Answer:
x = -2 and y = -2Step-by-step explanation:
The expression for calculating the point that divides the coordinate of two endpoints A(x, y) and B (x₁, y₁) in the ratio a:b with point C(X, Y) on the line is as shown below;
[tex]B[/tex][tex](X, Y) =[/tex] [tex](\dfrac{ax_1+bx}{b+a}, \dfrac{ay_1+by}{b+a})[/tex]
Given B(X, Y) = (4, 1), C(x₁, y₁) = (12,5) and AB:BC = a:b = 3/4
From the given coordinates, X = 4, Y = 1, x₁ = 12 y₁ = 5, a = 3 and b =4
From the coordinates above;
[tex]X = \dfrac{ax_1+bx}{b+a}[/tex]
[tex]4 = \dfrac{3(12)+4x}{4+3}\\\\4 = \dfrac{36+4x}{7}\\\\\\4*7 = 36+4x\\28 = 36+4x\\28-36 = 4x\\-8 = 4x\\x = -8/4\\x= -2[/tex]
Similarly to get y;
[tex]1 = \dfrac{3(5)+4y}{4+3}\\\\1 = \dfrac{15+4y}{7}\\\\\\1*7 = 15+4y\\7 = 15+4y\\7-15 = 4y\\-8 = 4y\\y= -8/4\\y= -2[/tex]
Hence the value of x is -2 and y is -2.
if
[tex] \frac{ {a}^{2x} }{ {a}^{(x - y)} } =a [/tex]
then y =
Answer:
y= 1-x
Step-by-step explanation:
● (a^2x)/a^(x-y) = a
This means that:
● 2x-(x-y) = 1
● 2x - x +y = 1
● x + y = 1
Substract x from both sides
● x+y -x = 1-x
● y = 1-x
Solve x^3 = 8/729 please answer
Answer:
x=2/9
Step-by-step explanation:
x^3=8/729
Hence,
x= cube root of (8/729)
x=cube root of 8
cube root of 729
x=2
9
Answer: decimal form : x=0.10475656
Step-by-step explanation:
Take roots of both sides and solve
evaluate the expression
Answer:
-5
Step-by-step explanation:
We are given the expression:
[tex]\frac{1}{4} [-5+5(-3)][/tex]
and asked to evaluate.
We must solve this expression according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.
Solve inside the brackets first. Multiply 5 and -3.
5 * -3= -15
[tex]\frac{1}{4} [-5+-15][/tex]
Add -5 and -15.
-5+-15= -20
[tex]\frac{1}{4} [-20][/tex]
Finally, multiply 1/4 and -20, or divide -20 by 4.
1/4 * -20 = -5 OR -20/4= -5
[tex]-5[/tex]
When evaluated, the expression 1/4 [ -5 +5(-3)] is equal to -5.
Multiplying two functions results in h(x) = 10x2 + 12x – 16, while adding the same functions results in j(x) = 7x. Which statements describe f(x) and g(x), the original functions? Select two options. Both functions must be linear. Both functions must be quadratic. Both functions must have a y-intercept of 0. The rate of change of either f(x) or g(x) must be 0. The y-intercepts of f(x) and g(x) must be opposites.
Answer:
Both functions must be linear. The y-intercepts of f(x) and g(x) must be opposites.
Step-by-step explanation:
First we need to solve.
h(x) = 10[tex]x^{2}[/tex] + 12[tex]x[/tex] - 16
It seems tricky at first but we know a couple things. When we add the factors of h(x) together we get j(x) = 7[tex]x[/tex] so we know that when we multiply 2 numbers together it should equal 10 but add up to 7.
Lets write the possible combinations of 10:
1 x 10 = 10
2 x 5 = 10
5 x 2 = 10
10 x 1 = 10
Now which combination will add or subtract to 7?
1 - 10 = 9 1 + 10 = 11
2 - 5 = -7 2 + 5 = 7 We can stop here!
2 and 5 are in our factor, so let's write it down.
(2x ) (5x ) We know there will one + and one - because the -16. If we had two + it would be positive 16, and is we had two - it would also be positive 16 because a - x - = +
Now the last number is 16. Let's find the possible combinations of 16.
1 x 16 = 16
2 x 8 = 16
4 x 4 = 16 We will stop here because we end up repeating posibilities.
Here is where we think critically. Whichever combination we choose has to be multiplied by 2 and 5 and end up equaling 12. I think 16 is too high so let's try 2 and 8.
2x * 2 = 4x 5x * 8 = 40x Now one is positive and the other is negative. Let's try each combination.
4x - 40x = -36x -4x + 40x = 36x Neither of those are 12x. So let's Try 4 and 4.
2x * 4 = 8x 5x * 4 = 20x One will be positive and the other will be negative. Let's try each combination.
8x - 20x = -12x -8x + 20x = 12x There is our combination! Remeber when you mutiply together you have to multiply the opposite factor. Here are the combinations:
(Ax + B )(Cx + D) = (Ax*Cx) + (Ax*D) + (B*Cx) + (B*D)
(Ax - B )(Cx + D) = (Ax*Cx) + (Ax*D) - (B*Cx) - (B*D)
(Ax + B )(Cx - D) = (Ax*Cx) - (Ax*D) + (B*Cx) - (B*D)
(Ax - B )(Cx - D) = (Ax*Cx) - (Ax*D) - (B*Cx) + (B*D)
So we have:
(2x + 4) (5x - 4)
Let's prove is and multiply it back out.
2x*5x - 2x*4 + 4*5x - 4*4
10[tex]x^{2}[/tex] - 8[tex]x[/tex] + 20
10[tex]x^{2}[/tex] + 12[tex]x[/tex] - 16 So we got it right!
Now let's see if they really add up to 7x.
(2x + 4) (5x - 4) which we now need to add together
2x + 4 + 5x - 4 Rearrange
2x + 5x + 4 - 4 Combine like terms
7x + 0 or 7x It works!
So our original functions are f(x) = 2x + 4 and g(x) = 5x - 4
Now to answer the question. Select 2 options.
Both functions must be linear. Yes, because an equation with only an [tex]x[/tex] will be a straight line, if we graph both functions they are both straight lines.
Both functions must be quadratic. No, because a quadratic equation is any equation that can be rearranged in standard form as [tex]ax^{2} + bx +c = 0[/tex] Neither f(x) or g(x) can be rearranged to fit that.
Both functions must have a y-intercept of 0. No, to find the y intercept we set x to 0 and solve for y.
2x + 4 = y 5x - 4 = y
2(0) + 4 = y 5(0) - 4 = y
0 + 4 = y 0 - 4 = y
y = 4 y = -4
Neither are 0.
The rate of change of either f(x) or g(x) must be 0. Let's find the rate of change for each equation.
We need an interval so we have to find one. Let's use 1 and 2 for x, but we have to solve for y to get the coordinate.
f(x[tex]_{1}[/tex]) = 2x + 4 f(x[tex]_{2}[/tex]) = 2x + 4 g(x1) = 5x - 4 g(x2) = 5x - 4
x[tex]_{1}[/tex] = 1 x[tex]_{2}[/tex] = 2 x
y[tex]_{1}[/tex] = 2(1) + 4 y[tex]_{2}[/tex] = 2(2) + 4 y
y[tex]_{1}[/tex] = 2 + 4 y[tex]_{2}[/tex] = 4 + 4 y
y[tex]_{1}[/tex] = 6 y[tex]_{2}[/tex] = 8 y
( 1 , 6 ) ( 2 , 8 ) ( 1 , 1 ) ( 2 , 6 )
Rate of change formula is:
[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
Now we just plug in for each function.
f(x) = 2x + 4 g(x) = 5x - 4
[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex] = [tex]\frac{8 - 6}{2 - 1}[/tex] = [tex]\frac{2}{1}[/tex] = 2
You can see the rate of change is not 0 for either function.
The y-intercepts of f(x) and g(x) must be opposites. Yes, we solved for the y intercepts earlier.
To find the y intercept we set x to 0 and solve for y.
2x + 4 = y 5x - 4 = y
2(0) + 4 = y 5(0) - 4 = y
0 + 4 = y 0 - 4 = y
y = 4 y = - 4
4 and - 4 are opposites, so this statement is also true.
Angle RST is a right angle. Angle RSU has a measure of 25°. Lines R S and S T connect to form a right angle. Another line extends from point S to point U. Angle R S U is 25 degrees. What is the measure of angle TSU? 25° 45° 65° 75°
Answer:
The measure of ∠TSU = 65°
Step-by-step explanation:
Since RST is a right-angled triangle and RS and ST connect to form a right angle, ∠RST = 90°. Also, since RS and ST connect to form a right angle, ∠RST = ∠RSU + ∠TSU.
We make ∠TSU subject of the formula. So,
∠TSU = ∠RST - ∠RSU
Given that angle ∠RSU = 25° and ∠RST = 90°, substituting these values into he expression for ∠TSU, we have
∠TSU = ∠RST - ∠RSU
∠TSU = 90° - 25°
∠TSU = 65°
So, ∠TSU = 65°
The measure of ∠TSU = 65°
Answer:
65
Step-by-step explanation:
you know it forms a right angle because of the marking on it
so take 90 because thats the degree of a right angle, and subtract 25 from it and you will get your other side
90-25=x
65=x
check by adding both angles
65+25=90
2 + 10 = 24
3 + 6 = 27
7 + 2 = 63
5 + 3 = ????
40
Step-by-step explanation:2 + 10 = 24
2(2 + 10) = 2×12 = 24
3 + 6 = 27
3(3 + 6) = 3×9 = 27
7 + 2 = 63
7(7 + 2) = 7×9 = 63
5 + 3 = 40
5(5 + 3) = 5×8 = 40
Find the value of X. I greatly appreciate your help
Answer:
x = 14
Step-by-step explanation:
comp = add up to be 90
3x + 14 + 2x + 6 = 90
5x + 20 = 90
5x = 70
x = 14
simplify : -2(3v - 6) ( WITH STEPS TOO)
please and thank you!!
Answer:
-2(3v - 6) = 0
-6v + 12 = 0
-6v = -12
v = -12/-6
v = 2 answer
Step-by-step explanation:
f(x)=2x+1 find x if f(x)=16 . Please help with this
Answer:
[tex]x=15/2=7.5[/tex]
Step-by-step explanation:
So we have the function:
[tex]f(x)=2x+1[/tex]
And we want to find x such that:
[tex]f(x)=16[/tex]
To do so, substitute 16 for f(x):
[tex]f(x)=2x+1\\16=2x+1[/tex]
Subtract 1 from both sides. The right side cancels:
[tex](16)-1=(2x+1)-1\\2x=15[/tex]
Divide both sides by 2. The left side cancels:
[tex](2x)/2=(15)/2\\x=15/2=7.5[/tex]
The value of x is 7.5
Answer:
[tex]x=\frac{15}{2}[/tex]
Step-by-step explanation:
We are given the value of f(x). Insert this value into the original equation:
[tex]f(x)=16\\\\16=2x+1[/tex]
Solve for x. Subtract 1 from both sides:
[tex]16-1=2x+1-1\\\\15=2x[/tex]
Divide both sides by 2 to isolate x:
[tex]\frac{15}{2} =\frac{2x}{2} \\\\\frac{15}{2}=x[/tex]
When f(x) equals 16, x is equal to [tex]\frac{15}{2}[/tex]
Wakaba buys some granola bars at $0.50 each and energy drinks at $2 each for a group hike. She buys twice as many granola bars as energy drinks. If she spends $27 in total, how many granola bars and energy drinks does she buy?
gronala bars:18
energy drinks:9
Step-by-step explanation:
$0.50 •18= $9
$2.00•9=$18
$9+$18=$27
please help im am timed
Answer:
________________________
I believe that it's 114 degrees.
________________________
Answer:
114
Step-by-step explanation:
angle Bcd=180-66=114 degrees
the two angles are supplementary equal to 180 degrees
explain about herb some lines
Answer:
Herbs are small plants that have a fleshy or juicy stem when they are young. The stems of some herbs develop hard, woody tissue when they grow old. Most herbs are perennials. This means that the tops of the plants die each growing season, but the roots remain alive and produce new plants year after year.
Step-by-step explanation:
Please help I will give out brainliest
Answer:
a. L.B. = 20.5
b. U.B. = 21.5
Step-by-step explanation:
Length is measured 21 cm correct to 2 significant figures
a. Lower bound of 21
= 20.5 < 21
= 20.5
b. Upper bound of 21
= 21 < 21.5
= 21.5
If the relation is a function, list the domain and range. If the relation is not a function, choose "not a function". C = {(9, 1) (8, -3) (7, 5) (-5, 3)} A: Domain: {9, 8, 7, -5} Range: {1, -3, 5, 3} B: Domain: {1, -3, 5, 3} Range: {9, 8, 7, -5} not a function
Answer:
A: Domain: {9, 8, 7, -5} Range: {1, -3, 5, 3}
Step-by-step explanation:
C = {(9, 1) (8, -3) (7, 5) (-5, 3)}
The domain is the inputs
Domain: { -5,7,8,9}
The range is the output
Range{ -3,1,3,5}
This is a functions since there is no input that goes to multiple outputs
Solve for x: the quantity of x plus 16 all over 3 = 3x (1 point) a x = −7 b x = −13 c x = 8 d x = 2
Answer:
D. X=2
Step-by-step explanation:
Answer:
X=2
Step-by-step explanation:
Jack had 3 bags of golf balls with bbb balls in each bag; then his friend gave him 6 more golf balls.
How many golf balls does Jack have now?
Write your answer as an expression.
Answer:
y=3b + 6 ................ . ..
The answer is 3b + 6 in Khan Accademy
Fuad’s model racing car drives at an average speed of 3 feet per second. Fuad records the distances and times in a table like the one shown below. Speed of Model Race Car Distance (ft.) 3 Time (s) 1 At this rate, how long will it take the car to travel 21 feet?
Answer:
7.0 seconds
Step-by-step explanation:
i did the test but how i know this is bc 3 divided by 21 is 7
NOT 9
DON'T USE 9 AS THE ANSWER
Answer:
7.0 seconds
Step-by-step explanation:
Inga knows that the radius of a certain cone is 4 cm and its volume is about 134 cubic centimeters. Which is the best estimate of the cone's height?
Answer:
h=8cm
Step-by-step explanation:
V= πr^2h/3
Where
V=volume of a cone
π=pi= 3.14
r= radius=4cm
h= height = ?
V= πr^2h/3
134= 3.14*4*4*h/3
134= 50.24h/3
Divide both sides by 50.24
h/3= 134 / 50.24
h/3= 2.67
Cross product
h= 2.67*3
h= 8.01
Approximately h= 8cm
The best estimate of the cone's height is 8cm
solve for x using zeros of function method
-x³+2x²+x-2=0
Answer:
x = - 1, x = 1, x = 2
Step-by-step explanation:
The coefficients of the polynomial sum to zero, that is
- 1 + 2 + 1 - 2 = 0
This indicates that x = 1 is a zero
let x = - 1, then
- (- 1)³ + 2(- 1)² + (- 1) - 2 = 1 + 2 - 1 - 2 = 0
Thus x = - 1 is a zero
let x = 2
- (2)³ + 2(2)² + 2 - 2 = - 8 + 8 + 2 - 2 = 0
Thus x = 2 is a zero
The 3 zeros are x = - 1, x = 1, x = 2
Preston adopted a cat from a rescue shelter. He needs to buy some cat litter, so he compares prices at different stores. He finds the best deal at Fluffy Felines Pet Shop, which sells a 20-pound jug of cat litter for $8.60. How much does the cat litter cost per pound?
Answer:
$0.43
Step-by-step explanation:
Preston adopted a cat from a rescue shelter
He needs to buy food for his new cat so he compared the price of cat litter at different stores
Preston gets the best deal at fluffy felines pet shop
They sell 20 pound jug litter for $8.60
Therefore the cost of the cat litter per pound can be calculated as follows
= 8.60/20
= 0.43
Hence the cost of the cat litter per pound is $0.43
sᴏʟᴠᴇ ɪᴛ ʙʏ sᴜʙsᴛɪᴛᴜᴛɪᴏɴ ᴍᴇᴛʜᴏᴅ
Answer:
x = 1
y = 1
Step-by-step explanation:
Given:
x/a + y/b = 1/a + 1/bx/a - y/b = 1/a - 1/bAdd up the two equations side-by-side, this will cancel y/b and 1/b:
x/a+x/a = 1/a+1/a2x/a=2/ax = 1Subtract the two equations side-by-side, this will cancel x/a and 1/a:
y/b+y/b = 1/b+1/b2y/b=2/by=1Answer:
x = 1, y = 1
Step-by-step explanation:
[tex] \frac{x}{a} + \frac{y}{b} = \frac{1}{a} + \frac{1}{b} .....(1) \\ \frac{x}{a} - \frac{y}{b} = \frac{1}{a} - \frac{1}{b} .....(2) \\ \\ let \: \: \frac{1}{a} = m, \:\:\&\: \: \frac{1}{b} = n \\ so \: equatin \: (1) \: reduces \: to: \: \\ \\ so \: equatin \: (1) \: reduces \: to: \: \\ mx + ny = m + n....(3)\\ and \: equatin \: (2) \: reduces \: to: \: \\ mx - ny = m - n....(4) \\ adding \: equations \: (3) \: (4) \\ mx + ny = m + n \\ mx - ny = m - n \\ - - - - - - - - - - \\ 2mx = 2m \\ x = \frac{2m}{2m} \\ \huge \red{ \boxed{x = 1}} \\ substituting \: x = 1 \: in \: equatin \: (3) \\ m \times 1 + ny \: = m + n \\ m + ny \: = m + n \\ ny = m + n - m \\ ny = n \\ y = \frac{n}{n} \\ \huge \purple{ \boxed{y = 1}}[/tex]
(7 thousands 3 tens) ÷ 10 =
Answer: 703
Step-by-step explanation:
This situation is the same as,
7,030 / 10 = 703
50 points pls answer I will give Brainlyist
Answer:
point A: 2
point B: -3
your friend is incorrect
Step-by-step explanation:
Answer:
point A: 2
point B: -3
your friend is incorrect
Step-by-step explanation:
How can I solve question b). ?
Answer:
It was not my intention to post that answer, as it does not solve the question, but hope it helps somehow.
Step-by-step explanation:
[tex]$\text{b)} \frac{\sin(a)}{\sin(a)-\cos(a)} - \frac{\cos(a)}{\cos(a)-\sin(a)} = \frac{1+\cot^2 (a)}{1-\cot^2 (a)} $[/tex]
You want to verify this identity.
[tex]$\frac{\sin(a)(\cos(a)-\sin(a))}{(\sin(a)-\cos(a))(\cos(a)-\sin(a))} - \frac{\cos(a)(\sin(a)-\cos(a))}{(\sin(a)-\cos(a))(\cos(a)-\sin(a))} = \frac{1+\cot^2 (a)}{1-\cot^2 (a)} $[/tex]
The common denominator is
[tex](\sin(a)-\cos(a))(\cos(a)-\sin(a))= \boxed{2\cos (a)\sin(a)-\cos ^2(a)-\sin ^2(a)}[/tex]
Solving the first and second numerator:
[tex]\sin(a)(\cos(a)-\sin(a))=\sin(a)\cos(a)-\sin^2(a)[/tex]
[tex]\cos(a)(\sin(a)-\cos(a))= \cos(a)\sin(a)-\cos^2(a)[/tex]
Now we have
[tex]$\frac{ \sin(a)\cos(a)-\sin^2(a) -(\cos(a)\sin(a)-\cos^2(a))}{2\cos (a)\sin(a)-\cos ^2(a)-\sin ^2(a)}$[/tex]
[tex]$\frac{ -\sin^2(a) +\cos^2(a)}{2\cos (a)\sin(a)-\cos ^2(a)-\sin ^2(a)}$[/tex]
Once
[tex]-\sin^2(a) +\cos^2(a) = \cos(2a)[/tex]
[tex]2\cos (a)\sin(a) = \sin(2a)[/tex]
Also, consider the identity:
[tex]\boxed{\sin^2(a)+\cos^2(a)=1}[/tex]
[tex]$\frac{ -\sin^2(a) +\cos^2(a)}{2\cos (a)\sin(a)-\cos ^2(a)-\sin ^2(a)}=\boxed{\frac{ \cos(2a)}{\sin(2a)-1}}$[/tex]
That last claim is true.
2x - y2
Z-5
Evaluate when x = 2, y = 4
z=3
Answer:
Putting the value in x = 2 , y =4 in 2x - 2y we get,
2 × 2 - 4× 2= 4-8 = -4
Putting the value in z = 3 in z - 5 we get,
z - 5 = 3 - 5 = -2
Write the slope intercept form of the equation of the line through (-4,5) and a slope of -2
Answer:
y=-2x-3
Step-by-step explanation:
y-y1=m(x-x1)
which property of equality was used to solve this equation
[tex]9x = 88 \\ \frac{9x}{9} = \frac{88}{9} \\ x = 9 \frac{7}{9} [/tex]
A. addition property of equality
B. subtraction property of equality
C. multiplication property of equality
D. division property of equality
Answer:
division property of equality.
Step-by-step explanation:
A species of phytoplankton measures about 2 × 10−6 in. A grain of sand measures about 1 × 10−4 in. About how many times longer is the grain of sand than the phytoplankton? A. 20 times greater B. 50 times greater C. 100 times greater D. 200 times greater
Answer:
B. 50 times greater
Step-by-step explanation:
Given;
size of phytoplankton = 2 × 10⁻⁶ in
size of sand grain = 1 × 10⁻⁴ in
Determine how many times longer the grain of sand is than the phytoplankton.
Divide the sand size by the phytoplankton size, to find out how much greater the sand is.
This can be done by equating it as follows;
2 × 10⁻⁶ (y) = 1 × 10⁻⁴
[tex]y = \frac{1*10^{-4}}{2*10^{-6}} \\\\y = 50[/tex]
Therefore, the grain of sand is 50 times greater than the phytoplankton
B. 50 times greater
Seven more than twice a number x is forty-seven
Step-by-step explanation:
Seven more than twice a number is 47. Let's break down this sentence into numbers so you can see what's going on.
"Seven more than twice a number" - This tells you that there is a number, let's call it y, that is 7 more than twice a different number, lets call this x. So in equation form this is y = 7 + 2x. Hmm this seems a little tricky, how do we find the answer? Well if we keep reading, it tells you that the number that is 7 more than twice another number is 47, so we now know that y = 47. So let's redo our equation by substituting y for the number 47:
47 = 7 + 2x
Now we have a workable equation. We need to solve for x. So let's rewrite this equation without changing it, just putting it in different order. Now we have 2x + 7 = 47. So how do we solve for x? First, we subtract 7 from both sides. Remember, when solving for x, anything you do to one side you must do to the other. So now we get this:
2x + 7 = 47 simplifies to 2x = 40
Now if we divide both sides by 2 to get x all by itself, we get x = 20. That is your answer. You can check it by substituting 20 for s in your original equation of 2x + 7 = 47, then you get 2(20) + 7 = 47. It works! Hope this helps!
A rectangular athletic field is twice as long as it is wide. If the perimeter of the athletic field is 72 yards, what are its dimensions?
what is the width? in yards
Answer:
Width= 12 yards
Length= 24 yards
Step-by-step explanation:
Perimeter of a rectangle= 2(length + width)
Let
w= width
Twice as long as it is wide
Length= 2w
Perimeter of the rectangle= 72 yards
Perimeter of a rectangle= 2(length + width)
72 = 2(2w + w)
72 = 4w + 2w
72 = 6w
Divide both sides by 6
72/6 = w
12= w
w=12
Therefore,
Width= 12 yards
Length= 2w
=2(12)
=24 yards