The required solution is 2t^2 -7t - 4.
It is required to find the product of the problem.
What is a distributive property?The distributive property of multiplication lets you simplify expressions wherein you multiply a number by a sum or difference. According to this property, the product of a sum or difference of a number is equal to the sum or difference of the products.
Given that:
By the distributive property to find the product of (2t + 1) ( t - 4).
=(2t +1)(t -4)
= 2t^2 + 1t -8t - 4
= 2t^2 -7t - 4
Therefore, the required solution is 2t^2 -7t - 4.
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Final answer:
The product of (2t + 1)(t - 4) is calculated using the FOIL method to be 2t² - 7t - 4.
Explanation:
To find the product of (2t + 1) and (t - 4), we use the distributive property (also known as the FOIL method in this context) to multiply each term in the first binomial by each term in the second binomial. Here is the step-by-step process:
Multiply the first terms: 2t × t = 2t².
Multiply the outside terms: 2t × -4 = -8t.
Multiply the inside terms: 1 × t = t.
Multiply the last terms: 1 × -4 = -4.
Add all the products together to get the final answer: 2t² + -8t + t + -4.
Combine like terms: 2t² - 7t - 4.
Thus, the product of (2t + 1)(t - 4) is 2t² - 7t - 4.
△VAT≅△BDT.
¯¯¯¯¯
What is length of BT ?
Answer:
[tex]BT=6.3[/tex]
Step-by-step explanation:
We have been given that triangle VAT is congruent to triangle BDT. We are asked to find the length of segment BT.
Since both triangles are congruent, therefore, their corresponding sides will be equal by the definition of congruence.
[tex]\Delta VAT\cong \Delta BDT[/tex]
By the definition of congruence:
[tex]VA=BD[/tex]
[tex]AT=DT[/tex]
[tex]VT=BT[/tex]
Since the length of side VT is 6.3 units, therefore the length of BT is 6.3 units as well.
Find the length of the hypotenuse if the legs of a triangle are 5cm and 12 cm.
Question 5 options:
7cm
13cm
17cm
169cm
Graph y+6=4/5(x+3) using the point and slope given in the equation. Use the line tool and select two points on the line.
Answer:
Look at pic...
The points were (-3,-6) and (2,-2)
Step-by-step explanation:
You could just use desmos graphing calculator
The equation of a line is a form of representing the set of points, which form a line in a coordinate system.
The two points on the line are (0, -3) and (1, -11/5).
What is equation of a line?The equation of a line is a form of representing the set of points, which form a line in a coordinate system.
The general equation of a straight line is given as:
y = mx + c,
where m = slope of the line and c = y-intercept.
We have,
y + 6 = 4/5 ( x + 3 )
Subtract 6 on both sides.
y = 4/5 ( x + 3 ) - 6
y = (4/5)x + 4/5 x 3 - 6
y = (4/5)x + 12/5 - 6
y = (4/5)x + (12 - 30)/6
y = (4/5)x - 3
The y-intercept is at -3.
We have a point as (0, -3).
For x = 1,
y = (4/5) x 1 - 3
y = 4/5 - 3
y = (4 - 15) / 5 = -11/5
The other point is (1, -11/5)
Thus,
The two points on the line are (0, -3) and (1, -11/5).
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Mary invests £12000 in a savings account. The account pays 1.5% compound interest per year. Work out the value of her investment after 2 years
Owen jarred 10 liters of jam after 2 days. How many days did Owen spend making jam if he jarred 15 liters of jam?
Which phrase best describes a rock? A. a chemical arranged in a lattice B. a gabbro of minerals C. a mixture of crystals D. a fire-formed crystal
A store owner ordered 132 boxes of erasers. There are 8 erasers in each box. Use place value and expanded form to write an expression that shows how to multiply 8 x 132.
Jane has a 5x7 inch photograph that she wants enlarged to a 10x14inch photograph. What is the scale factor from the original photograph to the enlarged photograph?
What is the remainder when the polynomial 8x^2+4x−3 is divided by 2x−1?
Answer:
1
Step-by-step explanation:
Given: A polynomial [tex]8x^{2} +4x-3[/tex] is divided by another polynomial [tex]2x-1[/tex]
To find: Remainder when [tex]8x^{2} +4x-3[/tex] is divided by [tex]2x-1[/tex]
Solution:
To find the remainder when [tex]8x^{2} +4x-3[/tex] is divided by [tex]2x-1[/tex]
First, equate [tex]2x-1[/tex] with 0.
Now, [tex]2x-1=0[/tex]
[tex]\implies2x=1[/tex]
[tex]\implies x=\frac{1}{2}[/tex]
Now, to find the remainder put [tex]x=\frac{1}{2}[/tex] in [tex]8x^{2} +4x-3[/tex]
So, we have
[tex]8\times(\frac{1}{2})^{2}+4(\frac{1}{2} )-3[/tex]
[tex]=8\times\frac{1}{4} +2-3[/tex]
[tex]=2+2-3[/tex]
[tex]=4-3[/tex]
[tex]=1[/tex]
Hence, the remainder is 1.
Expand and simplify 2(2x-3)+2(3x+4)
Heather and her family are going to the grand opening of a new amusement park. There is a special price on tickets this weekend. Tickets cost $42 each. This is 70% of the cost of a regular price ticket. What is the cost of a regular price ticket? Please explain! thanks!
twice the sum of a number and 5 equals 9 as a equation
Shelly can cut a lawn with a riding mower in 22 hours less time than it takes william to cut the lawn with a push mower. if they can cut the lawn in 33 hours working together find how long to the nearest tenth of an hour it takes for william to cut the lawn alone.
Hi! Please help me with this question! 12 points and brainliest to whoever answers it correctly first!
1. Given: -3x + y = 1. Write the equation in general form Ax + By + C =0.
3x - y + 1 = 0
-3x + y - 1 = 0 (not this one)
3x - y = -1
in diagram below, fg=10 and HJ=10. Which additional facts would guarantee that fghj is a parallelogram? Check all that apply.
The sum of three consecutive integers is 16 more than 2 times the smallest integer. find the integers
A baseball player got 102 hits in the last 300 times at bat.
What percent of the times at-bat did the player get a hit?
The player got a hit ? % of the time.
What is the reason for Statement 2 of the two-column proof?
a) Linear Pair Postulate
b) Definition of angle
c) Definition of bisect
d) Angle Addition Postulate
We have been given that PQ bisects [tex]\angle RPS[/tex]. In the second statement of the given two-column proof, the statement is [tex]\angle RPQ\cong\angle QPS[/tex].
This implies that the two angles formed by bisection of angle [tex]\angle RPS[/tex] by the line PQ are equal. We know that the reason for this is simple. It is the definition of bisection of an angle that the two smaller angles formed will be equal to each other.
Therefore, the reason for statement 2 of the given two column proof is c) Definition of bisect
PLZ Help I really need to know how to do this
SKIING The distance in meters that a person
travels on skis can be modeled by d(t) = 0.2t^2 + 3t,
where t is the time in seconds. Use the Remainder
Theorem to find the distance traveled after 45
seconds.
A bakery offers a sale price of $2.55 for 4 muffins. What is the price per dozen? The price per dozen muffins is $ .
Final answer:
To find the price per dozen, divide the sale price of $2.55 by 4 to get the price per muffin, then multiply by 12. The price per dozen muffins is $7.65.
Explanation:
To calculate the price per dozen muffins at the bakery when the sale price is $2.55 for 4 muffins, you first need to determine the price of one muffin. You can do this by dividing the sale price by the number of muffins in the offer:
$2.55 ÷ 4 = $0.6375 per muffin.
Next, because a dozen consists of 12 items, you would find the price per dozen by multiplying the price per muffin by 12:
$0.6375 × 12 = $7.65
Therefore, the price per dozen muffins is $7.65.
David cycles x km in 3 hours. if he maintains the same average speed, how far can he cycle in 12y minutes
David can cycle [tex]\( \frac{xy}{15} \)[/tex] kilometers in 12y minutes if he maintains the same average speed.
To find out how far David can cycle in 12y minutes, we first need to convert the time from minutes to hours, since David's speed is given in kilometers per hour.
Since there are 60 minutes in an hour, we can convert 12y minutes to hours by dividing by 60:
[tex]\[ \text{12y minutes} = \frac{12y}{60} = \frac{y}{5} \text{ hours} \][/tex]
Now, we know that David cycles x kilometers in 3 hours, so we can find his average speed:
[tex]\[ \text{Average speed} = \frac{\text{Distance}}{\text{Time}} \]\[ \text{Average speed} = \frac{x \text{ km}}{3 \text{ hours}} \][/tex]
Now, using the average speed, we can find the distance David can cycle in [tex]\( \frac{y}{5} \)[/tex] hours:
[tex]\[ \text{Distance} = \text{Average speed} \times \text{Time} \]\[ \text{Distance} = \left( \frac{x}{3} \right) \times \left( \frac{y}{5} \right) \]\[ \text{Distance} = \frac{xy}{15} \][/tex]
What are the x-intercepts of the graph of the function below? y=x^2+4x-32
Answer:
Option B is correct.
Step-by-step explanation:
Given Function is,
y = x² + 4x - 32
X-intercepts of the graph of given function is the solution of the equation when y is equal to 0 is substituted.
y = 0
x² + 4x - 32 = 0
x² + 8x - 4x - 32 = 0
x ( x + 8 ) - 4 ( x + 8 ) = 0
( x + 8 ) ( x - 4 ) = 0
x + 8 = 0 and x - 4 = 0
x = -8 and x = 4
So x-intercept are ( -8 , 0 ) and ( 4 , 0 )
Therefore, Option B is correct.
Ethan invested £500 in the bank for 2 years. he earned £40 simple interest in total. what was the simple interest rate per annum
Answer:
4%.
Step-by-step explanation:
We have been given that Ethan invested £500 in the bank for 2 years. He earned £40 simple interest in total. We are asked to find the annual interest rate.
We will use simple interest formula to solve our given problem.
[tex]I=Prt[/tex], where,
I = Amount of interest,
P = Principal amount,
r = Annual interest rate in decimal form,
t = Time in years.
Upon substituting our given values in above formula, we will get:
[tex]40=500*r*2[/tex]
[tex]40=1000*r[/tex]
Now, we will divide both sides of our given equation by 100.
[tex]\frac{40}{1000}=\frac{1000*r}{1000}[/tex]
[tex]\frac{4}{100}=r[/tex]
[tex]\frac{1}{25}=r[/tex]
[tex]0.04=r[/tex]
Since our given interest rate is in decimal form, so we need to convert it in percentage.
[tex]0.04\times 100\%=4\%[/tex]
Therefore, the simple interest rate per annum is 4%.
Which ordered triple is a solution of this system?
2x + y - z = 7
-x - 2y + 4z = -15
x + 2y - 5z = 17
a) (3, 1, 0)
b) (1, 3, -2)
c) (2, 5, 2)
d) (-2, 6, -5)
Answer:
b) (1, 3, -2)
Step-by-step explanation:
A suitable calculator can give you the answer to this right away. Or, you can try the answer choices in the equations to see which works.
The answer choice that works is choice B.
2·1 +3 -(-2) = 7
-1 -2(3) +4(-2) = -15
1 +2(3) -5(-2) = 17
135in.=___ft ___ in.
convert
1 foot = 12 inches
135 / 12 = 11.25 feet 0.25 feet = 0.25 * 12 = 3 inches
answer is: 11 feet 3 inches
Which is bigger, 978 centimeters or 12 meters?
A bag contains equal numbers of green and blue marbles. You can divide all the green marbles into groups of 12 and all the blue marbles into groups of 16. What is the least number of each color of marble that can be in that bags?
To solve this problem, we need to find for the LCM of each number. That is:
12: 12, 24, 36, 48, 60
16: 16, 32, 48, 64, 80
So we can see that the LCM is 48.
Therefore the least number of each color of marble must be 48.
Answer:48
Step-by-step explanation:love ya thank me later
96 points here, having to ask same question again - please help a brother out.
Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation. Show your work.
1. cot x sec^4 x = cot x + 2 tan x + tan^3 x
2. (sin x)(tan x cos x - cot x cos x) = 1 - 2 cos^2 x
3. 1 + sec^2 x sin^2 x = sec^2 x
4. ((sin x)/(1-cos x)) + ((sin x)/(1+cos x))=2csc x
5. - tan^2 x + sec^2x = 1
the equation is - tan2 x + sec2 x = 1.
Left hand side identity : - tan2 x + sec2 x.
Trigonometric function : tan x = sin x / cos x,
Reciprocal identity : sec x = 1/cos x.
- tan2 x + sec2 x = - (sin x/cos x)2 + (1/cos x)2
= - sin2 x/cos2 x + 1/cos2 x
= (1 - sin2 x)/cos2 x
Pythagorean identity : sin2 x + cos2 x = 1 .
= cos2 x / cos2 x
= 1
Two cars leave the origin; one goes north at 45 mph and the other goes south at 40 mph. after how many hours will they be 350 miles apart?
To find the time when two cars traveling in opposite directions are 350 miles apart, we calculate their relative speed, which is 85 mph. We then divide the distance (350 miles) by this speed to get approximately 4 hours and 7 minutes.
Explanation:The question is asking to find out after how many hours two cars traveling in opposite directions will be 350 miles apart, with one car going north at 45 mph and the other south at 40 mph. To solve this, we need to apply the concept of relative speed.
The relative speed is the sum of the individual speeds when two objects are moving in opposite directions. In this case, it's 45 mph + 40 mph = 85 mph. This is the speed at which the distance between the two cars is increasing.
Next, to find the time 't' when they will be 350 miles apart, we use the formula:
Distance = Speed × Time
350 miles = 85 mph × t
To solve for 't', we divide both sides by 85 mph:
t = 350 miles / 85 mph = 4.1176 hours, or approximately 4 hours and 7 minutes.
Jasmine bought computer which was discounted from 350 to 273. What is the discount rate
subtract the 2 numbers to find amount of discount
350 - 273 = 77
now divide 77 by 350 = 0.22
0.22 = 22% discount
Answer:
22%
Step-by-step explanation:
The discount rate given on the cost of an item is the ratio of the discount to the old price expressed as a percentage.
The discount is the difference between the old and new price while the new price is known as the discounted price.
the discount = $350 - $273
= $77
The discount rate
= $77/$350
= 0.22
= 22%