Answer:
-10
Step-by-step explanation:
x has to be less in value than -5 and -10 is the only one that is less in value
Hope it Helps!
if this helped can you mark as brainliest?
The hypotenuse of a right triangle is 1 centimeter longer than one side and 4 centimeters longer than three times the other side. Find the dimensions of the triangle.
Answer:
[tex]Hypotenuse = 25cm[/tex]
[tex]Opposite = 24cm[/tex]
[tex]Adjacent = 7cm[/tex]
Step-by-step explanation:
Represent:
The opposite with aThe adjacent with bThe hypotenuse with cGiven that:
[tex]c = 1 + a[/tex]
[tex]c = 4 + 3b[/tex]
Required
Solve for a, b and c
[tex]c = c[/tex]
So, we have:
[tex]1 + a = 4 + 3b[/tex]
Subtract 1 from both sides
[tex]a = 4 -1 + 3b[/tex]
[tex]a = 3 + 3b[/tex]
Apply Pythagoras Theorem
[tex]c^2 = a^2 + b^2[/tex]
Substitute 3 + 3b for a and 4 + 3b for c
[tex](4 + 3b)^2 = (3 + 3b)^2 + b^2[/tex]
Open brackets
[tex]16 + 12b+12b+9b^2 = 9 + 9b+9b+9b^2 +b^2[/tex]
[tex]16 + 24b+9b^2 = 9 + 18b+10b^2[/tex]
Collect Like Terms
[tex]10b^2 - 9b^2 + 18b - 24b + 9 - 16 = 0[/tex]
[tex]b^2 - 6b -7 = 0[/tex]
Expand
[tex]b^2 +b-7b-7=0[/tex]
Factorize:
[tex]b(b+1)-7(b+1) =0[/tex]
[tex](b-7)(b+1) = 0[/tex]
Split:
[tex]b - 7 = 0\ or\ b+1=0[/tex]
[tex]b = 7\ or\ b=-1[/tex]
But the adjacent of a triangle can't have a negative measurement.
So:
[tex]b = 7[/tex]
Recall that:
[tex]c = 4 + 3b[/tex]
[tex]a = 3 + 3b[/tex]
Substitute 7 for b in the above expressions
[tex]c = 4 + 3 * 7[/tex]
[tex]c = 4 + 21[/tex]
[tex]c = 25[/tex]
[tex]a = 3 + 3 * 7[/tex]
[tex]a = 3 + 21[/tex]
[tex]a = 24[/tex]
Hence, the dimensions of the triangle are:
[tex]Hypotenuse = 25cm[/tex]
[tex]Opposite = 24cm[/tex]
[tex]Adjacent = 7cm[/tex]
A party size bag of Takis cost $5.95. If it's 30% off, but has a sales tax of 7%, what is the final cost?
Answer:
The bag of Takis now costs $4.46.
Step-by-step explanation:
We are given that a bag of Takis costs $5.95. We are also told that a markdown of 30% is applied to the product.
[tex]\displaystyle 100\%-30\% = 70\%\\\\\frac{70}{100}=0.7\\\\5.95 \times 0.7 = 4.165 \approx \$4.17[/tex]
Our new price is equal to $4.17, but we are told that a sales tax of 7% is also applied to the Takis. Therefore:
[tex]\displaystyle 100\% + 7\% = 107\%\\\\\frac{107}{100} = 1.07\\\\4.17 \times 1.07 = 4.4619 \approx \$4.46[/tex]
Therefore, the item with a markdown and sales tax applied is approximately $4.46.
The 64-ounce carton of orange juice costs $4.69. Find the unit price per ounce to the nearest tenth of a cent.
Answer:
13¢ per ounce
Step-by-step explanation:
just divide 64/4.69
If A = { 2,3,5,7 } then find the value of n(A).
Answer:
We conclude that
n(A) = 4Step-by-step explanation:
Given the set
A = { 2,3,5,7 }If we closely observe, we can easily identify that set A has 4 elements, which are 2, 3, 5, and 7.
n(A) denotes the number of elements in a set.
Since set A has 4 elements, therefore the value of n(A) = 4
Thus, we conclude that
n(A) = 4105 is 42% of what
number?
Answer:
250
Step-by-step explanation:
you have to do [tex]\frac{42}{100}[/tex] x ×=105the multiply both sides by 100 and dividing both sides by 42
so you will get
x=105 ×[tex]\frac{100}{42}[/tex] and that's how you will get your answer
or you can do
105 × 100 ÷ 42 on a calculator and you will get the same answer
The number 105 is 42 percent of the number 250.
let the unknown number be x.
To find the number that corresponds to 105 being 42% of it, we can set up the equation:
105 = 0.42x
To solve for x, we divide both sides of the equation by 0.42:
105 / 0.42 = x
x ≈ 250
Therefore, 105 is 42% of approximately 250.
Learn more about Percentage here:
https://brainly.com/question/31323953
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which equation describes the line that passes through the point (-4,-8) and is parallel to the line represented by the equation 7x - 2y = 8
Answer:
The equation is;
2y = 7x + 12
Step-by-step explanation:
General equation form is ;
y = mx + b
where m is slope and b is y-intercept
Let us rewrite the first equation;
2y = 7x - 8
y = 7x/2 - 4
the slope here is 7/2
If two lines are parallel, their slopes are equal
so we use the point-slope form to get the second equation
y-y1 = m(x-x1)
(x1,y1) = (-4,-8)
Thus, we have
y + 8 = 7/2(x + 4)
2y + 16 = 7x + 28
2y = 7x + 12
simplify 26+(-84)÷(-2)?
Answer:
68
Step-by-step explanation:
26 + (-84) ÷ (-2)
26 + (-84 ÷ -2)
26 + 42
68
1/4 divided by 5/6 = 1/a× b/c
Answer:
a= 24b/5c b= 5ac/24 c= 24b/5a
Step-by-step explanation:
Put the problem into a calculator that can solve with variables.
The expression 3x minus 4(2x minus 5) is equivalent to the expression 20-5x true or false
simplify 2^5/4=2^5/2^a=2^b whats a b and c
Answer:
Fraction A (a/b). Fraction B (c/d) Find what is fraction addition for given input data Therefore, find lcm for two denominators (3, 2) = 6 The result is the sum of numerators over the LCM;; Simplify the result if needed. 5/2 + 3/7, 41/14.
I need someone to check number 3 on my proof plzz
Answer:
ASA.
Step-by-step explanation:
Its ASA not AAS.
-1/2 minus 1/5. reduce to the simpiliest form
Answer:
It should be -7/10
Answer: The answer is -7/10 :)
Step-by-step explanation:
-1/2-1/5=-7/10
ITS DUE IN 15 MINUTES PLS HELP. Challenge Schools A and B are competing in an academic contest. Correct answers earn 9 points,
Incorrect answers lose 6 points. In the final round, School A gives the same number of correct and
incorrect answers, School B gives no incorrect answers and the same number of correct answers as
School A. School A started the final round with 198 points, School B started with 72. The game ends
with the two schools tied. Let x represent the number of correct answers given by School A in the final
round. Write an equation that models the outcome of the contest. Then find the number of answers
that each school got correct in the final round,
Answer:
School A gave 12 correct and 12 incorrect answers. School B gave 12 correct answers and the competition was tied.
Step-by-step explanation:
School A points = 174
School B points = 102
Every correct answer is awarded 10 points and every incorrect answer reduces 6 points.
Let x be the number of correct answer given by school A and thus x is the number of incorrect answer given by school A. The, school B also gives x number of correct answers
Answer:
uhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Step-by-step explanation:
A sculptor is selling her work at an exhibit and hopes to earn at least $31,000 in revenue. Small pieces go for $780 and large pieces go for
$1,500.
If x represents the number of small pieces sold and y represents the number of large pieces sold, write an inequality that
describes this situation.
The answer should be
780x + 1500y=31000
please correct me if i'm wrong
Answer:
its 780x+1600>29,000
Step-by-step explanation:
Graph the inequality on the axes below.
2x + y > -8
Y
10
9
8
6
5
-9
-S
- -
5
--
3 -2
3
+
2
3
+
5
9 10
The first step is to graph the line 2x + y = -8. To do this, we can graph the x and y-intercepts. Letting x = 0, we get y = -8, so the y-intercept is -8. Letting y = 0, we get 2x = -8, so x = -4.
Graph the line between the points (-4, 0) and (0, -8). The line should be dotted, because this is a strict inequality (the points on the line are not part of the solution).
The next step is to substitute a point - I like to use (0,0): when x and y are equal to zero, we have 2(0)+0>-8, which is true. Therefore, the right side of the graph (which contains the point (0,0)) should be shaded. Note: If the inequality was not true, you would want to shade the opposite side of the graph.
write y=5/8x +6 in standard form using intergers
Answer:
5x - 8y = -48
Step-by-step explanation:
Move 5/8x to the y side to get (-5/8)x + y = 6. Multiply both sides by -8 to get 5x - 8y = -48.
HELP PLEASE I NEED IT RN
Answer:
maybe a
Step-by-step explanation:
sorry if this is wrong, lol
Answer:
D
Step-by-step explanation:
it's volume.
Vanessa's total sales = - $321.50 1. How much do the girls owe the school in concession fees (15%) from Vanessa's total sales?
Answer:
pretty easy i did the math and it is about 42.56
Step-by-step explanation:
The formula for potential energy is P = mgh. Solve the equation for h.
Answer:
P = mgh
P/mg = h
We can divide both sides by mg, since both mass and gravity are being multiplied and not added.
Hope this helps!! :)
Step-by-step explanation:
What is an equation of the line that passes through the points (-1.6) and (-1,-5)?
Answer:
y= -0.5x + 5.5
Step-by-step explanation: mark this as solved because this is correct
slope = -0.5
intercept = 5.5
Answer:
x=-1
Step-by-step explanation:
the points are both on the line x=-1.
For future reference, use demos graphing calculator and type in the points, you can drag your line through.
Find the slope using a table
Answer:
-1/2
Step-by-step explanation:
slope = (y2-y1)/(x2-x1)
(4-6)/(0--4) since it's minus a negative that becomes plus so it's really
(4-6)/(0+4)=-2/4 or -1/2
HURRY!! 20 POINTS!! What is the solution set of the equation x+3/x+2=3+1/x? Note: x≠0, −2
{2} {−1, 2} {−1, 1} {−1}
The solution set for the given equation is x=-1 .
Solution set is written as {-1}
for better understanding check the calculation below.
Calculation :We need to solve the given equation
[tex]\frac{x+3}{x+2} =3+\frac{1}{x}[/tex]
To solve any equation we take LCD.
LCD of the given equation is x(x+2)
Multiply LCD with each term to remove the denominator
[tex]\frac{x+3}{x+2}\cdot x(x+2) =3\cdot x(x+2)+\frac{1}{x}\cdot x(x+2)\\x(x+3)=3x(x+2)+x+2\\x^2+3x=3x^2+6x+x+2\\[/tex]
Subtract x^2 and 3x from both sides of the equation to get 0 on the left side of the equation
[tex]0=3x^2+6x+x+2-x^2-3x\\0=2x^2+4x+2\\[/tex]
Now divide the whole equation by 2 and then we factor it
[tex]0=x^2+2x+1\\0=(x+1)(x+1) \\x+1=0\\x=-1[/tex]
The solution set for the given equation is x=-1
Solution set is written as {-1}
Learn more information about the ' rational equaion ' here : brainly.com/question/8519709
Answer:
-1
Step-by-step explanation:
find the sum of 10x^2-6 and x +6
Answer:
10x2+x
Step-by-step explanation:
The sum of four multiples of 4 is 72. Find these numbers.
Answer:
x=5
Step-by-step explanation:
4(x+x+1+x+2)=72
3x+3=72/4
3x+3=18
3x=18-3
3x=15
x=15/3
x=5
What is the value of a5
Answer: 16
Step-by-step explanation: i'm pretty sure it's just 16, from looking at the table?
x^4-4x^2-32
x
4
−4x
2
−32
Answer:
x2 • (x2 - 32772)
Step-by-step explanation:
step 1: ((x4) - 22x2) - 32768x2
step 2: Pull out like factors :
x4 - 32772x2 = x2 • (x2 - 32772)
Factoring: x2 - 32772
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 32772 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
What is the interest earned on $3,000 at a rate of 0.04 for 3 years? (Hint: Use the formula i = prt, where i represents the interest earned, p represents the principal, r represents the rate, and t represents the time.)
$3,003.04
$3,360
$360
$120
Answer:
3,360
Step-by-step explanation:
3000(.04)(3)
3000 x. 04=12000
12000 x 3,360
Nina’s dog weighed 23.54 pounds last year. This year, her dog weighs 25.38 pounds. How many pounds did her dog gain this past year? PLS HELP ME!!!!!!!!!
Answer:
1.84
Step-by-step explanation:
25.38-23.54
Determine which postulate or theorem can be used to prove that
AREM= ADME.
R
H
M
A. AAS
B. SAS
C. ASA
D. SSS
PLEASE HELP!!
Answer:
D. SSS theorem can be applied to prove that.
ba - ha = c
solve for a
Answer:
h = [tex]\frac{c}{b-h}[/tex]
Step-by-step explanation:
Given
ba - ha = c ← factor out a from each term on the left side
a(b - h) = c ← divide both sides by (b - h)
a = [tex]\frac{c}{b-h}[/tex]
