Answer:6
Step-by-step explanation:
4(2)^4 − 2(7)^2 + 40
4(16)-2(7)^2+40
64-2(49)+40
64-98+40
-34+40
6
Answer:
6
Step-by-step explanation:
4a^4 - 2b^2 + 40
Put a = 2 and b = 7
4(2)^4 - 2(7)^2 + 40
Solve the powers first.
4(16) - 2(49) + 40
Multiply.
64 - 98 + 40
Add and subtract.
= 6
For which function defined by a polynomial, are the zeros of the polynomial -2 and -7?
Answer:
Step-by-step explanation:
f(x)=a(x+2)(x+7)=a(x²+2x+7x+14)
or f(x)=a(x²+9x+14)
it has zeros as -2 and -7.
Expand the brackets and solve
3(2x+1)=x-7
15 POINTS AND BRAINLIEST ANSWER ASAP!
Give an example of a set of five ordered pairs that is a function. Given another example of a set of five ordered pairs that is NOT a function. Explain why the first set is a function and why the second set is not a function.
give answer here:
These are Function (7,2), (1,1), (8,1), (4,2), (3,11) These are not Functions (7,2), (1,1), (8,1), (4,2), (1,11)
step-by-step explanation:
The first set is a function i know this because for example the inputs which are 7,1,8,4,3 are buyers for a car and the output is 2,1,1,2,1 1 and those are the cars but the input is different buyers, The 2nd one has two of the same inputs which means the same buyer is buying two cars which is not fair so it makes it a non function.
A function y=f(x) has the property that for any x in the domain there is exactly one value for y=f(x).
We can represent a function as a set of ordered pairs { (x₁,y₁), (x₂,y₂), ... }. Any set of ordered pairs where no value appears twice as the first element is a function. If the same x appears twice (with necessarily different ys because it's a set) that's not a function.
Function example: { (0,1), (1,3), (2,5), (3,7), (4,-13) }
Non-function example: { (0,1), (1,3), (2,5), (3,7), (3,-13) }
In the first set no x is duplicated so it represents a function; in the second 3 is the x in two of the pairs; not a function.
the altitudes of a triangle intersect at the______
Answer:
the altitudes of a triangle intersect at the "orthocenter".
Step-by-step explanation:
The orthocenter is the point where the three altitudes of a triangle meet if the triangle is acute.
Two triangles are similar. The sides of one are three times as long as the sides of the other. What is the ratio of the areas of the smaller to the larger?
Answer:
1 : 9
Step-by-step explanation:
Given 2 similar figures with sides in ratio a : b , then
ratio of areas = a² : b²
Here the ratio of sides = 1 : 3 , thus
ratio of areas = 1² : 3² = 1 : 9
The ratio of the areas of the similar triangles is 1 : 9
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be represented as ΔABC
Let the second triangle be represented as ΔDEF
And , they are similar triangles
Now , the sides of one are three times as long as the sides of the other
Let's call the sides of the smaller triangle a, b, and c, and the sides of the larger triangle 3a, 3b, and 3c. Then we know that:
a : 3a = b : 3b = c : 3c
Simplifying this, we get:
1 : 3 = 1 : 3 = 1 : 3
This means that the corresponding sides of the two triangles are in a ratio of 1:3
Now, let's use the formula for the area of a triangle:
A = ( 1/2 ) x base x height
The base and height of the two triangles are also in a ratio of 1:3, so the ratio of their areas is:
(1/2) x 1 x 1 : (1/2) x 3 x 3
So , the ratio is 1 : 9
Hence , the ratio of the areas of the smaller triangle to the larger triangle is given by 1 : 9
To learn more about similar triangles click :
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what is the inverse of the function f(x)=2x-10 ?
Answer:
1/2x +5
Step-by-step explanation: Right answer
Answer:
[tex]f^{-1} (x)=\frac{x+10}{2}[/tex]
Step-by-step explanation:
[tex]f(x)=2x-10[/tex]
[tex]y=2x-10[/tex]
[tex]y+10=2x[/tex]
[tex]\frac{y+10}{2}=x[/tex]
[tex]\frac{x+10}{2}=y[/tex]
[tex]\frac{x+10}{2}=f^{-1} (x)[/tex]
Please answer correctly !!!!!! Will mark brainliest !!!!!!!!!! No explanation needed !!!
Answer: x = 2
Step-by-step explanation:
Answer:
x = ± 2
Step-by-step explanation:
Given
(x² + 4)² - 11(x² + 4) + 24 = 0
Use the substitution
u = x² + 4, then
u² - 11u + 24 = 0 ← in standard form
(u - 3)(u - 8) = 0
Equate each factor to zero and solve for u
u - 3 = 0 ⇒ u = 3
u - 8 = 0 ⇒ u = 8
Change u back into terms of x
x² + 4 = 8 ( subtract 4 from both sides )
x² = 4 ( take the square root of both sides )
x = ± [tex]\sqrt{4}[/tex] = ± 2
One value of x tat is a solution is x = 2
please help!
Will Mark Brainlest!
Answer:
Scale factor could be calculated by the ratio of a pair of corresponding sides:
Here, select the top sides, scale factor = 44/22 = 2
Hope this helps!
:)
Euclidean Geometry
which distance measures 7 units
Answer:
Whichever distance you can count the metric units and see that the x value is 7 on
Step-by-step explanation:
Whichever distance you can count the metric units and see that the x value is 7 on
For every 1 litre of water used to make a medicine, 193ml of sucrose and 13ml of saline solution are used. Express the amount of water, sucrose and saline solution needed as a ratio in its simplest form.
Answer:
1000:193:13
Step-by-step explanation:
Requirement of water to make a medicine = 1 litre = 1000ml;
Amount of sucrose = 193ml;
Amount of saline solution = 13 ml;
Ratio of Water: Sucrose: Saline Solution is;
1000:193:13
It cannot be simplified further.
Thus, 1000:193:13 is the simplest form of ratio of the solutions
There are some oranges and apples in a box.
The total number of oranges and apples is 54
The ratio of the number of oranges to the number of apples is 1:5
Work out the number of apples in the box.
Answer:
45
Step-by-step explanation:
The total amount of oranges and apples in the box are 54.
54/(1+5)
54/6
= 9
Oranges to apples is in the ratio 1:5
1×9 : 5×9
9 : 45
The number of oranges in the box are 9.
The number of apples in the box are 45.
Answer:
45 apples and 9 oranges
Step-by-step explanation:
Total = 54
Ratio = 1:5
Total Parts = 1+5 = 6
Oranges:
=> [tex]\frac{1}{6} * 54[/tex]
=> 1*9
=> 9 oranges
Apples:
=> [tex]\frac{5}{6} * 54[/tex]
=> 5*9
=> 45 apples
guys can you please factor this out for me
21a+8xy^3 −24y^2−7axy
Answer:
(7 a - 8y^2) x (3-y)
Step-by-step explanation:
21a+8xy^3 −24y^2−7axy
factor out 3 from the expression
3( 7 a - 8 y^2) + 8y^3 - 7 a y
3(7 a - 8 y^2) - y x (-8y^2 + 7 a)
Factor out 7 a - 8y^2 from the expression
(7 a - 8y^2) x (3-y)
= (7 a - 8y^2) x (3-y)
Please answer correctly !!!!!!! Will mark brainliest !!!!!!!!!!!
Answer:
f(x) = x^2 - 2x + 12
Step-by-step explanation:
the f(x) equation has a y-intercept of 12 because f(x)=x^2 - 2x has a y-intercept of 0 and the + 12 at the end shifts the function up 12 units putting the y-intercept at (0,12) while on the graph of the function g(x) it intercepts the y-axis at (0,1).
Jeffrey loves living in the house where he grew up, but the house is starting to show its age. His latest project is to replace his kitchen countertops with granite, which he plans to pick up from the hardware store tomorrow. The granite weighs 16 pounds per square foot, and his pickup truck bed can safely hold half a ton of weight. If he also plans to pick up a 120-pound kitchen sink in the same trip, how many square feet of granite will his truck be able to carry?
Answer:
Jeffrey's pickup truck will be able to carry 55 square feet of granite.
Step-by-step explanation:
There are 2000 pounds in 1 Ton
Jeffrey's pickup truck bed can safely hold half a ton of weight.
So that means his pickup truck can hold
2000/2 = 1000 pounds
He also plans to pick up a 120-pound kitchen sink in the same trip.
So the remaining weight limit is
1000 - 120 = 880 pounds
Since the granite weighs 16 pounds per square foot
880/16 = 55 sq ft.
Therefore, Jeffrey's pickup truck will be able to carry 55 square feet of granite.
Answer:
The answer is 55
Step-by-step explanation:
Analía fue a comprar ropa a un negocio que vende al por mayor. Compró 12 camisas a $21 cada una, 24 remeras a $11 cada una, y 40 polleras a $56 cada una. Como tuvo que devolver 20 pantalones que había comprado antes, a $51 cada uno, se lo descontaron del total que debía pagar. El taxi para ir y volver del negocio le costó $40. ¿Le alcanzó el dinero, si llevó $2.000?
Answer:
A Analía sí le alcanzó el dinero pues aún tenía $224 de los $2000 que llevó.
Analía gastó en total $1776. Si llevó $2000, entonces aún tenía:
[tex] \\ \$2000 - \$1776 = \$224[/tex]
Step-by-step explanation:
Para resolver el problema se deben obtener los subtotales de cada una de las transacciones en los que Analía gastó el dinero:
Primera transacción: compra de 12 camisas
Compró 12 camisas a $21 cada una. El monto por esta transacción es:
[tex] \\ \frac{\$21}{camisa} * 12\;camisas = \$252[/tex]
Primera transacción: T1 = $252.
Segunda transacción: compra de 24 remeras
Compró 24 remeras a $11 cada una:
[tex] \\ \frac{\$11}{remera}*24\;remeras = \$264[/tex]
Segunda transacción: T2 = $264.
Tercera transacción: compra de 40 polleras
Compró 40 polleras a $56 cada una:
[tex] \\ \frac{\$56}{pollera}*40\;polleras = \$2240[/tex]
Tercera transacción: T3 = $2240.
Cuarta transacción: devolución de pantalones y descuento
Devolvió 20 pantalones (y se lo descontaron de lo que tenía que pagar). El costo de cada pantalón es de $51 cada uno:
[tex] \\ \frac{\$51}{pantalon}*20\;pantalones = \$1020[/tex]
Cuarta transacción: T4 = $1020.
Quinta transacción: pago de ida y vuelta en transporte
Finalmente, el taxi para ir y volver del negocio le costó $40.
Quinta transacción: T5 = $40.
¿Cuánto gastó en total Analía?
A todo lo que Analía gastó, le debemos restar lo obtenido en el descuento por la devolución de pantalones (Cuarta transacción). Este último dinero corresponde a una transacción a favor de Analía, por lo que se resta a lo que ella ha gastado. De esta manera:
[tex] \\ Total = T1 + T2 + T3 - T4 + T5[/tex]
[tex] \\ Total = \$252 + \$264 + \$2240 - \$1020 + \$40[/tex]
Para hacer más notorio el total de lo que gastó y lo que le descontaron a su favor, tenemos:
[tex] \\ Total = \$252 + \$264 + \$2240 + \$40 - \$1020[/tex]
[tex] \\ Total = \$2796 - \$1020[/tex]
[tex] \\ Total = \$1776[/tex]
Entonces, Analía gastó en total $1776. Si llevó $2000, entonces aún tenía:
[tex] \\ \$2000 - \$1776 = \$224[/tex]
En conclusión, a Analía sí le alcanzó el dinero pues aún tenía $224 de los $2000 que llevó.
What is the total number of digits required in numbering the pages of a book, which has 105 pages?
Answer:
207
Step-by-step explanation:
So list out the numbers from digits.
1 digit numbers: 9
2 digit numbers: 90
3 digit numbers: 6
9 * 1 = 9
90 * 2 = 180
3 * 6 = 18
9 + 18 + 180 = 207
Answer:
207
Step-by-step explanation:
207 all the way
32/34 Marks
Show that 155 can be expressed as the sum of a power of 2
and a cube number.
Answer:
[tex] 155 = {2}^{7} + {3}^{3} [/tex]
Step-by-step explanation:
[tex] \because \: 155 = 128 + 27 \\ 128 = {2}^{7} \: \: and \: \: {3}^{3} \\ \\ \huge \red{ \boxed{ \therefore \: 155 = {2}^{7} + {3}^{3} }}[/tex]
6a - 4b = 6b + 2a
solve for a
Answer:
[tex]a = \frac{5}{2}b[/tex]
Step-by-step explanation:
6a - 4b = 6b + 2a
Combine like terms:
6a - 2a - 4b = 6b (Subtract '2a' from both sides)
4a = 6b + 4b (Add '4b' to both sides)
4a = 10b
[tex]a = \frac{5}{2}b[/tex] (Divide both sides by 4)
Therefore, when simplified, [tex]a = \frac{5}{2}b[/tex].
Suppose a (the word 'a' means starting amount is 1) radioactive substance decays at a rate of 5% per hour, what percent of the substance is left after 10 hours? (make sure you convert your answer from decimal to percent and round to the nearest whole percent)
Answer:
The percentage of the substance is left after 10 hours is 60%.
Step-by-step explanation:
The expression representing the amount left after a certain period of decay is:
[tex]y=a(1-r)^{t}[/tex]
Here,
y = final amount
a = initial amount
r = decay rate
t = time taken
It is provided that:
a = 1
r = 5% / hour
t = 10 hours
Compute the percentage of the substance is left after 10 hours as follows:
[tex]y=a(1-r)^{t}[/tex]
[tex]=1\times (1-0.05)^{10}\\\\=0.95^{10}\\\\=0.598737\\\\\approx 0.60[/tex]
The percentage is: 0.60 × 100 = 60%.
Thus, the percentage of the substance is left after 10 hours is 60%.
Find all values of x where f(x)=0
Answer:
I think x has no value in that function
Step-by-step explanation:
If the 30/8 give me 3 6/8 explain to me how did I get 3 6/8 please
Answer:
See explanation.
Step-by-step explanation:
The question is not very clear, but I am assuming that you are asking how to get from 30/8 to 3 6/8
This is a mere simplification problem. We have simplified 30/8 into 3 6/8.
To start, let's check out the multiples of 8 that are less than 30
8, 16, 24. We want the largest multiple, 24. here we have
[tex]\frac{24}{8} + \frac{6}{8}[/tex]
Simplify 24/8 into 3.
Now you're done!
3 6/8!
Suppose a population of 250 crickets doubles in size every 3 months how many crickets will there be after 2 years ?
Answer: 64,000 crickets
Step-by-step explanation: 2 years = 24 months; every 3 months the crickets double in population, therefore the cricket population doubles 8 times. 250 x 2 = 500; 500 x 2 = 1,000; 1,000 x 2 = 2,000; 2,000 x 2 = 4,000; 4,000 x 2 = 8,000; 8,000 x 2 = 16,000; 16,000 x 2 = 32,000; 32,000 x 2 = 64,000
The number one is an example of an element in the set of natural numbers true or false
Find the midpoint of A and B where A has coordinates (-5, 3)
and B has coordinates (3,-1).
Answer:
(-1,1)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates and divide by 2
(-5+3)/2 = -2/2 = -1
To find the y coordinate of the midpoint, add the y coordinates and divide by 2
(3+-1)/2 = 2/2 = 1
(-1,1)
Answer:
(-1,1)
Step-by-step explanation:
The midpoint of a line can be found using the following formula:
[tex](x_m, y_m) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]
Basically, to find the midpoint, add the x-coordinates and divide by 2, then add the y coordinates and divide by 2.
X-coordinate
Add the x-coordinates of A and B, then divide by 2.
The x-coordinates are the numbers that comes first in the points.
A: (-5,3)
B: (3, -1)
The x coordinates are -5 and 3.
Add the x-coordinates.
-5+3=-2
Divide by 2
-2/2=-1
The x-coordinate of the midpoint is -1.
Y-coordinate
Add the y-coordinates of A and B, then divide by 2.
The y-coordinates are the second numbers in the points.
A: (-5,3)
B: (3,-1)
The y-coordinates are 3 and -1.
Add the y-coordinates.
3+-1=2
Divide by 2.
2/2=1
The y-coordinate of the midpoint is 1.
If the x-coordinate is -1 and the y-coordinate is 1, the midpoint is (-1,1)
During his hike, Milt drank 1 liter of water and 1 liter of sports drink. How many milliliters of liquid did he drink?
Answer: 2,000 milliliters.
Step-by-step explanation:
Hi, to answer this question we have to add the amount of water and the amount of sports drink that he drank:
1 liter + 1 liter = 2 liters of liquid.
Finally, we have to convert the result into milliliters.
Since 1 liter = 1000 liters
We have to multiply the liters drank by 1000.
2 x 1000 = 2,000 milliliters.
Feel free to ask for more if needed or if you did not understand something.
PLZ HELP ME I WILL MARK BRAINLIEST AND GIVE POINTS
x/3 -2y = 14
2x + 6y = -6
Given the equations what is the value of x-y?
PLZ HELP WILL MARK BRAINLIEST
Answer:
17
Step-by-step explanation:
Based on the 2nd equation, it seems that x=-3-3y. I got that by subtracting both sides by 6y and then dividing both sides by 2. Now substitute that in place of x in the first equation. (-3-3y)/3-2y=14. Simplify that and get -1-y-2y=14. Add 1 to both sides and simplify. You get -3y=15. Divide both sides by -3 and get y=-5. Now substitute -5 into the equation for x. x=-3-3(-5)
x=-3+15=12
So x=12 and y=-5. Now do 12-(-5)=12+5=17
a ferris wheel with a 40-ft diameter rotates once every 30 seconds. the bottom of the wheel is located 1.5 feet above the ground. you get on at the very bottom of the ferris wheel at time t = 0 and then the ferris wheel begins to turn counter-clockwise. for the problems below, assume the wheel makes 2 full rotations.
a. at what times are you at the top of the ferris wheel? what is the height at the top of the ferris wheel?
b. at what times are you at the bottom of the ferris wheel? what is the height at the bottom of the ferris wheel?
c. at what times are you in the exact middle of the ferris wheel? what is the height of the exact middle of the ferris wheel?
d. write a cosine function to model your height above the ground over time, t.
Answer:
Step-by-step explanation:
Let y = -A cos B(t -c) + D
A, amplitude = 20ft
Period = 2π / B ( B = π / 15)
= 30
c = 0
Vertical shift D = 21.5 ft
Equation becomes
[tex]y= -20 \cos \frac{\pi}{15}( t-0)+21.5[/tex]
[tex]\to y=-20\cos \frac{\pi}{15} t+21.5[/tex]
a) Top of the ferris wheel is
t = 15sec, 45sec, height = 41.5ft
b) At the bottom of the ferris wheel
t = 0, 30sec, 60 sec
height = 1.5ft
c) Exact middle of the ferris wheel
t = 15/ 2 = 7.5sec, 22.5sec, 37.5sec, 52.5sec
d) [tex]f(t) or h = -20 \cos (\frac{\pi}{15} t)+21.5[/tex]
What does pi equal??
WILL GIVE BRAINLIEST!!!!!!!!:)
Answer:
The digits go on for infinity (3.14159. . .), but the simplified version is equal to 3.14.
Step-by-step explanation:
What is the sum of Negative 8 + 6?
Answer:
-14 or -2
Step-by-step explanation:
-8+-6= -14
-8+6 = -2
Olivia has $143 in the bank. She withdraws $40. Then she deposits &92. Write an addition expression to represent the situation. Then find the sum.
Answer & Step-by-step explanation:
Answer after you have shown organized work to get to the solution. 4. If you have ... content that you may have trouble with- search under 6th and 7th grade math. If you are ... Olivia has $143 in the bank. She withdraws. $40. Then she deposits $92. Write an addition expression to represent the situation. Then find the sum. 8
