MATHEMATICS HIGH SCHOOL

Write a function rule that represents the sentence
y is 5 less than the product of 4 and x.

Answers

Answer 1

Answer: y=5-4x
since less than is subtraction
is means equals
and product means you have to multiply the numbers

Answer 2

Answer:

Final answer:

The function rule to represent the given sentence is y = 4x - 5.

Explanation:

To write a function rule that represents the sentence 'y is 5 less than the product of 4 and x,' we can use algebraic notation. The word 'less than' indicates a subtraction operation, so we can represent it as y = 4x - 5. In this function rule, 4x represents the product of 4 and x, and subtracting 5 from it gives us y.

Learn more about Function rule for subtraction here:

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The function H(t) = −16t2 + 96t + 80 shows the height H(t), in feet, of a projectile after t seconds. A second object moves in the air along a path represented by g(t) = 31 + 32.2t, where g(t) is the height, in feet, of the object from the ground at time t seconds. Part A: Create a table using integers 2 through 5 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? Part B: Explain what the solution from Part A means in the context of the problem.

Answers

A.
t H(t) g(t)
2 208 95.4
3 224 127.6
4 208 159.8
5 160 192

The solution for H(t) = g(t) is in between 4 and 5 seconds.

B.
Between 4 and 5 seconds, the projectile and the second object will have the same.

Answer and Explanation :

Given : The function $H(t)=-16t^2+96t+80$ shows the height H(t), in feet, of a projectile after t seconds.

A second object moves in the air along a path represented by $g(t) = 31 + 32.2t$ , where g(t) is the height, in feet, of the object from the ground at time t seconds.

To find :

Part A - Create a table using integers 2 through 5 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located?

Part B - Explain what the solution from Part A means in the context of the problem.

Solution :

For Part A -

Substitute the value of t from 2 to 5 in the equation H(t) and g(t)

t $H(t)=-16t^2+96t+80$ $g(t) = 31 + 32.2t$

2 $-16(2)^2+96(2)+80=208$ $31 + 32.2(2)=95.4$

3 $-16(3)^2+96(3)+80=224$ $31 + 32.2(3)=127.6$

4 $-16(4)^2+96(4)+80=208$ $31 + 32.2(4)=159.8$

5 $-16(5)^2+96(5)+80=160$ $31 + 32.2(5)=192$

To determine the interval in which H(t)=g(t), we have to plot the equation and the table points and see the intersection.

Refer the attached figure below.

The intersection point of both the equations are (4.647,180.62)

This point lies between t at 4 to 5.

Therefore, H(t)=g(t) between t=4 to t=5.

For Part B -

The Part A shows that the projectile destroyed along the path are same in interval [4,5] and gives the solution of equation.

2: find the slop and the y-intercept of the line represented by the equation.7x + y = 8
I am having trouble with these, could someone please help me.

Answers

$The\ slope-intercept\ form:y=mx+b\n\nm\ is\ the slope\nb\ is\ y-intercept\n\n7x+y=8\n\ny=-7x+8\n\nthe\ slope:m=-7\ny-intercept:b=8$

What are the Coefficients in 4e + 7e + 5

Answers

Answer:

4 and 7

Step-by-step explanation:

Coefficients are just bassically the numbers behind the variable, hope this helps!

Can anyone help me out with this

Answers

Answer:

X = 62.4

Step-by-step explanation:

To find x or the weight of water per one cubic foot we take the 12.48 and divide it by two

12.48 = 6.24

Then multiply 6.24 by ten because 6.24 is the weight of .1 cubic feet

6.24 * 10 = 62.4

To check and make sure we calculated it correctly we can do 6.24 * 17 to find the weight of the larger tank

6.24 * 17 = 106.08

And 6.24 * 15 to find the weight of the smaller tank

6.24 * 15 = 93.6

The subtract 93.6 from 106.08

106.08 - 93.6 = 12.48 which was the difference in weight between the two tanks.

Algebraically solve the system of equations shown below. Note that you can use either factoring or the quadratic formula to find the X – coordinates, but the quadratic formula is probably easier.

Answers

$6x^2+19x-15=-12x+15\n6x^2+31x-30=0\n6x^2+36x-5x-30=0\n6x(x+6)-5(x+6)=0\n(6x-5)(x+6)=0\nx=(5)/(6) \vee x=-6\n\ny=-12\cdot(5)/(6) +15\vee y=-12\cdot(-6)+15\ny=-10 +15\vee y=72+15\ny=5 \vee y=87\n\nx=(5)/(6) \wedge y=5\nx=-6 \wedge y=87$

$y=6x^2+19x-15 \ny=-12x+15 \n \n6x^2+19x-15=-12x+15 \n6x^2+19x+12x-15-15=0 \n6x^2+31x-30=0 \n \n a=6 \n b=31 \n c=-30 \n \n x=(-b \pm √(b^2-4ac))/(2a)=(-31 \pm √(31^2-4 \cdot 6 \cdot (-30)))/(2 \cdot 6)=(-31 \pm √(1681))/(12)=(-31 \pm 41)/(12) \n x=(-31 -41)/(12) \ \hbox{or} \ x=(-31+41)/(12) \nx=-6 \ \hbox{or} \ x=(5)/(6)$

$y=-12 \cdot (-6)+15 \ \hbox{or} \ y=-12 \cdot (5)/(6)+15 \ny=87 \ \hbox{or} \ y=5 \n \n \hbox{the answer:} \n \boxed{x=-6, \ y=87} \ \hbox{or} \ \boxed{x=(5)/(6), \ y=5}$

Find the value of x. Round to nearest hundredth if necessary.

Answers

The side on the front of 30° is 1/2 of hypytenuse
Then 1/2 of 4=2 and the ather side with theorem of pytagore is squares root of(4^2-2^2)=sq .root of 12
This side(square root of 12) is 1/2 of hypotenuse then
Hypotenuse is 2*square root 12
X^2=(2*sq .root12)^2 -(square root 12)^2
X^2=48-12=36
X=6

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