 miles in 8 hours at a constant speed. How long would it take him to drive 661.25 miles at that speeds?
Answer:
106
Step-by-step explanation:
Sksjwisjsjsoansnsan just to get points so give it a thanks thing ty
Answer:
x=11.5hours
Step-by-step explanation:
661.25miles÷57.5mph=11.5hours
How many oranges equal 6 cups of juice?
Answer:
1/3
Because 1/3 if divide into two, it'll be 0.5/3 but if the question says that the answer have to be in whole number, that means it must be 1/6.
Answer:12
Step-by-step explanation:
because it will take 2 to make a cup
POLYNOMIALS
1. Find a quadratic polynomial whose zeroes are 3 and -5
Answer:
y = x² + 2x - 15
Step-by-step explanation:
Given the zeros are x = 3 and x = - 5 then the factors are (x - 3) and (x + 5)
The polynomial is then the product of its factors, thus
y = (x - 3)(x + 5) ← expand using FOIL
y = x² + 2x - 15
Using inductive reasoning, determine the next two terms in each sequence. -3, 5, -7, 9, , A, C, F, J, , Blank 1: Blank 2: Blank 3: Blank 4:
Answer:
A = -11
C = 13
F = -15
J = 17
Step-by-step explanation:
Inductive reasoning is the use of observations to draw a conclusion.
The sequence of numbers in this problem is:
-3, 5, -7, 9, ...
A pattern is observed and that pattern is:
(n + 1) th term = |nth term| + 2 (with alternating negative signs)
for instance if (n+1)th term = 2nd term; nth term = 1st term
2nd term = |1st term| + 2
2nd term = |-3| + 2 = 5 (no negative sign since previous term had negative)
-3rd term = |5| + 2 = -7 (negative sign because the previous term was positive)
4th term = |-7| + 2 = 9 (no negative sign since previous term had negative)
-5th term (A)= |9| + 2 = - 11 (negative sign because the previous term was positive)
6th term (C) = |-11| + 2 = 13 (no negative sign since previous term had negative)
if you use the same sequence for F and J, you will get:
F = -15
J = 17
you should try them out to see if you will get the same solution.
Find the volume of a box with a height that is 4 inches less than the
length and a width equal to the length. Let x represent the length of the
box. (Formula for volume of a rectangular prism: V equals L times W
times H where L is length, W is width, H is height of the rectangular
prism)
Answer:
Volume of the box = x^3 - 4x^2
Step-by-step explanation:
V = L × W × H
Where,
V = volume of the rectangular prism
L= Length
W = Width
H = Height
volume of the rectangular prism = length × width × height
Length = x
Width= length = x
Height = x - 4
V = L × W × H
= x * x * (x - 4)
= x^2 (x - 4)
= x^3 - 4x^2
V = x^3 - 4x^2
Volume of the box = x^3 - 4x^2
Elliott put 7 cups of tea in to a jar. How many more cups of tea does he need to fill up the jar? Capacity: 4 quarts (1 quart = 4 cups)
Answer:
9 cups
Step-by-step explanation:
1 quart= 4 cups
4 quart= ? cups (crisscross)
4 quart=16 cups
16-7= 9 cups
Explicit equation:
Recursive:
y = 3x + 7
now = previous term + 3
50
term #
1
2
value
10
13
...
Find the value of the 50th term.
Explanation:
Answer:
50th term = 157
Step-by-step explanation:
Explicit equation for the given table is,
y = 3x + 7
And recursive formula is,
Now = previous + 3
To find the 50th term explicit formula should be used because it will be very difficult to find all 50 terms with the use of recursive formula.
From explicit formula,
y = 3x + 7
y = 3(50) + 7
= 157
Therefore, 50th term of the given table will be 157.
side length of 216 cubic yards
Answer:
6 yards
Step-by-step explanation:
a³ = 216
a = ∛ 216
= 6 yards
Answer:
6 yards
Step-by-step explanation:
The volume of a cube can be found using the following formula.
[tex]v= s^3[/tex]
We know the volume is 216 cubic yards, so we can substitute 216 yd³ in for v.
[tex]216 yd^3=s^3[/tex]
We want to find the side length. Therefore, we must isolate the variable, s, on one side of the equation.
s is being cubed. The inverse of cubed is the cube root. Take the cube root of both sides of the equation.
[tex]\sqrt[3]{216 yd^3}=\sqrt[3]{s^3}[/tex]
[tex]\sqrt[3]{216yd^3}=s[/tex]
[tex]6yd=6[/tex]
The side length of the cube is 6 yards.
Help please 45³+78-64
Answer:
91267
Step-by-step explanation:
?
3k12 + 23k4 – 18k? _71
Answer:
Step-by-step explanation:
Something
f(x)=x2-x find f (3)
Answer:
f(3) =6
Step-by-step explanation:
[tex]f(x) =x^2 -x\\\\f(3) = ?\\\\f(3) = (3)^2 -3\\f(3) = 9-3\\f(3) =6[/tex]
Answer:
[tex]\huge \boxed{\sf{f(3)=6}}[/tex]
Step-by-step explanation:
[tex]\sf f(x)=x^2-x[/tex]
For f(3), the input or x value is 3.
[tex]\sf f(3)=3^2-3[/tex]
Evaluate the expression.
[tex]\sf f(3)=9-3[/tex]
[tex]\sf f(3)=6[/tex]
Solve for c .
A(c+b)=d
answer choices are in the pic
Answer:
A(c+b)=d.
Ac+Ab=d.
Ac=d-Ab.
Divide through by A.
c=d-ab/a.
Option A.
Steps to solve:
a(c + b) = d
~Distribute
ac + ab = d
~Subtract ab to both sides
ac = d - ab
~Divide a to both sides
c = d-ab/a (Option 1)
Best of Luck!
What is the slope of
3y = -4x + 6
Answer:
Hey there!
3y=-4x+6
y=-4/3x+2
Thus, the slope is -4/3.
Hope this helps :)
Answer:
the slope is -4/3
Step-by-step explanation:
3y = -4x + 6
y=-4/3 x +6/3
y=-4/3 x+2
the slope is -4/3
It takes a bus 6 hours to take a trip. The train takes only 4 hours to make the same trip. The train travels at a rate of speed that is 25 mph more than the speed of the bus. What is the rate of the bus and the rate of the train? State what x represents, state the equation, and then state the answer.
Answer:
x represents the trip distance.
x = 300 miles
Rate of bus = 50 mph
Rate of train = 75 mph
Step-by-step explanation:
Let the trip distance be x miles.
[tex] \because \: speed = \frac{distance}{time} \\ time \: taken \: by \: bus \: to \: complete \: \\ the \: trip \: = 6 \: hours \\ \therefore \: speed \: of \: bus = \frac{x}{6} \: mph \\ \\ time \: taken \: by \: train \: to \: complete \: \\ the \: same \: trip \: = 4 \: hours \\ \therefore \: speed \: of \: train = \frac{x}{4} \: mph \\ \\ \because \: \: speed \: of \: train \\ =speed \: of \: bus \: + 25 \: mph \\ \therefore \: \frac{x}{4} = \frac{x}{6} + 25 \\ \\ \therefore \: \frac{x}{4} - \frac{x}{6} = 25 \\ \\ \therefore \: \frac{6x - 4x}{4 \times 6} = 25 \\ \\ \therefore \: \frac{2x}{24} = 25 \\ \\\therefore \: \frac{x}{12} = 25 \\ \\ \implies \: x = 25 \times 12 \\ \implies \: x =300 \: miles \\ \\ rate \: of \: bus = \frac{x}{6} = \frac{300}{6} = 50 \: mph\\ \\ rate \: of \: train = \frac{x}{4} = \frac{300}{4} = 75 \: mph[/tex]
a garden is in the shape of a rhombus whose each side is 15 and it's one of two diagonal each 24 find the area of Garden
Answer:
Hey there!
A=[tex]0.5p\sqrt{4a^2-p^2}[/tex]
A=216
Hope this helps :)
Can someone help me with part a?
Answer:
[tex]F(x)=\left\{\begin{array}{cl}15(40-x)&\text{if $0<x<40$}\\0&\text{if $40\le x\le65$}\\15(x-65)&\text{if $x>65$}\end{array}\right.[/tex]
Step-by-step explanation:
(a) For x below 40, the number of miles per hour below 40 is (40-x). Then the fine for that speed is 15(40 -x).
For x between limits, the fine is zero.
For x above 65, the number of miles per hour above 65 is (x-65). Then the fine for that speed is 15(x -65).
[tex]F(x)=\left\{\begin{array}{cl}15(40-x)&\text{if $0<x<40$}\\0&\text{if $40\le x\le65$}\\15(x-65)&\text{if $x>65$}\end{array}\right.[/tex]
Please help me whoever does it first will get brainliest!!! a) Write a ratio of girls to boys in three ways b) Write an equivalent ratio to the one you wrote in part a. c) Write the ratio of boys to girls in simplest form
Answer:
see below (I hope this helps!)
Step-by-step explanation:
a) There are 20 girls and 16 boys so three different ways to write the ratio could be 20:16, 20 / 16 or, in verbal form, 20 to 16.
b) An equivalent ratio to 20:16 is 10:8, all we do to get this is divide the ratio by 2.
c) Since there are 16 boys and 20 girls, the ratio is 16:20 which simplifies to 4:5.
- = 0.393 as a fraction?
Answer:
The answer is 393/1000
Step-by-step explanation:
Answer:
131/333 is the correct answer
Step-by-step explanation:
4) Given that x is an integar
find the three greatest value
of x which satisfies the lines
inequality 7x < 2x - 13
Answer:
The three greatest are -3, -4, -5
Step-by-step explanation:
7x < 2x - 13
Subtract 2x from each side
7x-2x < 2x-2x - 13
5x < -13
Divide by 5
5x/5 < - 13/5
x < - 2 3/5
Since x is an integer
-3 is the largest integer that fits the inequality
The three greatest are -3, -4, -5
Which properties can be used to solve 7y − 15 = −29? Select all that apply.
Answer:
addition property of equality
inverse property of multiplication
Step-by-step explanation:
7y − 15 = −29
Add 15 to each side using the addition property of equality
7y -15+15 = -29+15
7y = -14
Divide each side by 7 using the inverse property of multiplication
7y/7 = -14/7
y =2
Answer:
[tex]\Large \boxed{\mathrm{Addition \ Property \ of \ Equality}} \\\\\\ \Large \boxed{\mathrm{Inverse \ Property \ of \ Multiplication}}[/tex]
Step-by-step explanation:
[tex]\sf 7y-15=-29[/tex]
Using the additive property of equality, we add 15 to both sides of the equation.
[tex]\sf 7y-15+15=-29+15[/tex]
[tex]\sf 7y=-14[/tex]
Using the inverse property of multiplication, we divide both sides of the equation by 7.
[tex]\displaystyle \sf \frac{7y}{7} =\frac{-14}{7}[/tex]
[tex]\sf y = -2[/tex]
A group of boys went on a camping trip. They spent the night in 5 tents and 4 cabins. There were 9 boys in each tent and 7 boys in each cabin. How many boys went on the trip?
Answer:
Step-by-step explanation:
In a tent, there are nine boys.
There were five tents.
5 tents containing 9 boys can equal 45 boys.
(5 x 9 = 45)
In a cabin, there are seven boys.
There were four cabins.
4 cabins containing 7 boys can equal 28 boys.
(4 x 7 = 28)
Now, to find all the boys, add the numbers together.
28 boys with 45 boys will equal 73 boys.
Please check my answer for no one, not even me is right.
Good luck :)
write the polynomial the product and sum of whose zeroes are -9/2 and-3/2
Answer:
y = 2x² + 3x - 9
Step-by-step explanation:
Given αβ = - [tex]\frac{9}{2}[/tex] = [tex]\frac{c}{a}[/tex]
and α + β = - [tex]\frac{3}{2}[/tex] = - [tex]\frac{b}{a}[/tex]
Then a = 2, b = 3 and c = - 9, thus
y = 2x² + 3x - 9
Is 7,548,123 rational or irrational
Answer:
irrational number
Step-by-step explanation:
Answer:
I'm pretty sure its rational.
Step-by-step explanation:
Rational, I'm pretty sure is like above negative numbers. Irrational is like negative numbers, and yeah...I could be wrong. But I'm sure its rational.
i Find a rational number between -1/2 and 3/4 ?
Answer:
5/8
Step-by-step explanation:
Find the rational number half way between 1/2 and 3/4
First add 1/2 and 3/4
1/2 + 3/4 = 2/4 + 3/4 = 5/4
Next, divide this sum by 2
5/4 divided by 2/1 = 5/4 * 1/2 = 5/8
5/8 is half from 1/2 and 3/4
1/2 < 5/8 > 3/4
point w is on line segment VX. Given vx=4x, vw=3x and wx=5 determine the numerical length of vx
Answer:
Numerical length of VX = 20
Step-by-step explanation:
Given that VX is a line segment which has a point W on it.
Kindly refer to the attached diagram for the given points.
We are also given the following dimensions:
[tex]VX=4x\\VW=3x\ and \\WX=5[/tex]
To find:
Numerical length of VX = ?
Solution:
As we can clearly see from the attached diagram:
[tex]VX = VW + WX[/tex]
Putting the given values:
[tex]4x=3x+5[/tex]
Now, let us solve for [tex]x[/tex] and then will put the value of [tex]x[/tex] back to find the numerical value of VX.
[tex]\Rightarrow 4x-3x=5\\\Rightarrow x =5[/tex]
Now,
[tex]VX = 4 \times x = 4\times 5 =\bold{20}[/tex]
Therefore, numerical value of VX is 20.
what is: −6 − (−4)? i need to know
Answer:
-2
Step-by-step explanation:
-6-(-4)
-6+4
-2
Answer:
-2
Step-by-step explanation:
Make it simpler: -6 + 4-6 + 4 = -2Why:
When you subtract a negative, it automatically becomes a positive. That's why when we were making it simpler above, we canceled out the two minus signs (subtractions sign and negative sign) to make a positive 4. That's why we added a positive instead of subtracting a negative.A negative plus a positive will get bigger. That's why -6 + 4 = -2. The -2 is larger than -6 when you look at it on a number line. It's closer to 0 and the positives.at 7:00 am the temperature in wilton was -6 degrees. by 8:00 am the temperature was 2 degrees. what is the difference in the temperature between 8:00 am and 7:00 am?
Answer:
Step-by-step explanation:
at 7 the temperature=-6
at 8 the temperature=2
difference=8 degree
Answer:
- 8°
Explanation:
→ We write the data problems.
→ in Wilton - 7:00 am ⇒ - 6°
8:00 am ⇒ 2°
What is the difference in the temperature between 8:00 am and 7:00 am?
- 6° - 2° = - 8°
What is the difference between 6^ and ^ 6 ?
What type of number is 0.25726?
A) Rational, specifically an integer
B) Rational, not an integer
C) Irrational
Answer:
B. Rational, not an integer