Answer:
Step-by-step explanation:
I'm going to assume you meant y = ab^x. If this is not correct, leave a comment.
x = 0
y = 7
7 = a * b^0
anything to the zero power is 1
y = a*b^0
y = a*1
7 = a
So far what you have is
y = 7 * b^x
Now let
x = 9
y = 3584
3584 = 7 * b^9 Divide by 7
3584/7 = b^9
512 = b^9
If you knew how to use logs, that would be the surest way to do this question. However I'm going to make an assumption again and assume that you have not taken those yet.
So the easiest way is to find out what raised to the 9th power will equal 512
Could b = 5?
5^9 = 1 million 9 hundred thousand something. 5 is far too big. Make sure you understand why. 1 million is far greater than 512
So let's try b = 3
3^9 = 19 thousand which is still far too big. 19 thousand something is far larger than 512.
We have just one more number that we can try.
2^9 = 512 and we have it
Answer y = 7*2^x
The expression 2x+(x-7)^2 is equivalent to x^2+bx+49 for all values of x.
what is the value of b?
A. 12
B. -12
C. 14
D. -14
The expression [tex]2x+(x-7)^2[/tex] is equivalent to [tex]x^2+bx+49[/tex].
Then Value of b is - 12.
Option(B) is correct answer.
What is an expression?An expression is a mathematical phrase combining numbers and/or variables using mathematical operations. Both sides of an equation are expressions.
According to the question,
The expression [tex]2x+(x-7)^2[/tex] is equivalent to [tex]x^2+bx+49[/tex].
[tex]2x+(x-7)^{2}=x^{2} +bx+49[/tex]
⇒ [tex]2x+(x-7)^{2}=x^{2} +bx+49[/tex]
⇒[tex]2x+x^{2} -14x+49=x^{2} +bx+49[/tex]
⇒ [tex]x^{2} -12x+49=x^{2} +bx+49[/tex]
⇒[tex]-12x=bx[/tex]
⇒ [tex]b=-12[/tex]
∴ [tex]b=-12[/tex]
Hence, the expression [tex]2x+(x-7)^2[/tex] is equivalent to [tex]x^2+bx+49[/tex].
Then Value of b is - 12.
Option(B) is correct answer.
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Mr. Dominguez wrote the formula below to calculate o, the acceleration of his motor.
V-S
а
t-b
Solve Mr. Dominguez's formula for t, the final time.
Answer:
t = {(v - s) + ab} / a
Step-by-step explanation:
a = (v - s) / (t - b)
Make t the subject of the equation
a = (v - s) / (t - b)
Cross product
a * (t - b) = (v - s)
at - ab = (v - s)
Add ab to both sides
at = (v - s) + ab
t = {(v - s) + ab} / a
The drama club is running a lemonade stand to raise money for its new production. A local grocery store donated cans of lemonade and bottles of water. Cans of lemonade sell for $2.50 each and bottles of water sell for $1.25 each. The club needs to raise at least $600 to cover the cost of renting costumes. The students can accept a maximum of 460 cans and bottles.
Write a system of inequalities that can be used to represent this situation.
The club sells 144 cans of lemonade. What is the least number of bottles of water that must be sold to cover the cost of renting costumes? Justify your answer.
Answer:
Step-by-step explanation:
The drama club is running a lemonade stand to raise money for its new production. A local grocery store donated cans of lemonade and bottles of water. Cans of lemonade sell for $2.50 each and bottles of water sell for $1.25 each. The club needs to raise at least $600 to cover the cost of renting costumes. The students can accept a maximum of 460 cans and bottles.
Write a system of inequalities that can be used to represent this situation.
The club sells 144 cans of lemonade. What is the least number of bottles of water that must be sold to cover the cost of renting costumes? Justify your answer
Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
can someone please help me with this?? please please please help me
Step-by-step explanation:
base is 12, hypotenuse is 20
so X² is h²-b²
so X=16
A 200 foot long zipline cable is attached to the top of a tree and extends to an anchor on the ground. The cable makes an angle of 61º with the ground. Calculate how far away the foot of the cable is to the base of the tree.
Answer:
~ 97 ft
Step-by-step explanation:
cos = adj/hyp
cos61 = adj/200
200 * cos61 = adj
adj = 96.961924049267406
~ 97 ft
The foot of the cable is 95 feet away from the base of the tree.
What is Trigonometric Function?Trigonometric functions are mathematical functions that relate the angles of a right triangle to the ratios of the sides of the triangle.
We have,
The angle between the ground and the cable is given as 61º.
In a right triangle, the side opposite the angle (in this case, the height of the tree) is related to the hypotenuse (the length of the cable) and the adjacent side (the distance from the foot of the cable to the base of the tree) by the trigonometric function cosine.
Cosine(angle) = adjacent/hypotenuse
Cos(61º) = adjacent/200 ft
adjacent = Cos(61º)x200 ft
adjacent ≈ 0.475 x 200 ft
adjacent ≈ 95 ft
Therefore, the foot of the cable is 95 feet away from the base of the tree.
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Given: m∠ELG = 124°
Prove: x = 28
3 lines are shown. A line with points D, L, G intersects a line with points E, L, H at point L. Another line extends from point L to point F between angle E L G. Angle D L E is (2 x) degrees.
Complete the steps in the two-column proof.
♣:
♦:
Answer:
clover
Step-by-step explanation:
because
The measure of angle ∠x = 28°.
We have a geometrical figure [Refer to the image attached in the end].
We have to prove that x = 28°.
What is the measure of a Straight angle.The measure of straight angle is 180°.
According to the question -
Line DLG is a Straight line. Therefore -
2∠x + 124° = 180°
2∠x = 56°
∠x = 28°
Hence Proved.
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Lisa took a survey of her classmates' favorite sport and recorded their genders. The results are in the table below:
What is the marginal relative frequency of survey participants who are girls?
0.06
0.5
0.43
17
Using it's concept, it is found that the marginal relative frequency of survey participants who are girls is of 0.43.
What is a relative frequency?A relative frequency is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that there were 2 + 3 + 5 + 4 + 3 + 8 + 2 + 6 + 4 + 3 = 40 participants, of which 17 are girls, hence the relative frequency is given by:
f = 17/40 = 0.425
Which is rounded to 0.43.
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Which of these is an example of typing at a rate of 42 words per minute?
A typing 21 words in 2 minutes
B typing 84 words in 3 minutes
C typing 210 words in 5 minutes
D
typing 400 words in 10 minutes
what is. perfect square
Answer:
a four sided parallelogram where all angles are the same and all sides are the same length
^^the question above in the photo
Answer:
11
Step-by-step explanation:
Which line is the correct graph for y = -3/4x
A/ blue line
B/ purple line
C/ green line
D/ red line
Answer:D
Step-by-step explanation:
christian has a collection of 18 shark teeth he has 6 tiger shark what precentage is tiger
Answer:
33.3% I think lpl
Step-by-step explanation:
The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water is the pool?
Answer:
The height of the water increases 2 inches per minute. Or A
Step-by-step explanation:
Edge
Answer: A ( The height of the water increases 2 inches per minute)
I am making two kinds of cookies: chocolate chip and lemon cookies.
(a)
Chocolate Chip Cookies
It takes 0.25 cup of sugar to make a batch of chocolate chip cookies. I have 5.50 cups of sugar. How many batches of cookies can I make?
I can make
batches of chocolate chip cookies.
You may use the scratchpad to show your work.
(b) Lemon Cookies
It takes 0.75 cups of sugar to make a batch of lemon cookies. I have 5.5 cups of sugar. How many batches can I make?
I can make
batches of lemon cookies.
You may use the scratchpad to show your work
Enter your answer as a fraction
Uhh sorry to bother again I’ve had no motivation haven’t been paying attention so uh yea
22 chocolate cookies can be made from 5.50 cups of sugar and 7 lemon cookies can be made from 5.50 cups of sugar
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The chocolate cookies is given as:
Number of chocolate cookies = 5.50 cups / 0.25 cup per cookie = 22
The lemon cookies is given as:
Number of lemon cookies = 5.50 cups / 0.75 cup per cookie = 7
22 chocolate cookies can be made from 5.50 cups of sugar and 7 lemon cookies can be made from 5.50 cups of sugar
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The equation SA = 6s can be used to calculate the surface area, SA, of a cube with side length S. What is the
surface area, in square meters, of a cube with a side length of 0.5 meter?
A woman invested 4 times much at 4% as she did at 9%. The total amount of interest she earns in 1 year from both accounts is $500. How much did she invest at each rate?
Answer:
$2,000 at 9%
$8,000 at 4%
Step-by-step explanation:
(4x * .04) + (x * .09) = 500
.16x + .09x
.25x = 500
x = $2,000 at 9%
4x = $8,000 at 4%
Answer:
2000 at 9%
8000 at 4%
Step-by-step explanation:
Let the principle at 9% = x
The principle at 4% = 4*x
Together they give 500 dollars.
9% = .09
4% = ,04
Both are invested for 1 year
0.09 * 1 * x + 0.04 * 1 * 4x = 500
0.09x + 0.16x = 500
0.25x = 500
x = 500 / 0.25
x = 2000
She invested 2000 at 9%
She invested 4 * 2000 at 4%
Help plzzzz !!!!!!!!!
1. The function h defined by h(t)=(49 + 4.9t)(10 - t) models the height, in meters, of an object t seconds after it is dropped from a helicopter. Find or approximate the time when the object hits the ground. Explain your method.
2.The function h defined by h(t)=(49 + 4.9t)(10 - t) models the height, in meters, of an object t seconds after it is dropped from a helicopter.
From what height is the object dropped? Explain how you know.
Answer:
Step-by-step explanation:
Let's FOIL this out and get it into standard form. That gives us:
[tex]h(t)=-4.9t^2+490[/tex] For #1, then:
The height of something when it is on the ground is 0; that means that the h(t) is 0. This allows us to factor the quadratic and solve for t:
[tex]-4.9t^2=-490[/tex] and divide both sides by 4.9 to get
[tex]t^2=100[/tex] so
t = 10. Notice that one of the factors for that quadratic is 10 - t. That factor represents the time it takes to hit the ground. So you might ask why, then, we FOILed this out in the first place if the answer was ight in front of our noses. The reason is becase of #2 that is asking us what the initial height of the object was. That is found in the standard form...in the constant in particular. The initial height is 490 m. That's how you know (because the constant represents the height from which an object is dropped in either free fall, which this is, or in parabolic motion).
determine whether the given lines are parallel or not right with the reason
Answer:
[tex]AB[/tex] is parallel to [tex]CD[/tex] ([tex]AB ||CD[/tex])
Step-by-step explanation:
In a set of parallel lines cut by the traversal, [tex]\angle AHG[/tex] and [tex]\angle DGH[/tex] are alternate interior angles. In a set of parallel lines cut by a traversal, alternate interior angles are always equal. Therefore, since [tex]\angle AHG=\angle DGH=115^{\circ}[/tex] (they are equal), the lines AB and CD must be parallel.
*A set of parallel lines proves that alternate interior angles are always equal, but the converse is also true in that equal alternate interior angles proves a set of parallel lines. This is because if you changed the angle measure of either of the angles, the relative slope of the lines must change and they would no longer be parallel.
Why are (1, 2) and (2, 1) sot equal ordered pairs
Answer:
Step-by-step explanation:
(1,2) and (2,1) are not equal ordered pairs becasue their corresponding elements are not equal.
Two Ordered Pairs are said to be equal if the corresponding first components are equal alongside the corresponding second components are equal.
for example:
(3,1) and (3,1)
here corresponding element of 3 is 3 and of 1 is 1 .so they are called equal ordered pairs.
The vertices of quadrilateral DEFG are D(-2, 6), E(-4, 6), F(-6, 9), and G(-1, 9). Find the coordinates of the image of quadrilateral DEFG after a translation using the rule (x, y) → (x + 1, y - 6), a reflection over the x-axis, and a reflection over the y-axis
Answer:
the coordinates from all of the transformations are (1,0) (3,0) (5,-3) (0,-3)
Step-by-step explanation:
after using the first rule the coordinates were (-1,0)(-3,0)(-5,3)(0,3)
after reflectiong it over the x-axis (-1,0)(-3,0)(-5,-3)(0,-3)
after reflecting it over the y-axis it gave the final answer of (1,0) (3,0) (5,-3) (0,-3)
Find the lateral area of a cone with a diameter of 10 centimeters and a slant height of 9 centimeters round to the nearest tenth
Answer:
The lateral area of a cone is 141.4 square centimeters
Step-by-step explanation:
Mathematically, we have the formula for the lateral area of a cone as;
A = pi * r * l
where r is the radius of the cone and l
is the slant height of the cone
Mathematically, the radius is simply half the measure of the diameter
we have that as 10/2 = 5 cm
So substituting these values;
A = 22/7 * 9 * 5
A = 141.4 square centimeters
Solve for the answer.
Let x=10
4x + 12=
(A) 0.52
(B) 5.2
(C) 52
Answer:
c 52
Step-by-step explanation:
x=10
4 ×10=40
40+12=52
For the Transformation T write the T-1
T: (x, y) = (x + 4, y + 3)
Т-1 (x, y) -
(x+3, y + 2)
(x-4, y-3)
(x+, y + 3)
Answer:
(T - 1)(x, y) = (x - 4, y - 3)
Step-by-step explanation:
For a given transformation:
T(x, y) = (x', y')
the inverse transformation is defined by:
(T - 1)(x', y') = (x, y)
So, if our transformation is:
T(x, y) = (x + 4, y + 3)
Then for the inverse transformation, we should have:
(T - 1)(x + 4, y + 3) = (x, y)
So the inverse transformation reduces the x-value by 4, and reduces the y-value by 3.
Writing the inverse transformation for a generic (x, y) point, we get:
(T - 1)(x, y) = (x - 4, y - 3)
How do you know you're good at sleeping I need help
Answer:
You can do it with your eyes closed
Step-by-step explanation:
PLS ANSWER ASAP PLS DUE AT 9:35
Answer:
your answer is option B
Answer:
Your answer came out to be B.
after reading the directions to paint,on the paint drum, the information indicated two coats of paints is required when using the 5 liter paint and one coat with the 20 liter drum. With both paints 1 litre of paint covers 9 meter squared.
There are 28 rooms to be painted.Show with calculations which will be cheaper paint to buy
 can someone pls help for brainlest
Answer:
[tex]surface \: area = area \: of \: base + area \: of \: the \: 4 \: triangular \: faces \\ = (l \times w) + 8 \times ( \frac{1}{2} \times base \times height) \\ = (4 \times 4) + 8 \times ( \frac{1}{2} \times 2 \times 7) \\ = 16 + 56 \\ = { \boxed{72}} \: square \: millimeters[/tex]
Warm-Up
Construct a perpendicular bisector to PQ
by following these steps.
1. Move the compass center to P and
draw a long arc that intersects PQ.
Then move the compass to Q and
draw an arc that intersects the first
arc in two places.
Note that the perpendicular bisector to line PQ is constructed and attached accordingly. Here is how to do it.
Note that the first stage is to draw a line PQ. But this has already been done.
Next is to place the compass on P as shown in the image above. If you allow you compass (locked at the same degree) to rotate about point P, you will get a circle. However, that is not the objective.
If you also place your compass on point Q, locked to the same degree as when it was on P, and take a rotation around point Q, you will also get a circle.
At some point, you will notice that both circles intersect at two point, which we can call AB₁ and AB₂.
Now you are done with the compass. Take up your ruler, and place it such that it meet both AB₁ and AB₂ but allowing you space to mark a line connecting both points.
Next, using your live or online pencil tool, draw the line from AB₁ to AB₂. Now you have the Perpendicular bisector which you can call AB₁₂.
Note that a perpendicular bisector is a line or plane that intersects a line segment at its midpoint, forming a right angle and dividing the segment into two equal parts.
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