The solution to given system of linear equations is (7, 3)
What is linear equation?
A linear equation is defined as an equation in which the highest power of the variable is always one.
Given,
x-3y = -2
x+3y =16
Adding the both equations,
2x=14
So, x=7
Substitute the value of x=7 in equation x+3y =16
7+3y =16
3y =16-7
y=3
Thus, the solution to given system of linear equations is (7, 3)
Learn more about linear equation
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Answer: A. (7,3)
Step-by-step explanation: I just did the quiz and got 100%, hope this helps!
1. 21 + x = 26
2. 12 + 2x = 16
3. 4x - 2 = 10
4. x + 7 = 12
algebra I hat it please help me
Answer:
hope it will help uh ...u will slowly get over it..
A bread recipe calls for 2 1/2 cups of whole wheat flour 2/3 cups of rice flour 2 1/4 cups of white flour how many total cups of flour are needed write your answer as a simplified mixed number
Answer:
5 5/12
Step-by-step explanation:
you find the common denominator which is 12
2 6/12
8/12
2 3/12
now u add them all
hope this helps
Answer:
5 5/12 cups
Step-by-step explanation:
a patient receives 65 grams of medicine if its increased by 20% how many grams is that
Responda:
13 gramas
Explicação passo a passo:
65 + 20% = 13
For the x-values 1, 2, 3, and so on, the yvalues of a function form a geometric
sequence that decreases in value. What type of function is it?
Answer:
exponential function
Step-by-step explanation:
A geometric sequence is a representation of an exponential function.
__
There are a couple of ways an exponential function can decrease in value. It can be a decaying function, or it can be a growth function that is reflected across the x-axis.
Want Brainliest? Get this correct Which of the following is the quotient of the rational expressions shown below? Make sure your answer is in reduced form.
Answer:
B.
Step-by-step explanation:
First, notice that we can cancel out an x in the second term. Thus:
[tex]\displaystyle \frac{3x^2}{x^2+x} =\frac{3x^2}{x(x+1)} =\frac{3x}{x+1}[/tex]
As with the last question, change the sign to multiplication and "flip" the second term:
[tex]\displaystyle \frac{2x-1}{x+1}\cdot \frac{x+1}{3x}[/tex]
Multiply straight across:
[tex]\displaystyle =\frac{(2x-1)(x+1)}{(x+1)(3x)}[/tex]
We can cancel the (x + 1) term:
[tex]\displaystyle =\frac{2x-1}{3x}[/tex]
This cannot be simplified further. Hence, our answer is B.
Answer:
It is B)
Step-by-step explanation:
Ap3x Approved
Brainliest to correct answer!! What is the least common denominator of the rational expressions below?
Answer:
least common denominator of the rational expressions below is x(x-7)(x+3)
Step-by-step explanation:
factotized form of denominators
x²-7x
=x(x-7)
x²-4x-21
=x²-7x+3x-21
=x(x-7)+3(x-7)
=(x+3)(x-7)
i hope this will help you :)
Answer:
least common denominator of the rational expressions below is x(x-7)(x+3)
Step-by-step explanation:
factotized form of denominators
x²-7x
=x(x-7)
x²-4x-21
=x²-7x+3x-21
=x(x-7)+3(x-7)
=(x+3)(x-7)
i hope this will help you :)
Heather is writing a quadratic function that represents a parabola that touches but does not cross the x-axis at x = –6. Which function could Heather be writing? f(x) = x2 + 36x + 12 f(x) = x2 – 36x – 12 f(x) = –x2 + 12x + 36 f(x) = –x2 – 12x – 36
Answer:
f(x) = –x^2 – 12x – 36
Step-by-step explanation:
The parent function, x^2, touches the x-axis at x=0. Translating it 6 units left replaces x with x-(-6) = x+6, so the function is ...
f(x) = (x+6)^2 = x^2 +12x +36
Reflecting the graph across the x-axis doesn't change the x-intercept, so Heather could be writing ...
f(x) = -x^2 -12x -36
It's D.
I have to have at least 20 characters.
5/6-2/7 the answer isnt 23/42 or 8/21
Answer:
Common denominator - 42
Step-by-step explanation:
6 - 6, 12, 18, 24, 30, 36, 42
7 - 7, 14, 21, 28, 35, 42
Hope this helps! :)
If you are given only the measurements of the three angles of a right triangle, can you find the lengths of the three sides?
Answer:
No
Because you can't find any of the length if you don't have two other lengths
Step-by-step explanation:
study cosine rule and sine rule
you use cosine rule when you have one angle in-between two length
while you use sine rule when you have two angles and one length
just study cosine rule and sine rule you will understand what am saying
Answer:
no
Step-by-step explanation:
The additive inverse of x/y is
Answer
The additive inverse is
-x/-y
That is equal to x/y
hope this may help you
translate the sum of x and one half of x into a mathematical expression
Answer:
The above statement is written as
[tex]x + 1 \times \frac{1}{2} of \: x[/tex]
of means multiplication
So the final answer is
[tex]x + \frac{3}{2} x[/tex]
Hope this helps you.
Explain why the following expression is false. |x| < -4
Step-by-step explanation:
Whenever we put a negative number inside a modulus function it will give us the positive output. For example , |-3| = 3 , |-6|=6, |5|= 5 ,etc.
So a modulus function i.e. |x| is always greater than zero ( positive ) when x is any number except 0 and it is equal to zero when the value of x is 0.
So |x| can't be less than -4 as |x| is always positive . So the statement is false.
The expression |x| < -4 is false because all Positive numbers are greater than all negative numbers.
Modulo of a numberThe modulo of a number x as denoted by; |x| is the positive value of number x irrespective of the value of x.
Hence, the number x, whether positive or negative becomes a positive number and hence;
|x| > -4 which renders the given expression falseRead more on modulo of a number;
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Vector A has components (5,6) and vector B has components (-12, 3). What is the direction of the vector C
Vector A has components (5,6) and vector B has components (-12, 3). What is the direction of the vector C = 2A - B
Answer:
22.24° to the positive x-axis.
Step-by-step explanation:Given vectors:
A (5, 6)
B (-12, 3)
C = 2A - B ------------(i)
First let's represent the two vectors in unit notation as follows;
A = 5 i + 6 j
B = -12 i + 3 j
Now substitute these vectors into equation (i) as follows;
C = 2(5 i + 6 j) - (-12 i + 3 j)
C = 2(5 i + 6 j) + (12 i - 3 j)
C = 10 i + 12 j + 12 i - 3 j [collect like terms]
C = 10 i + 12 i + 12 j - 3 j
C = 22 i + 9 j ----------------(ii)
The direction, θ, of vector C can be calculated as follows;
θ = tan⁻¹([tex]\frac{9}{22}[/tex])
θ = tan⁻¹(0.409)
θ = 22.24°
Since both the x and y components of vector C are positive, the direction of the vector is 22.24° to the positive x-axis.
Eric works for salary of $3,500 per month. He has federal income withheld at the rate of 15%, Social Security tax at the rate of 6.2%, Medicare tax at the rate of 1.45% and health insurance premiums of $48 per month. Erik also contributes to a savings plan. Each month, 2% of his gross pay is placed in the savings plan.
After Erik pays the taxes on his money what is Eric's net pay?
A. (1,448.45)
B. (1,799.05)
C. (2,589.25)
D. (2799.05)
Answer:
C. 2,589.25
Step-by-step explanation:
Salary=$3500
Less:
Federal income withheld
15% of $3500
=15/100×$3500
=$525
Social security tax of 6.2%
6.2% of $3500
=6.2/100 × $3500
=$217
Medicare tax of 1.45%
1.45% of $3500
1.45/100 × $3500
=$50.75
Health insurance premium=$48
Savings plan of 2%
2% of $3500
=2/100 × $3500
=$70
Total less:= $525 + $217 + $50.75 + $48 + $70
Eric's net pay =$3500 - $910.75
=$2,589.25
Answer:
c
Step-by-step explanation:
4
The equation of a circle is x2 + y2 + x + Dy+ E= 0. If the radius of the circle is decreased without changing the coordinates of the center point, how are the coefficients CD,
and E affected?
O A CD, and E are unchanged.
Answer:
Step-by-step explanation:
in x²+y²+2gx+2fy+c=0
center=(-g,-f)
radius=√((-g)²+(-f)²-c)
if center is not changed ,then c will change .
Here only coefficients of E will change.
check all that apply
Answer: B & C
Step-by-step explanation:
Putting the values of x & y in all 4 equations we see that the values satisfy equations B & C only. Hence B & C are correct answers
If we are testing for the difference between the means of 2 independent populations presuming equal variances with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to a. 38. b. 19. c. 18. d. 39.
Answer:
Null hypothesis: [tex]\mu_1= \mu_2[/tex]
Alternative hypothesis:[tex]\mu_1 =\neq \mu_2[/tex]
And for this case we assume that we have equal variances so that means:
[tex]\sigma =\sigma_1 =\sigma_2[/tex]
For this case the degrees of freedom are given by:
[tex] df= n_1 +n_2 -2[/tex]
And replacing we got:
[tex] df= 20+20 -2= 38[/tex]
And the best answer would be:
a. 38
Step-by-step explanation:
For this problem we want to test the following:
Null hypothesis: [tex]\mu_1= \mu_2[/tex]
Alternative hypothesis:[tex]\mu_1 =\neq \mu_2[/tex]
And for this case we assume that we have equal variances so that means:
[tex]\sigma =\sigma_1 =\sigma_2[/tex]
For this case the degrees of freedom are given by:
[tex] df= n_1 +n_2 -2[/tex]
And replacing we got:
[tex] df= 20+20 -2= 38[/tex]
And the best answer would be:
a. 38
Consider the following results for two independent random samples taken from two populations.
Sample 1 Sample 2
n1 = 50 n2 = 35
X1 = 13.6 X2 = 11.6
1 = 2.2 1 = 3.0
1. What is the point estimate of the difference between the two population means?
2. Provide a 90% confidence interval for the difference between the two population means (to 2 decimals).
3. Provide a 95% confidence interval for the difference between the two population means (to 2 decimals).
Answer:
1. Point estimate Md = 2
2. The 90% confidence interval for the difference between means is (1.01, 2.99).
3. The 95% confidence interval for the difference between means is (0.82, 3.18).
Step-by-step explanation:
a) The point estimate of the difference between the two population means is the difference between sample means:
[tex]M_d=M_1-M_2=13.6-11.6=2[/tex]
2. We have to calculate a 90% confidence interval for the difference between means.
The sample 1, of size n1=50 has a mean of 13.6 and a standard deviation of 2.2.
The sample 2, of size n2=35 has a mean of 11.6 and a standard deviation of 3.
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{2.2^2}{50}+\dfrac{3^2}{35}}\\\\\\s_{M_d}=\sqrt{0.097+0.257}=\sqrt{0.354}=0.5949[/tex]
The degrees of freedom for this confidence interval are:
[tex]df=n_1+n_2-2=50+35-2=83[/tex]
The critical t-value for a 90% confidence interval is t=1.663.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_{M_d}=1.663 \cdot 0.5949=0.99[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M_d-t \cdot s_{M_d} = 2-0.99=1.01\\\\UL=M_d+t \cdot s_{M_d} = 2+0.99=2.99[/tex]
The 90% confidence interval for the difference between means is (1.01, 2.99).
2. We have to calculate a 95% confidence interval for the difference between means.
The critical t-value for a 95% confidence interval and 83 degrees of freedom is t=1.989.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_{M_d}=1.989 \cdot 0.5949=1.18[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M_d-t \cdot s_{M_d} = 2-1.18=0.82\\\\UL=M_d+t \cdot s_{M_d} = 2+1.18=3.18[/tex]
The 95% confidence interval for the difference between means is (0.82, 3.18).
5. Which of the following is an equivalent form of the parabola y = x - 4x - 12 that displays
the x-intercepts?
A) y + 12 = x² - 4x
B) y = (x - 2)2 - 16
C) y=(x-6) (x + 2)
D) y = x (x – 4) - 12
Answer:
Your answer is B. Tell me if you need graphics)
it would be C
My best assumption here is you misplaced x^2 in this function. Mostly what is done with the answer C is the function is being FACTORED, and broken down into its simplest form.
an item is on sale at 40% off the regular price. it is tax at a rate of 6%. if the final sale price including tax is 50.88 then what is the sale price of the item without tax what was regular price
the sale price of the item without tax was
the regular price of the item is
Answer:
$48, $80
Step-by-step explanation:
$50.88 is the price including tax and the discount. The discount is applied first. Then the tax is applied.
The tax is 6%, so $50.88 is 106% of the discounted price.
$50.88/1.06 = $48
$48 is the discounted price.
The discount is 40% of the original price, so the pre-tax discounted price is 60% of the original price.
$48/0.6 = $80
The original price was $80
One movie ticket costs $7, and one small bag of popcorn costs $3. Write two equivalent expressions for the total cost of four movie tickets and four bags of popcorn. Then find the cost. a. 4($7 + $3), 4($7) + 4($3); $40 c. $4(7 + $3), $4(7) + $4($3); $12 b. 4($7 x $3), 4($7) x 4($3); $84 d. $4($7), $4($3); $28
Answer:
Option A
Step-by-step explanation:
=> 1 ticket = $7
=> 1 bag = $3
Expression # 1:
=> 4($7+$3)
Expression # 2:
=> 4($7)+4($3)
Solving it:
=> $28+$12
=> $40
Answer:
4(7+3)=28+12=40, 4(3)+4(7)
Answer: A and C
Step-by-step explanation:
Find the area of the irregular figure. Round to the nearest hundredth.
Answer:
23.14
Step-by-step explanation:
Solve for the area of the figure by dividing it up into parts. You can divide into a half-circle and a triangle
Half-Circle
The diameter is 6. This means that the radius is 3. Use the formula for area of a circle. Divide the answer by two since you only have a half-circle.
A = πr²
A = π(3)²
A = 9π
A = 28.274
28.274/2 = 14.137
Triangle
The base is 3 and the height 6. Use the formula for area of a triangle.
A = 1/2bh
A = 1/2(6)(3)
A = 3(3)
A = 9
Add the two areas together.
14.137 + 9 = 23.137 ≈ 23.14
The area is 23.14.
Answer:
23 sq. unitsStep-by-step explanation:
The figure consists of a semi circle and a triangle
Area of the figure = Area of semi circle + Area of triangle
Area of semi circle is 1/2πr²
where r is the radius
radius = diameter/2
radius = 6/2 = 3
Area of semi circle is
1/2π(3)²
1/2×9π
14.14 sq. units
Area of a triangle is 1/2×b×h
h is the height
b is the base
h is 6
b is 3
Area of triangle is
1/2×3×6
9 sq. units
Area of figure is
14.14 + 9
= 23.14
Which is 23 sq. units to the nearest hundredth
Hope this helps you.
Triangle ABC is drawn inside regular hexagon ABCDEF. What is the ratio of the area of triangle ABC to the area of the hexagon?
The sides of the regular hexagon ABCDEF can be posed as a. If so, the area of ABCDEF should be 6 times the are of the interior angle in the hexagon, considering there are 6 equilateral triangle that can fit in this regular hexagon,
Area = 6( a * a * sin 60 ) / 2,
Area = ( About ) 2.6 sq units
Now applying cosine for triangle ABC -
AC^2 = AB^2 + BC^2 – ( 2*AB*BC*cos 120 ),
a^2 + a^2 – ( 2a^2 * ( - 0.5 ) ) = a^2 + a^2+a^2 =3a^2,
AC = a√3
The area of ABC should thus be the following -
( a√3 * a√3 * sin 60 )/2 = 1.299038106 sq units
As you can see, the area of ABC is half the area of ABCDEF, thus the ratio of the area of ABC to ABCDEF is 1 : 2
Answer:
3.5 units
Step-by-step explanation:
Question # 9 help please!!
Answer:
answer is C
Step-by-step explanation:
..........
Answer:
im pretty sure the answer is either C or D. i think it's C though. good luck on your test/assignment!
Step-by-step explanation:
6. the price of an item with a 15% discount
The price of an item with a 15% discount would be 85% of the original price, so if the original price was x, the discounted price would be: [tex]\frac{85x}{100}[/tex]
hey guys please help me
Answer:
5/6
Step-by-step explanation:
The probability of the 10th roll will be 6 is 1 out 6 because there's only one side with 6 (we spouse the dice is not biased) so the probability of the roll not to be 6 is 5/6
Write log√3x in expanded form.
Answer:
log (3) log (x)
--------- + ---------
2 2
Step-by-step explanation:
a. distribute to get → log (3) log (x)
--------- + ---------
2 2
Hope this helped! :)
log√(3x) can be written in the expanded form as [tex]\frac{1}{2}[/tex] [log (3) + log (x)].
What are Logarithms?A logarithm is simply the opposite function of the exponentiation.
It is the exponent to which a number or value is raised to get some other number.
That is, if c = aˣ, then we can write it as x =logₐ c.
We know that,
√a can be written as (a) ^(1/2).
Similarly,
log√(3x) = log (3x)^(1/2)
Now, we have a rule for logarithms that, log aᵇ = b log a.
So,
log√(3x) = log (3x)^(1/2)
= [tex]\frac{1}{2}[/tex] log (3x)
Using the multiplication rule of logarithms, log (ab) = log (a) + log(b),
= [tex]\frac{1}{2}[/tex] [log (3) + log (x)]
Hence the expanded form is [tex]\frac{1}{2}[/tex] [log (3) + log (x)].
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A metal alloy is 27% copper. Another metal alloy is 52% copper. How much of each should be used to make 22 g of an alloy that is 36.09% copper?
Answer:
14.0008 grams of 27% and 7.9992 grams of 52%
Step-by-step explanation:
We know that in the end we want 22 grams of 36.09% copper, meaning in the end we want 36.09% of the 22 grams to be copper. This means we can multiply 36.09% by 22 to see how much copper we want in the end.
To find out how much of each alloy to use, we can multiply the percentage of copper in the alloy be a variable x, which will be how much of that alloy we use. For the other alloy, we can multiply the percentage by (22-x) grams as we know in the end we want 22 grams and if x+y=22, than y would equal 22-x, and in this case this simplifies it to only use a single variable.
Now finally, making the equation we get 27x+52(22-x)=36.09(22). We can solve this and get 27x+1144-52x=793.98, then combine like terms and get -25x+1144=793.98. Next you have to subtract 1144 from both sides to get -25x=-350.02. Dividing both sides by -25 we get x=14.0008. This is how many grams of 27% copper was used. Now we can subtract this from 22 to get how much 52% copper was used, and we get 22-14.0008=7.9992 grams of 52% copper.
1. What line forms when a plane and a cylinder intersect?
O A. Parallel line
O B. Broken line
O C. Curved line
O D. Straight line
Answer:
A. Parallel line
Parallel line forms when a plane and a cylinder intersect
hope this helping you..
when a plane and a cylinder intersect it forms into parallel line
A.Parallel line
Which best describes the relationship between the line that passes through the points (-9, 2) and (-5, 4) and the line that passes through the points (-3, 4) and (1, 6)?
Answer:
Parallel!
Step-by-step explanation:
If you put these points on a graph and connect the dots to be two lines, they are perfectly side to side :)