Answer:
∠ACB==50°
b=15.6 units
c=11.9 units
Step-by-step explanation:
step 1
Find the measure of angle BCA
we know that
The sum of the interior angles of a triangle must be equal to 180 degrees
∠ABC+∠BAC+∠ACB=180°
substitute the given values
90°+40°+∠ACB=180°
∠ACB=180°-130°=50°
step 2
Find the measure of side b
Applying the law of sines
a/sin(∠BAC)=b/sin(∠ABC)
substitute the given values
10/sin(40°)=b/sin(90°)
b=10/sin(40°)
b=15.6 units
step 3
Find the measure of side c
Applying the law of sines
c/sin(∠ACB)=a/sin(∠BAC)
substitute the given values
c/sin(50°)=10/sin(40°)
c=[10/sin(40°)]*sin(50°)
c=11.9 units
ANSWER:
C=11.9
ABC=90 deg.
BAC=40 deg.
A=10
(1/(x-1))-(3/(x^2+2x-3))
[tex] \frac{1}{x - 1} - \frac{3}{x {}^{2} + 2x - 3 } [/tex]
[tex]
\dfrac{1}{x-1}-\dfrac{3}{x^2+2x-3} \\
\dfrac{1}{x-1}-\dfrac{3}{(x+3)(x-1)} \\
\dfrac{1\cdot(x+3)-3}{(x+3)(x-1)} \\
\dfrac{x+3-3}{(x+3)(x-1)} \\
\dfrac{x}{(x+3)(x-1)}
[/tex]
Hope this helps.
r3t40
How many square inches are in 60 square feet?
Answer:
8640 in ^2
Step-by-step explanation:
1 ft = 12 in
60ft^2 * 12 inches * 12 inches
-------------- -------------- = 8640 in ^2
1 ft 1 ft
Answer:8640
Step-by-step explanation:
A taxi cab costs $1.50 for the first mile and $0.75 for each additional mile. Which equation could be solved to find how many miles you can travel in a taxi for $10 given that x is the number of additional miles?
A. 1.5x - 0.75= 10
B.0.75x + 1.5= 10
C. 0.75x - 1.5=10
D. 1.5x + 0.75=10
Answer:
B.0.75x + 1.5= 10
Step-by-step explanation:
Answer:
B. 0.75(x)+1.50 = 10
and 11.333333333....
Step-by-step explanation:
Which expression is equivalent to log5^(x/4)^2?
2log5(x) + log5(4)
2log5(x) + log5(16)
2log5(x) - 2log5(4)
2log5(x) - log5(4)
Answer:
2log5(x) - 2log5(4)
Step-by-step explanation:
An expression is defined as a set of numbers, variables, and mathematical operations. The expression that is equivalent to log₅(x/4)² is 5log(x) - 5log(4).
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression log₅(x/4)² can be expressed as,
log₅(x/4)²
= 5log(x/4) {∵ log(aᵇ) = b log(a) }
=5[log(x) - log(4)]
= 5log(x) - 5log(4)
Hence, the expression that is equivalent to log₅(x/4)² is 5log(x) - 5log(4).
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-2(7a+4b)-6c=
Simplify
Answer:
Because of the minus sign
2 becomes - 2
The answer is -2
Multiply a and 7
Multiply a and 1
The a just gets copied along.
The answer is a
a
7*a evaluates to 7a
Multiply b and 4
Multiply b and 1
The b just gets copied along.
The answer is b
b
4*b evaluates to 4b
7*a+4*b evaluates to 7a+4b
Multiply -2 by 7a+4b
we multiply -2 by each term in 7a+4b term by term.
This is the distributive property of multiplication.
Multiply -2 and 7a
Multiply 1 and a
The a just gets copied along.
a
-2 × 7a = -14a
Multiply -2 and 4b
Multiply 1 and b
The b just gets copied along.
b
-2 × 4b = -8b
-2*(7*a+4*b) evaluates to -14a-8b
Multiply c and 6
Multiply c and 1
The c just gets copied along.
The answer is c
c
6*c evaluates to 6c
The answer is -14a-8b-6c
-2*(7*a+4*b)-6*c evaluates to -14a-8b-6c
The final answer is
-14a-8b-6c
Step-by-step explanation:
Please mark brainliest and have a great day!
The quotient of the difference of 5 times x cubed and 4 and x
Answer:
a system of equations has 1 solution. if 4x-y=5 is a new of the equations which could be the other equation
The question asks for an algebraic expression. Based on the phrases used, the expression can be written as (5x³ - 4)/x.
Explanation:The subject of your question involves algebra, which is a branch of mathematics. When the question asks for the 'quotient of the difference of 5 times x cubed and 4 and x', it is asking for an algebraic expression. This expression can be written as (5x³ - 4)/x. This expression cannot be simplified further as the terms in the numerator are not like terms.
Remember that the 'difference' refers to subtraction, 'quotient' refers to division, and 'times' refers to multiplication in algebra. Also, 'x cubed' means x is being raised to the power of 3.
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A number is 5 more than 3 times another number. The sum of the two numbers is 33. As an equation, this is written x + 3x + 5 = 33, where x represents the smaller number. Plug in the numbers from the set {3, 5, 7, 9} to find the value of x.
The value of x that holds true for the equation is blank . So, the smaller number is blank and the larger number is blank .
Answer:
x=7
Step-by-step explanation:
Solve for x:
3 x + x + 5 = 33
x + 3 x = 4 x:
4 x + 5 = 33
Subtract 5 from both sides:
4 x + (5 - 5) = 33 - 5
5 - 5 = 0:
4 x = 33 - 5
33 - 5 = 28:
4 x = 28
Divide both sides of 4 x = 28 by 4:
(4 x)/4 = 28/4
4/4 = 1:
x = 28/4
The gcd of 28 and 4 is 4, so 28/4 = (4×7)/(4×1) = 4/4×7 = 7:
Answer: x = 7
The larger number is 26 and the smaller number is 7.
What are the numbers?To determine the solution, take the following steps:
The given equation is x + 3x + 5 = 33
Combine similar terms: x + 3x =33 - 5
Add similar terms: 4x = 28
Divide both sides by 4 : 7
The larger number = 33 - 7 = 26
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Miles paid $5824, including 4% sales tax, for an out-of-state purchase of a car. In order to calculate the amount of sales tax he owes in his state, he must first determine the price of the car without sales tax. How much did the car cost before sales tax?
Answer: $5,591
Step-by-step explanation:
4% = .04
5824 x .04 = 232.96
5824 - 232.96 = 5591
Before sales tax, the car cost $5591
Which expression best estima
18-3
0 -18-3
-18+(-3)
18+(-3)
Answer:
18 + -3
Step-by-step explanation:
It is not really an estimate because it is obviously seen that +- = -.
if f(x)=4x^2+1 and g(x)=x^2-5 find(f+g)(x)
Answer:
answer
Step-by-step explanation:
f(x) = 4x² + 1
g(x) = x² - 5
Then
(f + g)(x) = 4x² + 1 + x² - 5
= 5x² - 4
Answer: 5x² - 4
What is the smallest angle of rotational symmetry for a square
Answer:
90°
Step-by-step explanation:
a full rotation is 360° but since there are 4 angles, then divide the 360 by 4 and you'll get 90°
What is the value of K?
Answer:
2
Step-by-step explanation:
m² = 4² + 8²
m² = 16 + 64
m² = 80
l² = k² + 4²
l² = k² + 16
m² + l² = (k + 8)² m² = 80, (b)
80 + k² + 16 = k² + 16k + 64
k² - k² - 16k = 64 - 80 -16
-16k = -32
k = -32/-16
k = 2
What is the solution to the equation 7/8=m/32.
14
24
28
30
Answer: 28
Step-by-step explanation:
7/8 = m/32
cross multiply the expression
8m = 224
m = 224/8 = 28
Hope it helped!
[tex]\huge{\boxed{m=28}}[/tex]
[tex]\frac{7}{8}=\frac{m}{32}[/tex]
Since [tex]8[/tex] is multiplied by [tex]4[/tex] to get 32, you also multiply [tex]7[/tex] by [tex]4[/tex] to get [tex]m[/tex].
[tex]7*4=28[/tex]
Factor completely 2x5 + 10x4 - 22x3.
Answer: 2x³(x² + 5x - 11)
Step-by-step explanation:
2x⁵ + 10x⁴ - 22x³
Factor out the GCF (2x³)
2x³(x² + 5x - 11)
Since there are no values whose product is -11 and sum is +5, this cannot be factored further.
What is 2y^4 x 5y^3 simplified?
Answer:
10y^7
Step-by-step explanation:
Do 2(5) and do y^4 times y^3!
2(5)=10
if you have to write out what y^4 means and y^3...
How many factors of y do you have 7... so y^4*y^3=y^7
The answer is 10y^7
I to the exponent of 65
Answer:
Step-by-step explanation:
A= 1 * 1 = 2
A2 = 1 * (1 * 1)
A2 = 1 * 1
A2 = 1
a3 = 1 * 1 * (1 * 1)
a3 = 1 *1 * 1
a3 = 1 * (1*1)
a3 = 1* 1
a3 = 1
You keep on going in this manner until you hit 1^65 = 1
The only thing you have to accept is that (1 * 1) = 1
Evaluate e1/2 to one decimal place.
1.6
13.6
3.7
7.4
I believe its 1.6
For this case we have the following expression:
[tex]e ^ {\frac {1} {2}}[/tex]
We must evaluate the expression, then:
[tex]e ^ {0.5} =[/tex]
If we enter the expression in a calculator we have that the decimal form is given by:
[tex]1.64872127[/tex]
If we round the expression we have to:
[tex]e ^ {\frac {1} {2}} = 1.7[/tex]
The option that is closest is option A.
Answer:
Option A
According to the synthetic division below, which of the following statements are true
Answer:
B and D
Step-by-step explanation:
The polynomial x² + 6x - 8 ( from values in first row )
is being evaluated at x = - 5 thus the factor is (x + 5)
If (x + 5) is a factor the remainder = 0
Hence (x + 5) is not a factor since remainder = 12 ≠ 0
When the polynomial is evaluated at x = 5 it's value is 12
The remainder theorem states that f(h) = remainder, hence
f(- 5) = 12 ← remainder
What is the name of a pattern of two-dimensional shapes that can be folded to make a model of a solid figure?
A)prism
B)net
C)surface area
D)face
Answer:
The correct option is B.
Step-by-step explanation:
The correct option is net.
A geometric net is a 2-dimensional shape that can be folded to form a 3-dimensional shape or a solid. Or you can say that a net is a pattern made when the surface of a three-dimensional figure is laid out flat showing each face of the figure. A solid may have different nets.
The basic steps to determine whether a net forms a solid: are:
1. Make sure that the solid and the net have the same number of faces and that the shapes of the faces of the solid match the shapes of the corresponding faces in the net.
2. Visualize how the net is to be folded to form the solid and make sure that all the sides are properly fit together.
Nets are helpful when we need to find the surface area of the solids....
Convert 15/9 to a decimal
Answer:
15/9 =1.7
if u divide 3 by both of them you will have 5/3 .5/ 3 with give you 1.666666667 aproximately to 1.7 that is in one decimal plave
Step-by-step explanation:
The graph for the equation y=x-4 is shown below.
Which equation, when graphed with the given equation, will form a system that has an infinite number of solutions?
A. y - x = -4
B. y - x = -2
C. y - 4 = x
D. y + 4x = 1
Answer:
A. y - x = -4
Step-by-step explanation:
y=x-4
To get infinite equations, the equation must be equal to y=x-4
We will solve each of these for y to see if they are identical
A. y - x = -4
Add x to each side
y-x+x = x-4
y = x-4
This is the same
It will give infinite solutions
B. y - x = -2
y-x+x = x-2
y =x-2
This is not the same.
It is parallel and will give no solutions
C. y - 4 = x
y-4+4 = x+4
y = x+4
This is parallel and will give no solutions
D. y + 4x = 1
y +4x-4x = -4x+1
This will intersect at a point
Answer: The correct answer is c.
Step-by-step explanation:
I just answered the question for school
Complete the square for 2x2 - 4x = 14.
Answer:
2x^2-4x=14
x^2-2x=7
x^2-2x+1=8
(x-1)^2=8
Which expression is equivalent to?...
Answer:
B x^9 ∛ y
Step-by-step explanation:
(x^27 y) ^ (1/3)
x^27^(1/3) y^(1/3)
We can distribute the exponent a^b ^c = a^(b*c)
x^(27*1/3) y^(1/3)
x^9 y^(1/3)
Consider the expression below.
9 + 4(x + 2) – 3.1
Select the term that best describes "3" in the given expression.
O A.
coefficient
variable
exponent
constant
Which is the solution the equation 3.5(2h + 4.5)
[tex]\text{Hey there!}[/tex]
[tex]\text{In order for you to solve this equation, you need to DISTRIBUTE!}[/tex]
[tex]\text{The algebraic formula for distribution is: a(b+c) = a(b)+a(c) = ab + ac}[/tex]
[tex]\text{Now, that we have that portion solved, we can answer your question!}[/tex]
[tex]\text{3.5(2h) + 3.5(4.5)}[/tex]
[tex]\text{3.5(2h) = 7h}[/tex]
[tex]\text{3.5(4.5) = 15.75}[/tex]
[tex]\text{= 7h + 15.75}[/tex]
[tex]\boxed{\boxed{\bf{Answer:7h+15.75}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Simplify 24÷(-2)(3)+7
a. -29
b. 3
c. 11
Answer:
a. -29
Step-by-step explanation:
The expression is:
24÷(-2)(3)+7
We can see that there is division, multiplication and addition involved. We will use the mathematical DMAS rule to solve the problem. So, division will be done first,
Division will give us:
24÷(-2)*(3)+7
= -12 * 3 + 7
After division, multiplication will be done:
Multiplication will give us:
= -36 +7
which equals to -29
So, option a is the correct answer ..
Find the difference.
(-5ab+a+3) - (ab+2)
Enter the correct answer.
Need help ASAP !!!!
Answer:
-6ab+a+1
Step-by-step explanation:
add or subtract like terms.
The difference between (-5ab+a+3) and (ab+2) is calculated by combining like terms and performing the subtraction, resulting in -6ab + a + 1.
To find the difference between the two expressions (-5ab+a+3) and (ab+2), we need to subtract the second expression from the first. Applying the distributive property of subtraction over addition (i.e., a - (b + c) = a - b - c), we get:
-5ab - ab: Combine like terms by subtracting ab from -5ab which gives us -6ab.+ a: There's no like term to combine with a in the second expression, so it remains as is.+ 3 - 2: Subtract 2 from 3 which gives us +1.Putting it all together, the difference of the two expressions is -6ab + a + 1.
What is the order of magnitude for
the total weight of 5 cars that weigh
3,000 pounds each?
An expression is defined as a set of numbers, variables, and mathematical operations. The order of magnitude for the total weight of 5 cars that weigh 3,000 pounds each is 4.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The total weight of the five cars each weighing 3,000 pounds is,
Total weight = Number of cars × Weight of each car
= 5 × 3,000 pounds
= 15,000 pounds.
= 1.5 × 10⁴ pounds
Hence, the order of magnitude for the total weight of 5 cars that weigh 3,000 pounds each is 4.
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Adam has some candy to give to his three children. He first took seven pieces for himself and then evenly divided the rest among his children. If Adam started with 13 pieces, how many did each child receive
-2(5x+8)=14+6x complete the statements below with the process used to achieve steps 1-4
Expand -2(5x+8), simplify, isolate x by moving terms, and solve to get x = -15/8.
To solve the equation -2(5x + 8) = 14 + 6x step by step, here's what was done:
Step 1: Expand the left side of the equation by distributing -2 across the terms inside the parentheses:
-2(5x + 8) = -2 * 5x - 2 * 8 = -10x - 16
So, the equation becomes: -10x - 16 = 14 + 6x
Step 2: Group like terms together. Subtract 6x from both sides to get all the x terms on one side of the equation:
-10x - 6x = 14 + 16
This simplifies to: -16x = 30
Step 3: Now, isolate the variable by dividing both sides by -16:
(-16x)/(-16) = 30/(-16)
This simplifies to: x = -30/16 or x = -15/8
So, the solution for x is x = -15/8.
The complete question is here:
-2(5x+8)=14+6x The equation was solved using the following steps Step 1: -10z-16=14+6z Step 2: -16x-16=14 Step 3: -16x=30 Step 4: z= 21/-16 Step 5: z=- 15/8 Complete the statements below with the process used to achieve steps 1-4 Stop 12 to 5x and 8. Step 26x Step 3 : 16. Step 4: 16.