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Find the value of x in the isosceles triangle shown below.
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13
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10
Solve using the Addition Method.
5x/6 + y/3 = 4/3
2x/3 - y/2 = 11/6
Answer:
x = 2
y = - 1
Step-by-step explanation:
5x/6 + y/3 = 4/3
2x/3 - y/2 = 11/6
Multiply the above equation by 6 to express in linear form
6 × (5x/6 + y/3 = 4/3)
5x + 2y = 8.... (1)
6 × (2x/3 - y/2 = 11/6)
4x - 3y = 11.... (2)
Thus, the equation are:
5x + 2y = 8.... (1)
4x - 3y = 11.... (2)
Next, multiply equation (1) by 3 and equation (2) by 2. This is illustrated below:
3 × (5x + 2y = 8)
15x + 6y = 24 ..... (3)
2 × (4x - 3y = 11)
8x - 6y = 22 ... (4)
Next, add equation 3 and 4 together. This is illustrated below:
.. 15x + 6y = 24... (3)
+ 8x - 6y = 22 .... (4)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
23x = 46
Divide both side by 23
x = 46/23
x = 2
Next, substitute the value of x into any of the equation. Here, we shall substitute the value of x into equation (3). This is illustrated below:
15x + 6y = 24... (3)
x = 2
15(2) + 6y = 24
30 + 6y = 24
Collect like terms
6y = 24 - 30
6y = - 6
Divide both side by 6
y = - 6/6
y = - 1
Therefore, the value of x and y is
x = 2
y = - 1
Which is 65% of 35??
Answer:
22.75 .
Step-by-step explanation:
65 x 35 / 100 = 22.75.
The percentage expression 65% of 35 is 22.75
How to evaluate the percentage expressionFrom the question, we have the following parameters that can be used in our computation:
65% of 35
Express as products
So, we have the following representation
65% of 35 = 65% * 35
Express 65% as 0.65
So, we have the following representation
65% of 35 = 0.65 * 35
Evaluate the products
So, we have the following representation
65% of 35 = 22.75
Hence, the solution is 22.75
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three signals that beep.
signal a beeps every 25 seconds
signal b beeps every 30 seconds
signal c beeps every 100 seconds.
The three signals start beeping at the same time.
How many times in one hour will the three signals beep?
Answer:
The number of times signal a beeps in 1 hour = 144 times
The number of times signal b beeps in 1 hour = 120 times
The number of times signal c beeps in 1 hour = 36 times
The number of times three signals bee in one hour = 12 times
Step-by-step explanation:
The given parameters are;
The period for each signals beep are;
Signal a beeps every 25 seconds
Signal b beeps every 30 seconds
Signal c beeps every 100 seconds
Therefore, in one hour, signal a will beep 1× 60 × 60/25 = 3600/25 = 144 times
In one hour, signal b will beep 1×60×60/30 = 3600/30 = 120 times
In one hour, signal c will beep 1×60×60/100 = 3600/100 = 36 times
Therefore, we have;
The number of times signal a beeps in 1 hour = 144 times
The number of times signal b beeps in 1 hour = 120 times
The number of times signal c beeps in 1 hour = 36 times
From Excel, we can see that the three signals beep the same time at 300, 600, 900, 1200, 1500, 1800, 2100, 2400, 2700, 3000, 3300, and 3600
The number of times three signals bee in one hour = 12 times
signal a beeps every 25 seconds
signal b beeps every 30 seconds
signal c beeps every 100 seconds.
Answer to the above questions is 300,600,900 if the signal beep at the same time 12 times
Explanation to the above questions
One hour contains 3600 secondsSignal a beep 3600/25=144Signal b beep 3600/30=120signal c beep 3600/100=36At the same time all the signal beep than 144+120+36=300we conclude that it will beep 12 times because 300,600,900,1200,1500,1800,2100,2400,2700,3000,3300,3600
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Write an equation of a line whose slope is -2 and whose crosses the y-axis
at 5
Answer:
2x + y = 5 is the required equation.
Step-by-step explanation:
using slope intercept form,
i.e. y = mx + c
or, y =( -2 ) x + 5
or, y + 2x = 5
3/5 + (-1/5)
A. -2/5
B. 4/5
C. 2/5
Answer:
C
Step-by-step explanation:
3/5 + (-1/5) =(3-1)/5=2/5
Square RSTU is inside trapezoid RSVU. What is the measure, in degrees, of angle VSR? R. REN T Only 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, -, -, and / are allowed in your answer. Answers that are mixed numbers must be entered as an improper fraction or decimal. Your answer
Answer:
135°
Step-by-step explanation:
m<VSR = m<RST + m<VST
Each angle at the vertices of a square is equal to 90°. <RST is one of the vertices of square RSTU, therefore,
m<RST = 90°
also, m<VST = 90 - 45 = 45°
m<VSR = m<RST + m<VST
Thus:
m<VSR = [tex] 90 + 45 = 135 [/tex]
Measure of angle VSR is 135°
The angle VSR will be equal to 135°.
What is an angle?
The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
m∠VSR = m∠RST + m∠VST
Each angle at the vertices of a square is equal to 90°. ∠RST is one of the vertices of square RSTU, therefore,
m∠RST = 90°
also, m∠VST = 90 - 45 = 45°
m∠VSR = m∠RST + m∠VST
Thus:
m∠VSR = 135
Therefore the measure of angle VSR is 135°
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In the polynomial below, what number should replace the question mark to produce a difference of squares? X^2 + ?x -49 A. 0 B. 14 C. 49 D.7
Answer:
A
Step-by-step explanation:
The difference of squares formula is a² - b² = (a + b)(a - b). We want this polynomial to be in the form a² - b². We notice that x² and 49 are perfect squares already which means that we don't need the x term. To get rid of it, its coefficient must be 0 because 0 times anything is 0, thus the x term will be removed and we'll be left with x² - 49 which is a difference of squares.
Can someone please help me with this question, I will mark branliest if it’s correct
Measures of two supplementary angles are consecutive odd integers find the angles
Supplementary angles are those angles which add upto 180°. They may or may not be linear pair.
We have,
Two consecutive odd angles.They are supplementary[tex].[/tex]Let,
One of the angles be xThen, other angle will be x + 2°Then,
➝ x + x + 2° = 180°
➝ 2x + 2° = 180°
➝ 2x = 178°
➝ x = 89°
Other angle = x + 2° = 91°
Answer - 89° and 91°
⚘ Hence, solved !!
━━━━━━━━━━━━━━━━━━━━
Answer:
Step-by-step explanation:
Let the numbers are x, x+1
The sum of supplementary angles is 180°
X+x+1=180
2x+1=180
2x=180-1
2x=179
X=179/2
X=89.5
X+1=89.5+1=90.5
The integers are 89.5,90.5
(3x2+2x+ 4)- (x2+ 2x+1)=
4x - 2y +z = 6, -2x + y = -4, 3y - 2z = 4 x= y= z=
The required simplified value of x, y, and z is 2, 2, and 2.
Given that,
The system of the equation is given
4x - 2y +z = 6,
-2x + y = -4,
3y - 2z = 4
And also x= y= z
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Since, x = y = x
taking any one equation
4x - 2y +z = 6
Now,
4x - 2x + x = 6
3x = 6
x = 2
Thus, the required simplified value of x, y, and z is 2, 2, and 2.
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Josh is at the airport and calls for a Uber. He knows the driver will charge $10 to pick
him up and $3 per mile he will drive from the airport to home . if T(x) is the total cost
which equation models this situation
T(x) = 10 + 3x
The answer is not
here
T(x) =13x
T (X) = 10x + 3
Answer:
the answer is 10 +3x
Step-by-step explanation:
"the answer is not here" what do you mean
You want to buy birthday hats, cards, and teddy bears for your best friends birthday party. You buy the products for wholesale prices, from the local party store.
The hats cost $2.50, cards cost $0.90, and the teddy bears cost $3.10. You want to decorate each item for the party and the decorations for the hats cost $1.50, the decorations for the cards cost $0.60, and the decorations for the teddy bears cost $1.70.
In your own words, explain how you would construct a matrix to contain this data. Make sure you include the size and shape of the matrix and your logic for your construction methods.
Answer:
I will create a five by four matrix to indicate the costs of the products. The matrix will have five vertical columns and four horizontal rolls. The vertical columns will show the product categories and the total costs for all the products and decorations. The horizontal rolls will show the product costs, the decoration costs, and the total costs for each product category.
The size and shape of the matrix will be 5 by 4 with squared boxes.
Step-by-step explanation:
Products/Costs Hats Cards Teddy Total Costs
Product costs $2.50 $0.90 $3.10 $6.50
Decoration costs $1.50 $0.60 $1.70 $3.80
Total costs $4.00 $1.50 $4.80 $10.30
Combine Like terms of y+ 3y
Answer:
4y
Step-by-step explanation:
To combine like term, add the coefficient of each term
Coefficient of y = 1
Coefficient of 3y = 3
y + 3y = 4y
A box contains 4 red pencils, 3 blue pencils, and
3 yellow pencils. What is the probability that a
student randomly selects a blue pencil, keeps it,
and then a second student randomly selects a
yellow pencil? *
Step-by-step explanation:
Red=4
Blue=3
Yellow=3
Total=10
Pr(BY) without replacement= 3/10 *3/9
=6/90
=1/15
2. What is the area of the shaded region below? Notice
that the angle is 120 degrees and the radius of the
circle is 8 inches.
8
120
Answer:
Approximately 67 square inches.
Step-by-step explanation:
The area of a circle is given by the formula:
[tex]A=\pi r^2[/tex]
And the sector area of a circle is given by the formula:
[tex]A=\frac{x\textdegree}{360\textdegree}(\pi r^2)[/tex]
Where x is the degree measurement of the sector.
We want to find the sector of the circle with a radius of 8. The degree measurement of the sector is 120. Therefore, plug 8 in for r and 120 for x:
[tex]A=\frac{120\textdegree}{360\textdegree}(\pi(8)^2)[/tex]
The fraction reduces to 1/3. 8^2 is 64:
[tex]A=\frac{1}{3}(64\pi)[/tex]
This is equivalent to:
[tex]A=\frac{64}{3}\pi\\ A\approx67.0206 \text{ in}^2[/tex]
Using the equation F = ma, find the acceleration (a) of a 15 kg mass (m) that is acted on by 3 Newtons of Force (F). Group of answer choices
Answer:
Step-by-step explanation:
Yes
Answer:
a = 0.20 m/s²
Step-by-step explanation:
F = 3 N
m = 15 kg
F = m * a
find mass m:
3 = 15 * a
a = 3 / 15
a = 0.20 m/s²
if the 3rd and 9th term of an ap are 4 and -8 respectively then which term of AP is zero
Answer:
fifth term
Step-by-step explanation:
The n th term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₃ = 4 and a₉ = - 8 , then
a₁ + 2d = 4 → (1)
a₁ + 8d = - 8 → (2)
Subtract (1) from (2)
6d = - 12 ( divide both sides by 6 )
d = - 2
Substitute d = - 2 into (1)
a₁ + 2(- 2) = 4
a₁ - 4 = 4 ( add 4 to both sides )
a₁ = 8
Thus equating the n th term formula to zero and solving for n
8 - 2(n - 1) = 0 ( subtract 8 from both sides )
- 2(n - 1) = - 8 ( divide both sides by - 2
n - 1 = 4 ( add 1 to both sides )
n = 5
The fifth term is equal to zero
The table shows the estimated number of lines of code written by computer programmers per hour when x people are working. A 2-column table with 6 rows. The first column is labeled people working with entries 2, 4, 6, 8, 10, 12. The second column is labeled lines of code written hourly with entries 50, 110, 160, 210, 270, 320. Which model best represents the data?
Answer:
We make the table of these values at different values of x.
x A B C D
2 66.66 49.3 52.5 50
4 94.57 71.44 106.3 104
6 134.14 103.57 160.1 158
8 190.27 150.14 213.9 212
10 269.91 217.64 267.7 266
12 382.85 315.5 321.5 320.
Hence, the function that best represents the data is:
Option C.
y=26.9x-1.3
Step-by-step explanation:
Considering the situation described, it is found that a linear model best represents the data, because there is a relatively consistent additive rate of change.
When to use a linear model and when to use an exponential model?If the rate of change is additive, that is, the difference between consecutive terms is the same, a linear model is used.If the rate of change is multiplicative, that is, the quotient between consecutive terms is the same, an exponential model is used.In this problem, when the input changes by 2, the output always increases between approximately 50 and 60, that is, the same values, hence a linear model best represents the data, because there is a relatively consistent additive rate of change.
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the difference in the measure of 2 complementary angle is 12 degrees. Find the measure of the angles.
Answer:
39
Step-by-step explanation:
Let one angle be x
Then,
Its complementary angle will be =(90-x)
ATQ,
x-(90-x)=12
x-90+x=12
x+x=12+90
2x=102
x=102/2
x=51
Thus,
x=51
(90-x)=(90-51)=39
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what is the density of carbon dioxide gas if 0.196 g occupies a volume of 100ml?
Answer:
The answer is 2Step-by-step explanation:
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i need the answer please i've tried working it different ways and i just don't get it
Answer:
tan A = 12/ 35
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp / adj
tan A = CB/ AB
tan A = 12/ 35
Identify a pattern and find the next number in the pattern.
-0.4, -1.2, -3.6, -10.8
Answer:
-32.4
Step-by-step explanation:
-1.2/(-0.4) = 3
-3.6/(-1.2) = 3
-10.8/(-3.6) = 3
Each new terms is the previous term multiplied by 3.
-10.8 * 3 = -32.4
A cylinder has a height of 5.3 cm and a diameter of 3.0 cm. What is its volume? (Hint: Volume of a cylinder = r2h ) 25.0 cm3 66.2 cm3 149.9 cm3 37.5 cm3
Answer:
37.5 cm³ .
Step-by-step explanation:
h = 5.3 cm
diameter = 3 cm
r = 3/2 = 1.5 cm
Volume of cylinder = πr²h {Plug in the values of h & r }
= 3.1428 * 1.5 * 1.5 * 5.3
= 37.5399
= 37.5 cm³
Answer:
37.5cm3
Step-by-step explanation:
Diameter = 3cm
Radius = 3cm÷2
= 1.5cm
Volume of cylinder= πr²h
= π(1.5²)+5.3
= 37.5 (3 S.F.)
PLEase help please help
Answer:
10 m
Step-by-step explanation:
490[tex]\pi[/tex]=[tex]\pi[/tex](7²)h
490[tex]\pi[/tex]/[tex]\pi[/tex]49=h
10=h
which expressions are equivalent to 1/4 -2/3-(1/2+5/6)
Answer:
Fraction Equivalent Fractions
4/5 8/10 12/15
1/6 2/12 3/18
5/6 10/12 15/18
1/7 2/14 3/21
Step-by-step explanation:
We say that 1/2 is equivalent to 2/4. Fractions are determined to be equivalent by multiplying the numerator and denominator of one fraction by the same number. This number should be such that the numerators will be equal after the multiplication.
Step-by-step explanation:
The expression 1/4 - 2/3 - (1/2 + 5/6) is equivalent to -7/4.
What is Simplification?Simplification in mathematical terms is a process to convert a long mathematical expression in simple and easy form.
The given expression is,
1/4 - 2/3 - (1/2 + 5/6)
To solve the expression, first simplify bracket term,
1/4 - 2/3 - (8/6)
(3 - 8)/12 - 8/6
-5/12 - 8/6
-21/12
-7/4
The simplified form of the expression 1/4 - 2/3 - (1/2 + 5/6) is -7/4.
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2. How do you find P(A or B) if A and B are independent events for one action, such as spinning a four-color spinner once and finding P(red or blue)?
Answer:
P(red or blue) = [tex]\frac{7}{16}[/tex].
Step-by-step explanation:
We have to find P(A or B), if A and B are independent events for one action, such as spinning a four-color spinner once.
Firstly, as we know that the formula for finding P(A or B) is given by;
P(A or B) = P(A) + P(B) - P(A and B)
Since it is stated that event A and B are independent, this means that there is no dependence of any one event on another event, so;
P(A and B) = P(A) [tex]\times[/tex] P(B)
Now, we can find P(A or B) = P(A) + P(B) - P(A) [tex]\times[/tex] P(B); is we know that the probabilities of happening of both events.
Similarly, P(red or blue) = P(red) + P(blue) - P(red) [tex]\times[/tex] P(blue).
Since the event is spinning a four-color spinner once and assuming there are four different colors, so the probability of wheel stopping on each color is ([tex]\frac{1}{4}[/tex]).
So, P(red or blue) = [tex]\frac{1}{4} +\frac{1}{4} -(\frac{1}{4} \times \frac{1}{4} )[/tex]
= [tex]\frac{2}{4} -\frac{1}{16}[/tex] = [tex]\frac{7}{16}[/tex].
When two fair 6-sided dice are tossed, the numbers $a$ and $b$ are obtained. What is the probability that the two digit number $ab$ (where $a$ and $b$ are digits) and $a$ and $b$ are all divisible by 3?
=================================================
Explanation:
If either a or b (or both) are multiples of 3, then so is a*b
Consider 'a' being a multiple of 3. This means a = 3k for some integer k. Multiply both sides by b to get ab = 3k*b, and we see that 3 is a factor of ab, making ab to be a multiple of 3.
----------
There are six sides to the dice and those sides are {1,2,3,4,5,6} of which only {3,6} are multiples of 3.
If we want both dice to be multiples of 3, then the possible outcomes are
(3,3)(3,6)(6,3)(6,6)There are four outcomes. This is out of 6*6 = 36 total outcomes overall.
Dividing the values gives 4/36 = 1/9 as the probability we want
----------
Side note: for a roll like (a,b) = (6,3) we see that a*b = 6*3 = 18, which is a multiple of 3. The same happens with the other three (a,b) pairings mentioned above.
What is the area of a rectangle that is 3.1 cm wide and 4.4 cm long?
Answer: 13.64 cm squared
Step-by-step explanation: Area of a rectangle is l x w so 3.1 x 4.4 = 13.64