Answer:
12 is the answers for the question
Step-by-step explanation:
please mark me as brainlest
[tex] - | - x| = - 12 \\ - x = - 12 \\ x = 12 \: \: \: or \: \: \: x = - 12 \\ [/tex]
Solution :{-12,12} so it's D
Please give brainliest
What is the equation of the blue line?
Answer:
y = - 3x - 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 2) and (x₂, y₂ ) = (0, - 1)
m = [tex]\frac{-1-2}{0-(-1)}[/tex] = [tex]\frac{-3}{0+1}[/tex] = [tex]\frac{-3}{1}[/tex] = - 3
the line crosses the y- axis at (0, - 1 ) ⇒ c = - 1
y = - 3x - 1 ← equation of line
Parallelogram ABCD has vertices: A(-3, 1), B(3, 3), C(4, 0), and D(-2, -2). In two or more complete sentences, explain how you can use the coordinates of the vertices to prove that parallelogram ABCD is a rectangle.
please help
Step-by-step explanation:
via the distance formula (based on Pythagoras) I can prove that ABC is a right-angled triangle, and that ADC is fully congruent to ABC.
so, together these 2 triangles (joined at their Hypotenuses, the diagonal AC) build a rectangle.
Giving my all points away! What is the Value of log5512, when log 2 = 0.3010 and log 3 = 0.4771?
[tex]\\ \rm\Rrightarrow log_5512[/tex]
[tex]\\ \rm\Rrightarrow log_52^9[/tex]
[tex]\\ \rm\Rrightarrow 9log_52[/tex]
Use change of base[tex]\\ \rm\Rrightarrow 9\dfrac{log2}{log5}[/tex]
[tex]\\ \rm\Rrightarrow 3.876[/tex]
If your question is something different let me know by which I can change my answer
Answer:
3.876 (3 d.p.)
Step-by-step explanation:
Given:
[tex]\log_{10}2=0.3010[/tex][tex]\log_{10}3=0.4771[/tex]Please note: The question gives two values of log base 10 which should be used to help find the value of [tex]\log_5512[/tex]
Log Law: Change of Base
[tex]\log_ba=\dfrac{\log_xa}{\log_xb}[/tex]
Change the given expression to log base 10:
[tex]\implies \log_5512=\dfrac{\log_{10}512}{\log_{10}5}[/tex]
Replace 512 with 2⁹, and 5 with 10/2:
[tex]\implies \dfrac{\log_{10}{2^9}}{\log_{10}\frac{10}{2}}[/tex]
[tex]\textsf{Apply the Power Log law}: \quad \log_ax^n=n\log_ax[/tex]
[tex]\implies \dfrac{9\log_{10}{2}}{\log_{10}\frac{10}{2}}[/tex]
[tex]\textsf{Apply the Log Quotient law}: \quad \log_a\frac{x}{y}=\log_ax - \log_ay[/tex]
[tex]\implies \dfrac{9\log_{10}{2}}{\log_{10}10-\log_{10}2}[/tex]
[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]
[tex]\implies \dfrac{9\log_{10}{2}}{1-\log_{10}2}[/tex]
Given:
[tex]\log_{10}2=0.3010[/tex]Substitute this into the expression and simplify:
[tex]\implies \dfrac{9(0.3010)}{1-0.3010}[/tex]
[tex]\implies \dfrac{2.709}{0.699}[/tex]
[tex]\implies 3.876\:(\sf 3\: d.p.)[/tex]
On a coordinate plane, a right triangle has points A (negative 5, negative 6), B (negative 5, negative 2), C (negative 2, negative 2).
Examine the right triangle ABC. Which rise and run would create a similar right triangle on the same line?
a rise of 6 and a run of 8
a rise of 8 and a run of 6
a rise of 6 and a run of 5
a rise of 5 and a run of 6
A rise of 8 and a run of 6. Then the correct option is B.
What is a coordinate geometry?Coordinate geometry is the study of geometry using the points in space.
On a coordinate plane, a right triangle has points A (-5, -6), B (-5, -2), and C (-2, -2).
The distance between AB will be
AB² = (-5 + 5)² + (-2 + 4)²
AB² = 4²
AB = 4
The distance between BC will be
BC² = (-2 + 5)² + (-2 + 2)²
BC² = 3²
BC = 3
Then the rise and run will be
rise / run = 4 / 3
Then this can be written as
rise / run = 8 / 6
Then the correct option is B.
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A circle has a diameter with endpoints (-7, 1) and (-3, 7).
What is the equation of the circle?
r2 = ( x - 3) 2 + ( y + 4) 2
r2 = ( x + 3) 2 + ( y - 4) 2
r2 = ( x + 5) 2 + ( y - 4) 2
r2 = ( x - 5) 2 + ( y + 4) 2
The ratio of boys to girls in a classroom is 2 : 3. If there are
20 children in total, how many boys are there?
Answer:
8
Step-by-step explanation:
let the ratio constant be 'x'
=> 2x:3x
sum = 2x + 3x = 5x
Total number of boys
=>(2x/5x)20 = 8
The ratio of boys and girls in a classroom is 2 : 3 respectively. If the total number of children is 20. How many boys are there in the class ?
Explanation -:In this question we are provided with the ratio of boys isto girls that is 2 : 3 it is also given that total number of children are 20. We are asked to calculate number of boys.
[tex] \green{ \small \pmb{\tt{ First \: we \: will \: form \: an \: equation }}}[/tex]
Let us assume the number of girls as 3x and number of boys as 2x.
Total number of children = 20
3x + 2x = 20
[tex] \orange{\small \pmb{\tt{ Now \: we \: will \: solve \: this \: equation }}}[/tex]
[tex] \small\frak{ 3x + 2x = 20}[/tex]
[tex] \small\frak{ 5x = 20}[/tex]
[tex] \small\frak{ x = \dfrac{20}{5} = 4}[/tex]
[tex] \small \underline{ \boxed{\pmb{x = 4} }} \large \: \star[/tex]
Boys = 2 × 4 = 8
Girls = 3 × 4 = 12
Hence 8 boys and 12 girls are there in the classroom.[tex] \tiny \tt{spbankingandsscseries}[/tex]
solve: √2x-8= √x+4 the equation.
Answer:
(a) x = 12
Step-by-step explanation:
The radicals in this equation can be eliminated simply by squaring both sides. Then the resulting linear equation is solved in two steps.
__
square[tex]\left(\sqrt{2x-8}\right)^2=\left(\sqrt{x+4}\right)^2\\\\2x-8=x+4\qquad\text{simplify}\\\\x-8=4\qquad\text{subtract $x$}\\\\\boxed{x=12}\qquad\text{add 8}[/tex]
_____
Additional comment
You know the contents of each radical must not be negative. That means 2x-8 ≥ 0, or x≥4. We know x=4 doesn't work in the equation (0≠√8), so we only need to check the answers x=12 and x=7. Of those, only x=12 satisfies the equation.
Helppppppppp I don’t have much time shoe your work
Answer:
x = 4
Step-by-step explanation:
Use order of operations (PEMDAS) to simplify and solve algebraic equations:
P - Parentheses: Simplify all parentheses in the equation first.
E - Exponents: Evaluate all exponential expressions in the equation next.
M/D - Multiplication/Division: After P and E, Multiplication in the equation comes next. These are interchangeable, so if these are the only operations left, calculate in the direction left to right.
A/S - Addition/Subtraction: After everything else has been done, move on to Addition/Subtraction. These two are also interchangeable, so you must also calculate in the direction left to right.
First, implement the order of operations to simplify the equation:
2²(x + 3) + 9 - 5 = 32 --- Evaluate the exponent.
4(x + 3) + 9 - 5 = 32 --- Use the Distributive Property to multiply.
4x + 12 + 9 - 5 = 32 --- Add/Subtract (Combine like terms).
4x + 16 = 32
Next, isolate the variable x to solve for its value:
4x + 16 = 32 --- Subtract 16 from both sides of the equation.
4x = 16 --- Divide both sides of the equation by 4 to get the value of x.
x = 4
To confirm that x = 4, you can substitute x for 4 in the original equation and see if both sides of the equation are equal:
2²[(4) + 3] + 9 - 5 = 32 --- Simplify the parentheses.
2²(7) + 9 - 5 = 32 --- Evaluate the exponent.
4(7) + 9 - 5 = 32 --- Multiply.
28 + 9 - 5 = 32 --- Simplify the equation using Addition/Subtraction.
32 = 32
After using substitution, we can confirm that x = 4.
To solve for the x-variable in a linear equation, we will need to isolate it on one side of the equation. If the x-variable is inside a parenthesis, we will need to open the parenthesis first, then isolate the variable. To solve/simplify the equation, we will need to use PEMDAS. It is a common method used to simplify equations and inequalities through priorities.
Concept: PEMDASThe word "PEMDAS" is a shortened word of "Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction". We follow this order (left-right) to simplify algebraic terms. Since parenthesis is the first priority, we would simplify the expression inside the parentheses. There are two exceptions to this priority in PEMDAS. (1) One of the terms in the expression is a variable, so the expression cannot be simplified, or (2) if there was no parenthesis in the first place. The next priority is "Exponents". This priority is used if there are any exponents used in the equation. The only exception to this priority is when there are no exponents used in the equation. The next priority is "Multiplication". This means that you have to simplify any products "multiplying terms" first. The only exception to this is when there are no terms being multiplied. The next priority is "Division". This priority tells that we need to simplify any division occurring the equation next. There is only one exception to this priority. Only possible if there is no division occurring in the equation. Then, we have "addition" as our 5th priority. This priority states that simplifying any expression that is being added next. The only exception to this priority is when there are no terms being added. The last and final priority is subtraction. This priority states that simplify any expression that is being subtracted. There is no exception to this priority.
Solving for the x variable:Simplifying the equation using PEMDAS:
We have the following equation: 2²(x + 3) + 9 - 5 = 32
Let us simplify using our first priority. Unfortunately, there is a variable inside the parenthesis. Therefore, we can't simplify the expression inside the parenthesis. Let us now simplify using out second priority. We can see a term outside the parenthesis "2²". Since that term has an exponent, let us simplify that term! Eventually, the term will simplify to 4.
⇒ 4(x + 3) + 9 - 5 = 32Before we move onto the next priority, let us open the parenthesis as we need to isolate the x-variable. This basically means that we need to simplify the distributive property. To simplify the distributive property, we need to multiply the term outside the parenthesis to all the terms inside the parenthesis. So, we have the following simplified equation:
⇒ 4(x) + 4(3) + 9 - 5 = 32⇒ 4x + 4(3) + 9 - 5 = 32Our next priority is multiplication. So, let us simplify any products occurring in the equation. We can see 4 being multiplied to 3. Therefore, let us simplify that term! Simplifying that term basically gives us 12. So:
⇒ 4x + 12 + 9 - 5 = 32Now, our next priority is division. However, we do not see any division occurring in the equation. Therefore, this follows the exception of the division priority in PEMDAS. So, let us move on to the next priority.
The next priority is addition. We can see 12 being added to 9. Therefore, let us simplify the expression. Simplifying that expression gives us 21. So:
⇒ 4x + 21 - 5 = 32The last and final priority is subtraction. We can see 5 being subtracted from 21. Therefore, let us simplify the expression, which gives us 16. So:
⇒ 4x + 16 = 32Solving for the x-variable by isolating it:
Now, let us isolate the x-variable to determine its value. This can be done by subtracting 16 on both sides of the equation. Then, we can divide 4 both sides to cancel out the coefficient of x.
⇒ 4x + 16 - 16 = 32 - 16⇒ 4x = 16⇒ 4x/4 = 16/4⇒ x = 4Therefore, the value of x in the equation is 4.
On a coordinate plane, the x-axis is labeled minutes and the y-axis is labeled Blocks. Line A goes through points (10, 4), (15, 12), and (20, 20). Line B goes through points (5, 8), (10, 16), (15, 24). Line C goes through points (5, 24), (15, 16), (20, 12).
The table shows Jose’s rate of bicycle riding.
A 2-column table with 3 rows. Column 1 is labeled Minutes with entries 5, 10, 15. Column 2 is labeled Blocks with entries 8, 16, 24.
Which line on the graph shows the proportional relationship in the table?
Line
on the graph shows the proportional relationship.
The proportional relationship given in the table is y = 1.6x, and line B shows this relationship.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
The constant of proportionality, considering the points on the table, is given as follows:
[tex]k = \frac{24}{15} = \frac{16}{10} = \frac{8}{5} = 1.6[/tex].
Hence the equation is:
y = 1.6x.
Line B gives the same points as the table, hence it shows the proportional relationship.
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Writing an Equation from a Table
A 2-column table with 6 rows. Column 1 is labeled x with entries 8, 12, 16, 20, 25, 28. Column 2 is labeled y with entries 2, 3, 4, 5, 6, 7.
Which equation produces the values in the table?
y = 4x
y = 4 + x
y = One-fourthx
y = 4 – x
The equation of the line will be y = 4x. Then the correct option is A.
What is the equation of line?The equation of line is given as
y = mx + c
Where m is the slope and c is the y-intercept.
Writing an Equation from a Table
A 2-column table with 6 rows. Column 1 is labeled x with entries 8, 12, 16, 20, 24, 28. Column 2 is labeled y with entries 2, 3, 4, 5, 6, 7.
Then at (2, 8) and (3, 12), we have
y – 8 = [(12 – 8) / (3 – 2)] (x – 2)
y – 8 = 4x – 8
y = 4x
Then the correct option is A.
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Find the measure of Angles A and B and the length of BC?
Answer:
dummy its 23 bc angel A
Step-by-step explanation:
WRITE iT dOwN nOW dUmMy
3. a 12 inch apple pie is sliced into 9 slices. what is the area of one slice of pie?
Answer:
4 pi ( = 12.566 in^2 )
Step-by-step explanation:
TOTAL area = pi r^2 = pi (6)^2 = 36 pi in^2
divide into 9 pieces 36 pi / 9 = 4 pi in ^2
A 1/25 scale model sports car is 5.5 in long. What was the length of the actual car to the nearest in?
Answer: 137.5 in
Step-by-step explanation: All we have to do is multiply 25 to 5.5 to get the original result. Since the scaling is 1/25, it means it is 25 times smaller. Thus, just multiply 25 to 5.5 and you get 137.5 in, the original result.
What is the measure of \angle x∠xangle, x?
Angles are not necessarily drawn to scale.
Answer:
Step-by-step explanation:
Comment
x and 133 sit on the the same straight line with MO in common. Therefore they are supplementary which means that the add to 180o.
Equation
x + 133 = 180
Solution
Subtract 133 from both sides
x + 133 = 180
x + 133 - 133 = 180 - 133
x = 47 degrees.
Answer
x = 47
I dive to 17 metres for 23 minutes. after a 30 minute surface interval, i plan to dive to 16 metres. what is the maximum allowable time for the second dive
Answer:
i don't know
Step-by-step explanation:
i don' know
48 girls, 41 boys, and 5 teachers sat in the gym. Write the ratio of girls to boys in three ways.
I took the text last month
Joshua is 1.45 meters tall. at 2 p.m., he measures the length of a tree's shadow to be 31.65 meters. he stands 26.2 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. find the height of the tree to the nearest hundredth of a meter .
Answer:
hes a titan
Step-by-step explanation:
Solve for x. Round to the nearest tenth, if necessary
The value of x in the triangle to the nearest tenth is calculated as; 1.1
How to use trigonometric ratios?
We have different trigonometric ratios such as;
sin θ = opp/hyp
cos θ = adj/hyp
tan θ = opp/adja
Thus, from the given triangle we can use the formula for cos θ to get the value of x. Thus;
cos 41° = 0.8/x
x = 0.8/cos 41
x = 1.06
To the nearest tenth, we have x = 1.1
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Which equation results from adding the equations in this system? Negative 2 x + y = 8. 5 x minus y = negative 5. 7 x = 13 7 x = 3 3 x = 3 3 x = 13'
The correct option is second one i.e 7x = 3
Therefore the results from adding the equation in this system are
7x = 3
Equations as,
What is the equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign.
2x+y=8 .......................1
5x-y=-5 .......................2
Result when adding equations 1 and 2 =?
On adding equations 1 and 2 the y term will get canceled and the like terms will combine is add (2x and 5x ) and ( 8 and - 5) as shown below
2x + y = 8
5x - y = - 5
-------------------------------------------
7x + 0 = 3
---------------------------------------------
Therefore the results from adding the equation in this system are 7x=3.
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Answer:
7x=3
Step-by-step explanation:
Select the correct answer.
Using synthetic division, find (2x + 4x³ + 2x² + 8x + 8) + (x + 2).
O A. 2x3 + 2x + 4
OB.
2x4 + 2x² + 4x
OC. 2x3 + 2x + 4 +
I
OD.
2x3 + 2x² + 4
1
+ 2
The synthetic division of the polynomial, (2x⁴ + 4x³ + 2x² + 8x + 8) / (x + 2) = 2x³ + 2x + 4.
Division of the polynomialThe division of the polynomial is determined as follows;
(2x⁴ + 4x³ + 2x² + 8x + 8) / (x + 2)
2x³ + 2x + 4
-------------------------
x + 2 √(2x⁴ + 4x³ + 2x² + 8x + 8)
- (2x⁴ + 4x³)
-------------------------------------
2x² + 8x + 8
- (2x² + 4x)
------------------------
4x + 8
- (4x + 8)
-------------------
0
Thus, the synthetic division of the polynomial, (2x⁴ + 4x³ + 2x² + 8x + 8) / (x + 2) = 2x³ + 2x + 4.
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Solve the following simultaneous equations. x + y = 3
x -y = 1
Answer:
x = 2, y = 1 or (2, 1)
Step-by-step explanation:
Solving by elimination method :
x + y + (x - y) = 3 + 12x = 4x = 22 - y = 1y = 1The solution is : x = 2, y = 1 or (2, 1)
Give the name (monomial,
binomial, trinomial etc.) and
degree of the polynomial.
15x²
Name? [?]
Degree? [ ]
Answer:
monomial and degree is 2
find the simplified trig ratio (fraction) of tan p
Answer:
8/15
Step-by-step explanation:
For right triangles tan p = opposite leg / adjacent leg
tan p = 24 /45 = 8/15
Use the zero product property to find the solutions to the equation (x 2) (x 3) = 12.
The solution of the given equation is -6 and 1.
What is Quadratic Equation?A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
Here, given equation:
(x+2)(x+3) = 12
x(x+3)+2(x+3) = 12
x² + 3x + 2x + 6 = 12
x² + 5x + 6 - 12 = 0
x² + 5x - 6 = 0
x² + 6x - x - 6 = 0
x(x+6) -1(x+6) = 0
(x+6)(x-1) = 0
Now, x + 6 = 0 or x - 1 = 0
x = -6 or x = 1
Thus, the solution of the given equation is -6 and 1.
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PLEASE HELP ASAP
(Picture shown)
Answer:
-2x+3
Step-by-step explanation:
Gradient is change in y over change in x
[tex] \frac{2}{1} [/tex]
=2
and then
+3 because that's where it cuts the Y axis
The side of an equilateral triangle is given as 8cm, correct to the nearest centimeter. What is the possible least lenght of its perimeter?
Answer:
An equilateral triangle is a triangle with all 3 sides the same in size.
If one side is 8cm, then 8x3=24 cm
The perimeter is possibly 24 cm.
Please help i dont get this at all so please i will highly appreciate it .Thank youuu!!!
Answer:
D
Step-by-step explanation:
Trust me
Find the area of a circle with radius,
r
= 7.15m.
Give your answer rounded to 2 DP.
[tex] \boxed{\Large {\mathcal {{{\color{orange}{Area \: of \: circle \: = \: πr²}}}}}}[/tex]
r = 7.15m[tex]\large \rm \pink{ \: Area \: of \: circle }\:\large\blue\implies \tt \large πr²\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large \rm \pink{ \: Area \: of \: circle }\:\large\blue\implies \tt \large \frac{22}{7} \: \times\:{7.15}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\\large \rm \pink{ \: Area \: of \: circle }\:\large\blue\implies \tt \large \frac{22}{7} \: \times\:51.1225 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large \rm \pink{ \: Area \: of \: circle }\:\large\blue\implies \tt \large \frac{22}{ \cancel7} \: \times\: \cancel{51.1225} \: \: ^{ \red{7.303} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large \rm \pink{ \:Area \: of \: circle }\:\large\blue\implies \tt \large {22} \: \times\:7.303 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large \rm \pink{ \: Area \: of \: circle }\:\large\blue\implies \tt \large \: 160.666 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Hence , the area of circle is 160.66 m²
Given :-
Radius of circle = 7.15mTo Find :-
Area of circleSolution :-
Area of Circle = πr²
putting the value of π and rArea = 3.14×(7.15)² m²
= 160.52465 , which rounded off to 2DP would be 160.52 m²
Help asap!!! For a brainlest
33+6f<33
Shoe your work and steps
Answer:
f < 0
Step-by-step explanation:
33 + 6f < 33 ( subtract 33 from both sides )
6f < 0 ( divide both sides by 6 )
f < [tex]\frac{0}{6}[/tex] , that is
f < 0
Which of the following is a radical equation?
Ox+√5=12
O x² = 16
O 3+x√7=13
O 7√x = 14
Answer:
2
Step-by-step explanation:
because it's for the point s
The radical equation from the following equation is 3+x√7=13, the correct option is C.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given that;
Four equations
x+√5=12, x² = 16, 3+x√7=13, 7√x = 14
Now,
Out of the four options you gave, only one is a radical equation:
Ox+√5=12 O x² = 16 O 3+x√7=13 O 7√x = 14
Only 3+x√7=13 because x is under a cube root sign. The other options are not radical equations because they do not have variables under radicals.
Therefore, the radical equation will be 3+x√7=13.
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