Answer:
[tex]a = 2[/tex] and [tex]b = 4[/tex]
Step-by-step explanation:
Given
The expression is:
[tex]\frac{x^2 + ax - 4}{x + 2} + \frac{x + b}{x + 2} = x + 1[/tex] --- missing from the question
Required
Find a and b
Take LCM
[tex]\frac{x^2 + ax - 4+x + b}{x + 2} = x + 1[/tex]
Cross Multiply
[tex]x^2 + ax - 4+x + b = (x+2)*(x + 1)[/tex]
Open brackets
[tex]x^2 + ax - 4+x + b = x^2+2x + x + 2[/tex]
[tex]x^2 + ax - 4+x + b = x^2+3x + 2[/tex]
Collect Like Terms
[tex]x^2 + ax +x + b- 4 = x^2+3x + 2[/tex]
[tex]x^2 + (a +1)x + b- 4 = x^2+3x + 2[/tex]
By comparing the coefficients:
[tex]a + 1 = 3[/tex]
[tex]a = 3 - 1[/tex]
[tex]a = 2[/tex]
[tex]b - 4 = 2[/tex]
[tex]b = 4[/tex]
Hence,
[tex]a = 2[/tex] and [tex]b = 4[/tex]
Answer:
a = 2
b = 6
Edg 2021
A hemisphere-shaped security mirror fits exactly inside a rectangular prism box with a square base that has edge length 10 inches. What is a reasonable estimate for the volume of this mirror?
Answer:
?????????????????????????
Step-by-step explanation:
The solution is, final answer is 288 square inches.
What is area?Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
here, we have,
Given that Area of the square mirror = 256 square inches
We know that area of square is given by formula
Area = x^2, where x is the side of the square
plug the given value
256=x^2
take square root
16=x
Hence width of the square is 16 inches.
Given that a rectangular mirror has a width the same as the square mirrors width.
Then width of the rectangle = 16 inches
Length of the rectangle = 16+2 = 18 inches
Area of rectangle = Length * width = 16*18 = 288
Hence final answer is 288 square inches.
To learn more on Area click:
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ayudaaa es para hoy ;-;
múltiplos de 3: 6-9-12-15-18-21-24. etc
múltiplos de 3 que también son de 6:12-18-24.etc
múltiplos de 6: 12-18-24-30-36-42-48-54-. etc
múltiplos de 10:20-30-40-50-60-70-80.etc
múltiplos de 5:10-15-20-25-30-35-40-45-50-55.etc
múltiplos de 5 que tambien son de 10:20-30-40-50. etc
NEED ANSWERS ASAP!!!!! NUMBER 4!!
Answer:
The angle of the last point would also be 35 because both sides are congruent. I don't know what else you are asking.
Answer:
Your answer is 35
Step-by-step explanation:
This is an isosceles triangle and that means 2/3 of the sides are the same length.
Red and grey bricks were used to build a decorative wall. The number of red bricks and grey bricks was 5/2. There were 140 bricks used in all. How many red bricks were used?
Group of answer choices
40
100
20
28
Answer:
100 red bricks
Step-by-step explanation:
Let's say red bricks is equal to 5x
Gray bricks is equal to 2x
We have an equation
2x + 5x = 140
= 7x = 140
Divide through by 7 to get the value of x
X = 140/7
X = 20
Red bricks = 5(x)
= 5(20)
= 100
Gray bricks = 2(x)
= 2(20)
= 40
Therefore in conclusion the number of red bricks is 100.
Kevin says it will take him less than 1 hour to do homework and play soccer is he correct? Explain.
Answer:
I don't know how I would know but if he takes 30 minutes or less on each individual activity then he is correct, if he exceeds those limits, he is incorrect.
Step-by-step explanation:
what can be characterized the african music
Answer:
the melodies are usually short and simple. african music uses short bits of melody that are repeated over and over. singers or instrumentalists may change them at will, so that the performance becomes a theme with many variations.
Step-by-step explanation:
Answer:
champeta
Step-by-step explanation:
is danced in colombia but its it from africa
Complete the sentences. There are approximately 3,000 bass in a lake. The population grows at a rate of Complete the sentences.
There are approximately 3,000 bass in a lake. The population grows at a rate of 2% per year.
Round answers to the nearest tenth.
From Year 1 to Year 4, the average rate of change of the population was about _____
bass per year.
From Year 5 to Year 8, the average rate of change of the population was about_______
bass per year.
Answer:
From Year 1 to Year 4, the average rate of change of the population was about 61.8 bass per year.
Step-by-step explanation:
First you find 2% of 3000 which is 60
Next you find 2% of 3060 =61.2
next 2% of 3120 =62.4
last 2% of 3180 is 63.6
then you find the average of all the number combined is 61.8
Do the same with the other problem
The volume of gas a balloon can hold varies directly as the cube of its radius. Imagine a balloon with a radius of 3 inches can hold 108 cubic inches of gas. How many cubic inches of gas must be released to reduce the radius down to 2 inches?
Answer:76
Step-by-step explanation:
Answer:
76 in³Step-by-step explanation:
Volume of gas varies directly as the cube of its radius.
V = kr³Find k:
108 = k(3³)k = 108/27k = 4Volume of the smaller balloon:
V = 4r³V = 4(2³) = 32 in³The difference in volumes is the volume of released gas:
108 - 32 = 76 in³Please help me pls!!
Answer:
Step-by-step explanation:
Calculating the Perimeter of a Compound Shape made from Rectangles. A compound shape (or composite shape) is a more complex shape that is made up of two or more simple shapes. To find the perimeter, we simply add up the lengths of each outside edge.
HOPE IT HELPS
Write in radical form:
(7x)^2/5
Answer:
[tex]\sqrt[5]{(7x)^2}[/tex]
Step-by-step explanation:
What is the area of the triangular base?
Answer:
90cm2
Step-by-step explanation:
1/2x base x height.
1/2 x10 x 18
90cm2
find that area please
FOR THE LOVE OF GOD PLEASE HELP ME I WILL GIVE 30 points
Answer:
Eliminate y by adding equations (1) and (3) because the coefficients on y are opposites. Then eliminate y by multiplying equation (1) by 2 and adding it to equation (2).
Eliminate z by subtracting equations (1) and (2) because the coefficients are the same. Then eliminate z by multiplying equation (3) by 2 and adding it to equation (1).
Step-by-step explanation:
The variables have to be the same in both equations in the 2 × 2 system.
All of this should be included
BAKE SALE Cassandra and Alberto are selling pies for a fundraiser. Cassandra sold 3 small pies and 14 large pies for a total of $203. Alberto sold 11 small pies and 11 large pies for a total of $220. Determine the cost of each pie.
Answer:
Large pie = 13
small pie = 7
Step-by-step explanation:
hope this helps!
Taking into account the definition of a system of linear equations, the cost of each small pie is $7, while the cost of each large pie is $13.
A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
In this case, a system of linear equations must be proposed taking into account that:
x: cost of each small piey: cost of each large pieCassandra sold 3 small pies and 14 large pies for a total of $203. This is represented by: 3x + 14y= 203
Alberto sold 11 small pies and 11 large pies for a total of $220. This is represented by: 11x + 11y= 220
So, the system of equations to solve is:
[tex]\left \{ {{3x+14y=203} \atop {11x+11y=220}} \right.[/tex]
There are various methods to solve a system of equations, it is decided to solve by the substitution method, which consists of solving one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, isolating the variable y from the first equation, you obtain:
14y= 203 - 3x
y= (203 - 3x) ÷14
y= 14.5 - [tex]\frac{3}{14}[/tex]x
Replacing this expression in the second equation and solving, you obtain:
11x + 11×(14.5 - [tex]\frac{3}{14}[/tex]x)= 220
11x + 11×14.5 - 11×[tex]\frac{3}{14}[/tex]x= 220
11x + 159.5 - [tex]\frac{33}{14}[/tex]x=220
11x - [tex]\frac{33}{14}[/tex]x=220 - 159.5
[tex]\frac{121}{14}[/tex]x= 60.5
x= 60.5÷ [tex]\frac{121}{14}[/tex]
x= 7
Finally, to obtain the value of y, it is replaced in the expression previously obtained for y:
y= 14.5 - [tex]\frac{3}{14}[/tex]x
y= 14.5 - [tex]\frac{3}{14}[/tex]×7
y= 14.5 - [tex]\frac{3}{2}[/tex]
y= 13
Finally, remembering that x represents the cost of each small pie and y represents the cost of each large pie, so the cost of each small pie is $7, while the cost of each large pie is $13.
Learn more about system of equations:
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I WILL MARK BRAINLIEST PLEASE HELP ASAP!!!!! Sketch a new graph of this relationship. The equation is y=7/4x
Answer:
Step-by-step explanation:
Point X (-1, 6) is rotated 90 degrees about the origin using the transformation rule (x, y) --> (-y, x). What is the ordered pair of the Image X'? Please write your response as (x, y),
Answer:
The coordinates of the ordered pair of the Image X' are: X'(-6, -1)
Step-by-step explanation:
When a point A(x, y) is rotated 90° counterclockwise around the origin, we flip x and y and reverse the sign of y.
Thus,
The rule to rotate a point A(x, y) after a rotation 90° counterclockwise around the origin is:
A(x, y) → A'(-y, x)
In our case, the point X (-1, 6) is rotated 90° counterclockwise about the origin. Thus, the coordinates of P' will be:
A(x, y) → A'(-y, x)
X (-1, 6) → X'(-6, -1)
Therefore, coordinates of the ordered pair of the Image X' are: X'(-6, -1)
PLS HELPPPP with my IXL
Answer:
x = 17
Step-by-step explanation:
aren't NP and QP equal to each other? lmk if I'm wrong and what the right answer would be pls
Answer:
x = 17
Step-by-step explanation:
we know tangents from an external point are equal hence,
x-7 = 10x = 10 + 7x = 17x = 17
reciprocals in mix fraction form
Answer: improper fractions
Step-by-step explanation:
Multiply and Simplify. Show work to earn full credit. pls help and ty<3 20 pts
(3x-2) (5x^2-6x+2)
Answer:
15x^3 - 28x^2 + 18x -4
Step-by-step explanation:
(3x-2) (5x^2-6x+2)
[tex]15x^3 -18x^2 +6x - 10x^2 + 12x - 4[/tex]
[tex]15x^3 - 28x^2 + 18x -4[/tex]
Answer:
I just wanna steal your points :)
Step-by-step explanation:
NEED HELP FAST PLEASE !!
What is the value of x
Answer:
4.5
Step-by-step explanation:
use altitude rule
8 / 6 = 6 / x
8x = 36
x = 36/8 or 9/2 or 4.5
Please help due today
Answer:
The answer is C, A, B
Step-by-step explanation:
2y = -x-18
x-intercept:
y-intercept:
Answer:
Step-by-step explanation:
Solve the system of linear equations.
{x = 3
{y = 3
A. (3,3)
B. (-3,3)
C. (3,-3)
D. (-3,-3)
An appliance store decreases the price of a 19-in. television set 16% to a sale price of $509.88. What was the original price?
Answer:
the original price 3186.75
B. The time in Paris is 6 hours ahead of New York. Use P for Paris time and N for New York time to express P as a function of N. (Represent your answer in terms of a 12-hour clock.) How would you adjust your formula if P comes out greater than 12?
Answer:
P(N) = 6 + N ; if P(N) > 12 ; P(N) = 6 + N - 12
Step-by-step explanation:
Paris is 6 hours ahead of New York ;
P - Paris time
N - New York time
To represent P as a function of N
P(N) = 6 + N
If P comes out greater than 12 ; because we want a 12-hour clock :
If P(N) is > 12
P(N) becomes ;
P(N) = 6 + N - 12
I’f the vertical length is 10 what is the horizontal length
Answer:
Missing context,
Do you have a ratio I could work with?
Isaac's dad built a shelf for his video games that is 42inches wide. Each video game is 6/8inches wide. How many video games can Isaac fit on the shelf?
Answer:
56
Step-by-step explanation:
to find the answer, divide 42 by 6/8
42 x 8/6 = 56
Anika deposits $1,300 into an account that pays 1.7% interest, compounded monthly. Complete the following table. (Format the answers like the example provided. Round to the nearest cent.)
Year Amount
1 $1322.27
2
3
6
7
8
What is the average rate of return from the end of the first year to the end of the third year?
What is the average rate of return from the end of the sixth year to the end of the eighth year?
Answer:
i think it's about 20.4% per year
Kaylin buys a greeting card for $3.79. She then buys 4 postcards that all cost the same amount. The total cost is $5.11. How much is each postcard?
Answer:
$0.33
Step-by-step explanation:
5.11-3.79=1.32 1.32/4
Hope this helps :)
Answer:
each postcard cost .33 or 33 cent
Step-by-step explanation:
5.11(total cost)-3.79(greeting card)= 1.32
1.32(cost of all postcards)/4= .33
Ben has dollars. Sally has dollars less than Ben. Which expression represents the amount of money that Sally has?
Answer: m - 5
Step-by-step explanation:
Ben has m dollars.
Sally has $5 less than the amount that Ben has. This means that to find the amount of money Sally has, one needs to deduct $5 from the amount that Ben has.
Again, Ben has m. Sally's money is therefore:
= m - 5