Answers
Answer:
a = 2
Step-by-step explanation:
Here, we want to get the value of a
From the remainder theorem, if we the divisor to zero and get a value for the variable, then substitute this value into the polynomial, the result we have is the remainder
So;
set x + 1 = 0 ; and x = -1
substitute this into the polynomial
(-1)^3 + 2(-1)^2 -5(a)(-1) -7
= -1 + 2 + 5a -7 = 5a -6
For the second;
set x -2 = 0; x = 2
Substitute in the second polynomial;
2^3 + a(2)^2 -12(2) + 6
= 8 + 4a -24 + 6 = 4a -10
So therefore;
2(5a-6) + 4a - 10 = 6
10a-12 + 4a -10 = 6
10a + 4a -22 = 6
14a = 6 + 22
14a = 28
a = 28/14
a = 2
Related Questions
At the beginning of the year, Samantha deposits $1000 into a savings account that pays 2.5% interest. She does not deposit money into or withdraw money from
the account for 1 year.
What is the interest rate expressed as a decimal?
Answers
Answer:
0,025
Step-by-step explanation:
simply devide by 100,2,5% is out of 100%
What property was used in step 1 to arrive at step 2?
Step 1: 5 (x minus 7) = 55. Step 2: 5 x minus 35 = 55. Step 3: 5 x = 90. Step 4: x = 18.
distributive property
addition property of equality
subtraction property of equality
division property of equality
Answers
Answer:
distribute property
Step-by-step explanation:
5 is distributed into the parentheses.
5 × x = 5x
5 × (-7) = -35
5x - 35 = 55
Hope that helps.
The property used in step 1 to arrive at step 2 is the Distributive property, the correct option is A.
What is a Product?Product is the output of the mathematical operation Multiplication.
The Step 1: 5 (x minus 7) = 55.
Step 2: 5 x minus 35 = 55
In step 2 Distributive property is used to solve the expression.
According to Distributive property
The sum of multiplying a number by the addend of two numbers will the same result when each number which is being added is multiplied individually and then added.
a ( b+c) = a*b + a*c
5 (x -7) = 55.
5x - 35 = 55
Therefore, the distributive property is used.
To know more about Distributive Property
https://brainly.com/question/5637942
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The shortest side of an isosceles triangle is labeled, in inches, in the triangle below. The two longer sides are 6 inches longer than the shortest side. The perimeter of the triangle is 33 inches.
Answers
Complete question is;
The shortest side of an isosceles triangle is 2x - 3 inches long. the longer sides are 6 inches longer than the shortest side. the perimeter of the triangle is 33 inches. what is the length of each side of the longer sides of the triangle.
Answer:
Shortest side = 7 inches
Side 2 = 13 inches
Side 3 = 13 inches
Step-by-step explanation:
We are told that;
Triangle is isosceles
The shortest side is 2x - 3 inches
The other 2 sides which are equal because it's an isosceles triangle are both 6 inches longer than the shortest side. Thus;
Side 2 = side 3 = 2x - 3 + 6 = 2x + 3
Since perimeter = 33 and sum of all 3 sides is the perimeter. Thus;
(2x - 3) + 2x + 3 + 2x + 3 = 33
6x + 3 = 33
6x = 33 - 3
6x = 30
x = 30/6
x = 5
Thus;
Shortest side = 2(5) - 3 = 7
Other 2 sides are each; 2(5) + 3 = 13
A florist arranges some orchids in bouquets of 20 and some roses in bouquets of 10. She sells each orchid bouquet for $25 and each rose bouquet for $30. She earns a total of $390. If she sells four times as many orchid bouquets as rose bouquets, how many flowers does she sell altogether?
Answers
Answer:
270 flowers total she sell Together.
Step-by-step explanation:
According to the Question,
Given, A florist arranges some orchids in bouquets of 20 and some roses in bouquets of 10.Let, x = number of orchid bunches & y = number of rose bunches.
Now, She sells each orchid bouquet for $25 and each rose bouquet for $30. She earns a total of $390Therefore, 25x + 30y = 390 ⇒⇒ Equation 1
she sells 4 times as many orchid bunches as rose bunches,
Therefore, x = 4y ⇒⇒ Equation 2
Put The Value Of Equation 2 in Equation 1, We get25 × (4y) + 30y = 390
100y + 30y = 390
130y = 390 ⇔ y = 390 / 130 ⇒ 3
if y = 3, then x = 4y must be equal to x= 12.
Thus, she sold 12 orchid bunches and 3 rose bunches.
Verify, 25x + 30y = 390 ⇔ 12 × 25 + 3 × 30 = 390 (All okay)Now, Each orchid bunch contains 20 flowers and each rose bunch contains 10 flowers.
12 × 20 + 3 × 10 = 240 + 30 ⇔ 270 flowers total she sell Together.20 points!!! Tysmmm!! If you can help with other questions on my page to that would mean so much
Answers
Answer:
(2w+2)(w+8) ≤ 100
Step-by-step explanation:
Answer:
●(2w+2)(w+8)< 100 represents the inequality that combined the area of Garden and walk away.
Step-by-step explanation:
this is correct!!
HELP ASAP
Jim went to the bank and made of a deposit of $525 into his checking account. He had both cash and a check. The check he deposited was written for $250. How much cash did he deposit? Construct an equation to represent the situation. Make sure to identify and label your variable. Solve for the variable and describe your answer. Show your work and prove your solution to be correct.
Answers
Amount of Cash deposited = $275
For this equation, you are looking to find the amount of cash specifically withdrawn. The ‘x’ variable represents this.
The ‘d’ variable represents the total deposit amount, which is $525.
And the ‘c’ variable represents the check amount that was deposited.
All you have to do to solve it is replace the variables with the numbers provided.
x = 525 - 250
x = 275
What is the value of y
Answers
On Saturday, the fruit and juice bar was selling 20 glasses of fruit punch an hour. By 7 p.m., they had sold 180 glasses. If their goal was to sell more than 240 glasses of fruit punch, find the number of hours, h, they must stay open past 7 p.m. to make their goal.
Answers
======================================================
Explanation:
h = number of hours past 7 pm
20h = the number of glasses sold after h hours
20h+180 = adding on the 180 glasses already sold
20h+180 > 240 is the inequality to set up
Let's solve for h
------------------
20h+180 > 240
20h > 240-180
20h > 60
h > 60/20
h > 3
They must remain open more than 3 hours past 7 pm in order to sell more than 240 glasses of juice.
The earliest that they can close is 11 pm (since 4+7 = 11).
--------------------
If h = 3, then
20h+180 = 20*3 + 180 = 240
meaning that they haven't reached their goal of getting over 240
So they have to stay open that extra hour to get past 240.
Find the solution to the system
of equations (look at picture)
answer both please
Answers
Answer:
(-1, 1)
Step-by-step explanation:
(-1, 1) is the solution to this system of equations because it is the point of intersection. If you would want to solve this algebraically, you would need to use the equations of each line.
Answer:
the answer is (-1,1)
i think we needed to calculate the coordinates
hope it helps
the slope of the line
Answers
Answer: -2
Explanation: On the image we can see it goes down 4 units and right 2. Giving us the slope [tex]\frac{-4}{2}[/tex]
Simplified that is -2 which is the slope of the line
Hi! can someone help?
Answers
Answer:
129
Step-by-step explanation:
[tex]\frac{5^{4} }{5} +4[/tex]
[tex]\frac{625 }{5} +4[/tex]
[tex]125 +4[/tex]
129
Pls help I would APPRECIATE IT
Answers
Which measure of center best represents the data?
8,8,7,8,8,8,1,8,8
Answers
Answer:
8
Step-by-step explanation:
The median is 8 since 8 is the most common number
PLEASE help !! someone who knows fr ! pls
Answers
Answer:
It is the first option
Step-by-step explanation:
Sarah uses 3/4 pound of blueberries to make 2/3 cup of jam. How many pounds of blueberries does she need to make one cup of jam
Answers
Answer:
1/12
Step-by-step explanation:
i belive this is the answer
rationalising factor of 5 +root 7
Answers
Answer:
Therefore, lowest rationalizing factor is ( 7 + √7 ).
Step-by-step explanation:
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mark me as BRAINLIEST
100%sure
Answer:
5 - [tex]\sqrt{7}[/tex]
Step-by-step explanation:
To rationalise the factor multiply by the conjugate factor
The conjugate of 5 + [tex]\sqrt{7}[/tex] is 5 - [tex]\sqrt{7}[/tex] , then
(5 + [tex]\sqrt{7}[/tex] )(5 - [tex]\sqrt{7}[/tex] ) ← expand using FOIL
= 5² - ([tex]\sqrt{7}[/tex] )²
= 25 - 7
= 18
what is 0.00051 convert in standard form
Answers
The answer is:
5.1 x [tex]10^-4[/tex]
Step 1: Rewrite number
0.00051
Step 2: Make the number smaller
0.00051 can be used in scientific notation once you move the decimal. The decimal needs to be moved so that the number is between 1 and 10. When moving the decimal 4 places to the right, the number can be left at 5.1.
Step 3: Write in standard form
The number on the left side of the multiplication side will be the number that we made smaller. In this case, it is 5.1. The exponent next to the 10 will be of how many places the decimal was moved. This is -4. The negative sign is used since the decimal was moved to the right.
5.1 x 10^-4
Find the roots of the quadratic equation (4p-1)² = 4p²
( Please show me how it works , Thankiuuu ༎ຶ‿༎ຶ )
Answers
Answer:
p = 1/2
Step-by-step explanation:
(4p - 1)^2 = 4p^2
(4p - 1)^2 =(2p)^2
4p - 1 =[tex]\sqrt{(2p)^2}[/tex]
4p - 1 =2p
4p - 2p =1
2p = 1
p =1/2
A cone-shaped section is cut out of a cubic block of wood as shown. What is the volume of wood left after the cone is removed? Round to the nearest tenth.
12cm
12cm
12cm
Answers:
A. 371.5 in^3
B. 452.2 in^3
C. 1275.6 in^3
D. 1728.0 in^3
Answers
Answer:
Its A
Step-by-step explanation:
Its A
probability................................
Answers
Answer:
outcome 10
simple space10
A 5
B 5
C 5
Step-by-step explanation:
Hope this helps!!!
wats the answer of 3/4 of 7/15
Answers
Answer:
3/4 × 7/15 =7/20
just multiplication
can someone pls help for brainlest
Answers
Answer:60
Step-by-step explanation:20x6=120 120/2=60
Answer:
200 cubic centimetres
Step-by-step explanation:
Length = [tex]20 \: cm[/tex]
Width = [tex]6 \: cm[/tex]
Height = [tex]5 \: cm[/tex]
Volume = [tex] \frac{1}{3} \times w \times l \times h[/tex]
[tex] = \frac{1}{3} \times 20 \times 6 \times 5[/tex]
[tex] = \frac{20}{3} \times 6 \times 5[/tex]
[tex] = \frac{20}{3} \times (3(2)) \times 5[/tex]
[tex] = 20 \times 2 \times 5[/tex]
[tex] = 40 \times 5[/tex]
[tex] = 200 \: {cm}^{2} [/tex]
Hope it is helpful...pls help me solve pls show how you got the answer
Answers
Given:
The figure of a circle O.
To find:
The value of x.
Solution:
First, label some points on the given figure as shown below.
In triangle BOC,
[tex]OB=OC[/tex] (Radii of same circle)
It means [tex]\Delta BOC[/tex] is an isosceles triangle and the base angles of an isosceles triangles are congruent. So,
[tex]\angle OBC\cong \angle OCB[/tex]
[tex]m\angle OBC=m\angle OCB[/tex]
[tex]75^\circ=m\angle OCB[/tex]
In triangle [tex]\Delta BOC[/tex],
[tex]m\angle BOC+m\angle OBC+m\angle OCB=180^\circ[/tex] (Angle sum property)
[tex]m\angle BOC+75^\circ+75^\circ=180^\circ[/tex]
[tex]m\angle BOC+150^\circ=180^\circ[/tex]
[tex]m\angle BOC=180^\circ-150^\circ[/tex]
[tex]m\angle BOC=30^\circ[/tex]
Now,
[tex]m\angle BOC=m\angle BOC+m\angle COD[/tex]
[tex]m\angle BOC=30^\circ+94^\circ[/tex]
[tex]m\angle BOC=124^\circ[/tex]
Using the central angle theorem, we get
[tex]m\angle BAD=\dfrac{1}{2}\times m\angle BOD[/tex]
[tex]x=\dfrac{1}{2}\times 124^\circ[/tex]
[tex]x=62^\circ[/tex]
Therefore, the correct option is B.
pleaseeeee helppp meee!!!
Answers
Answer: 32x-48 should be your answer
Step-by-step explanation:
Answer:
32x - 48Step-by-step explanation:
-4(-8x + 12)
= -4 × (-8x) + (-4) × 12
= 32x + (-48)
= 32x - 48 (Ans)
100 points
This system of inequalities models the scenario:
2x + y ≤ 8
x + y ≥ 4
Part A: Describe the graph of the system of inequalities, including shading and the types of lines graphed. Provide a description of the solution set.
Answers
Answer:
Solution set include (1,5), (1,4)
Step-by-step explanation:
To solve, you would have to graph both lines, and shade, the sections that are applicable. For Example is if it tells you the 2x+y is less than or equal to 8, you would shade it.
The Solution set would be anything in the overlapping area between both line's shades.
The library has 215 new books 155 of those books already have been put on shelves .the rest of the books are divide equally amount 5 boxes
Answers
Answer:
Ok to do this question we must first put it into a algebraic equation.
215=5x-155
This is are equation. lets first get rid of the 155 by adding it to the 215 which is 370.
370=5x
Ok now we will divide 370 by 5 which is 74.
x=74
Your Welcome
BIFFY OUT!!!
a)
2(x + 3) = x-4
Can someone help me pls...??
Answers
Answer: -10 :))))
i hope this helps
can someone please help
Answers
Answer:
Concurrent as my perception
Pls help me I don’t understand this!!!!
Answers
Answer: D
Step-by-step explanation:
D The angle agacent to arc ML is half the degree. Your answer is 118
Answer:
D
Step-by-step explanation:
angle J is a circumference angle that insists on arc ML. the measure the angle of this arc is double of it
59 * 2 = 118 degrees
Someone pls help me ill give out brainliest pls don’t answer if you don’t know
Answers
Answer:
i think it is A
Step-by-step explanation:
Answer:
its A between -9 and -10
Step-by-step explanation:
