[tex]\textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh ~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ b=5.2\\ A=26.58 \end{cases}\implies 26.58=\cfrac{1}{2}(5.2)h \\\\\\ 26.58=2.6h\implies \cfrac{26.58}{2.6}=h\implies 10.22\approx h[/tex]
[tex]50 \times 8 + 25[/tex]what is 50 times 8 plus 25
The expression we have to solve is:
[tex]50\times8+25[/tex]When solving this kind of expression, we need to solve first any multiplication before solving the additions.
So we solve 5x8 (which results in 400) and we get:
[tex]400+25[/tex]And finally, we solve the addition:
[tex]400+25=425[/tex]Answer: 425
Factor 8y^2+18. Please show work!!!
Answer:
2*(4y² + 9)
Step-by-step explanation:
Factorize the expression:8y² = 2 * 2 * 2 * y²
18 = 2 * 3 * 3
GCF = 2
8y² + 18 = 2* 4y² + 2*9
= 2*(4y² + 9)
Ced is collecting baseball cards. He begins with 14 cards in his collection and adds 3 new cards per day. Determine
how many days it will take Ced to have 90 baseball cards in his collection
about 25-26 days....
Hope this helped!!
Answer:
26
Step-by-step explanation:
(90-14)/3
= 25..1
Therefore it will take Ced 26 days to complete his goal
7 3/4 divided by 1/3
Answer:
23.25 or 23 1/4
Step-by-step explanation:
keep change flip
7 3/4 = 31/4
31/4 x 3/1
31 x 3=93
4 x 1 =4
93/4 simplifies to 23 1/4 or 23.25
5/9 - 2/6 which equals what??
Answer:
2/9
Step-by-step explanation:
Step 1
We can't subtract two fractions with different denominators. So you need to get a common denominator. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.
So we multiply 5 by 6, and get 30.
Then we multiply 2 by 9, and get 18.
Next we give both terms new denominators -- 9 × 6 = 54.
So now our fractions look like this:
30
54
−
18
54
Step 2
Since our denominators match, we can subtract the numerators.
30 − 18 = 12
So the answer is:
12
54
Step 3
Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?
To find out, we try dividing it by 2...
Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:
12
54
÷ 2 =
6
27
Let's try dividing by 2 again...
Nope! So now we try the next greatest prime number, 3...
Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:
6
27
÷ 3 =
2
9
Let's try dividing by 3 again...
No good. 3 is larger than 2. So we're done reducing.
There you have it! The final answer is:
5
9
−
2
6
=
2
9
Which property can be used to show that if 16 = 9+ 7 then 9 + 7 = 16?
A) Reflexive Property of Equality
B) Symmetric Property of Equality
C) Transitive Property of Equality
D) Substitution Property of Equality
Answer: B) Symmetric Property of Equality
Step-by-step explanation:
symmetric property of equality is basically saying that if y = x, then x = y.
What transformation takes the graph of f(x)=4x+9 to the graph of g(x)=4x+7 ? translation 2 units righttranslation 2 units lefttranslation 2 units uptranslation 2 units down
If you compare the functions:
[tex]\begin{gathered} f(x)=4x+9 \\ g(x)=4x+7 \end{gathered}[/tex]Considering f(x) as the parent function, let's analyze each option:
1) Translation 2 units right.
To translate a function 2 units to the right, you have to subtract 2 to the x-term:
[tex]\begin{gathered} h(x)=f(x-2)=4(x-2)+9 \\ h(x)=4\cdot x-4\cdot2+9 \\ h(x)=4x-8+9 \\ h(x)=4x+1 \end{gathered}[/tex]As you can see the resulting function, h(x), is not equal to g(x), which means that the transformation applied was not a shift 2 units to the right.
2) Translation 2 units to the left
To translate the function two units to the left, you have to add 2 to the x-term:
[tex]\begin{gathered} i(x)=f(x+2)=4(x+2)+9 \\ i(x)=4\cdot x+4\cdot2+9 \\ i(x)=4x+8+9 \\ i(x)=4x+17 \end{gathered}[/tex]The resulting function, i(x), is not equal to g(x), which means that the transformation applied was not a shift of 2 units to the left.
3) Translation 2 units up
To translate a function 2 units up, you have to add 2 to the function, that is:
[tex]\begin{gathered} j(x)=f(x)+2=(4x+9)+2 \\ j(x)=4x+9+2 \\ j(x)=4x+11 \end{gathered}[/tex]The function j(x) is different from the function g(x), so the transformation applied was not a shift 2 units up.
4) Translation 2 units down
To shift a function two units down, you have to subtract 2 from the function:
[tex]\begin{gathered} k(x)=f(x)-2 \\ k(x)=(4x+9)-2 \\ k(x)=4x+9-2 \\ k(x)=4x+7 \end{gathered}[/tex]The functions k(x) and g(x) are equal, which means that to determine the function g(x) the function f(x) was translated 2 units down.
Answer:
1,3,4
Step-by-step explanation:
keep it easy
There are 10 less trumpet players than saxophone players. The number of saxophone players iS
3 times the number of trumpet players. How many trumpet players are there?
Step-by-step explanation:
t = number of trumpet players.
s = number of saxophone players.
t = s - 10
s = 3t
we use the second in the first equation
t = 3t - 10
-2t = - 10
2t = 10
t = 5
s = 3t = 3×5 = 15
there are 5 trumpet players (and 15 sax players).
The graphs of f (x) = x3 + x2 – 6x and g(x) = ex + 2 – 1 have which of the following features in common?
Rational function f of x increases from the left in quadrant 3 passing through the point negative 2 comma 0 and going to a local maximum and then decreasing through the point 0 comma 0 to a local minimum and then increasing through the point 3 comma 0 to the right and the exponential function g of x increases from the left in quadrant 3 asymptotic to the line y equals negative 1 and passes through the points negative 2 comma 0 and increases through the point 0 comma 6 to the right
x-intercept
y-intercept
End behavior
Range
The end behavior of the graphs of the functions f(x) and g(x) are common.
Consider the two functions,
f(x) = x³ + x² - 6x and g(x) = [tex]e^{x+2}[/tex] - 1
Now,
y = x³ + x² - 6x
The x-intercept will be:
0 = x³ + x² - 6x
x( x² + x - 6 ) = 0
x( x - 2 )( x + 3 ) = 0
So, x = 0, 2, - 3
Hence, the x-intercepts are ( 0, 0 ), ( 2, 0 ), and ( - 3, 0 ).
The y-intercept will be:
y = x³ + x² - 6x
y = (0)³ + (0)² - 6(0)
y = 0
Hence, the y-intercept is ( 0, 0 ).
The range of the function f(x) = x³ + x² - 6x is ( - ∞, ∞ ).
Using the degree 3 and the leading coefficient 1 of the function f(x) the end behavior of the function will be:
Falls to the left and rises to the right.
For the function,
y = g(x) = [tex]e^{x+2}[/tex] - 1
The x-intercept will be:
y = [tex]e^{x+2}[/tex] - 1
0 = [tex]e^{x+2}[/tex] - 1
[tex]e^{x+2}[/tex] = 1
[tex]e^{x+2}[/tex] = e⁰
x + 2 = 0
x = - 2
Hence, the x intercept is ( - 2, 0 ).
The y-intercept will be:
y = g(x) = [tex]e^{x+2}[/tex] - 1
y = e² - 1
Hence, the y-intercept will be ( 0, e² - 1 ).
The range of the function g(x) is ( - 1, ∞ ).
The end behavior of the function g(x) constantly rises to the right in the positive y-axis.
Hence, the functions f(x) and g(x) have the end behavior in common.
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Find the domain of the function.
1-
X
O all real numbers such that x ≥ -7 and x ≤ 0
O all real numbers except x > -7 and x ≤ 0
O all real numbers except x = -7 and x = 0
O only x = -7 and x = 0
O all real numbers
g(x) =
=
Need Help?
4
x+7
Read It
The domain of the given function is all real numbers expect x> -7 and x ≥ 0.
What is domain?The entire range of independent variable values is the domain of a function.
According to this definition, it means:
The collection of all x-values that can cause the function to "work" and produce actual y-values is known as the domain.
Keep these things in mind when locating the domain:
A fraction's denominator (bottom) cannot be 0.
In this section, the integer following a square root symbol must be positive.
Given,
g(x) = 1/x- 4/x+7
Applying the definition of rational function that denominator is non zero
x ≠ 0 and x+7 ≠ 0
solving the inequality,
x ≠ 0 and x ≠ -7
Combining the values,
x < -7 or -7 < x< 0 or x> 0.
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The Johnsons framed a family picture to hang on the wall. The perimeter of the frame is 72 inches. Use the formula
P = 2l + 2w to find the length of the frame if the width is 14 inches.
The length of the frame the width is 22
What is the perimeter of a frame whose length is 22 inches and whose breadth is 14 inches?
The distance around an object is called the perimeter.
For instance, the yard of your home is fenced in. The perimeter is the length of the fence. Your fence is 200 feet long if the yard is 50 feet by 50 feet.
The answer to the above-mentioned difficulty is provided here.
We will search for the length since the frame's breadth is 14 inches and its perimeter is 72 inches. 2L + 2W is the perimeter formula.
Therefore, let's swap the values.
P = 2L + 2w
72 = 2L + 2(14) (14)
72 = 2L + 28
72 -28 = 2L\s44 = 2L \s22 = L
Consequently, the picture frame's length
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A package of 6 pairs of insulated socks costs 49.74 $. What is the unit price of the pairs of socks ?
The pairs of insulated socks has a unit rate of $7.99
How to determine the unit rate?From the question, the given parameters are
Number of pairs of insulated socks = 6Cost of the insulated socks = $47.94The above parameters can be represented as the following points
(x, y) = (6, 47.94)
The unit rate of the points is then calculated as
k = y/x
Substitute the known values in the above equation
So, we have the following equation
k = 47.94/6
Evaluate the quotient
So, we have
k = 7.99
Hence, the unit rate is $7.99
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A factory produces widgets and zurls. The combined number of
widgets and zurls made each day cannot be more than 12. The
maximum number of widgets the factory can produce in a day is
4.
Select each ordered pair that represents an allowable
combination of widgets and zurls produced in one day.
(4,5)
(11,1)
(3,9)
(4,12)
(4,5) and (4,12) are this pair is allowable to the maximum number of widgets the factory can produce in a day is 4, so x ≤ 4 .
(11,1) and (3,9) are this pair is allowable to the combined number of widgets and zurls made each day cannot be more than 12, so x + y ≤ 12.
Let us assume the number of widgets = x
Let us assume the number of zurls = y
According to question,
The combined number of widgets and zurls made each day cannot be more than 12.
That means,
x + y ≤ 12 (Equation-1)
The maximum number of widgets the factory can produce in a day is 4.
That means,
x ≤ 4 (Equation-2)
So,
We can write each pair has,
(4,5)
x = 4,
y = 5
We can substitute values in equation 1 and 2,
x + y ≤ 12 ; x ≤ 4
4 + 5 ≤ 12 ; 4 ≤ 4
9 ≤ 12
Hence this pair is not allowable to the combined number of widgets and zurls made each day cannot be more than 12.
Hence this pair is allowable to the maximum number of widgets the factory can produce in a day is 4.
(11,1)
x = 11,
y = 1
We can substitute values in equation 1 and 2,
x + y ≤ 12 ; x ≤ 4
11 + 1 ≤ 12 ; 11 ≤ 4
12 ≤ 12
Hence this pair is allowable to the combined number of widgets and zurls made each day cannot be more than 12.
Hence this pair is not allowable to the maximum number of widgets the factory can produce in a day is 4.
(3,9)
x = 3,
y = 9
We can substitute values in equation 1 and 2,
x + y ≤ 12 ; x ≤ 4
3 + 9 ≤ 12 ; 3 ≤ 4
12 ≤ 12
Hence this pair is allowable to the combined number of widgets and zurls made each day cannot be more than 12.
Hence this pair is not allowable to the maximum number of widgets the factory can produce in a day is 4.
(4,12)
x = 4,
y = 12
We can substitute values in equation 1 and 2,
x + y ≤ 12 ; x ≤ 4
4 + 12 ≤ 12 ; 4 ≤ 4
16 ≤ 12
Hence this pair is not allowable to the combined number of widgets and zurls made each day cannot be more than 12.
Hence this pair is allowable to the maximum number of widgets the factory can produce in a day is 4.
Therefore,
(4,5) and (4,12) are this pair is allowable to the maximum number of widgets the factory can produce in a day is 4, so x ≤ 4 .
(11,1) and (3,9) are this pair is allowable to the combined number of widgets and zurls made each day cannot be more than 12, so x + y ≤ 12.
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The maximum number of widgets the factory can create in a day is 4, therefore x 4. (4,5) and (4,12) are this pair is permissible.
The total number of widgets and zurls produced each day is limited to 12, therefore (11,1) and (3,9) are acceptable. Therefore, x + y 12.
Let's assume there are x widgets.
Assume that y is equal to the number of zurls.
According to the inquiry,
There can never be more than 12 widgets and zurls produced each day.
That implies,
x + y ≤ 12 (Equation-1)
The maximum number of widgets the factory can produce in a day is 4.
That means,
x ≤ 4 (Equation-2)
So,
We can write each pair has,
(4,5)
x = 4,
y = 5
We can substitute values in equation 1 and 2,
x + y ≤ 12 ; x ≤ 4
4 + 5 ≤ 12 ; 4 ≤ 4
9 ≤ 12
Hence this pair is not allowable to the combined number of widgets and zurls made each day cannot be more than 12.
Hence this pair is allowable to the maximum number of widgets the factory can produce in a day is 4.
(11,1)
x = 11,
y = 1
We can substitute values in equation 1 and 2,
x + y ≤ 12 ; x ≤ 4
11 + 1 ≤ 12 ; 11 ≤ 4
12 ≤ 12
Hence this pair is allowable to the combined number of widgets and zurls made each day cannot be more than 12.
Hence this pair is not allowable to the maximum number of widgets the factory can produce in a day is 4.
(3,9)
x = 3,
y = 9
We can substitute values in equation 1 and 2,
x + y ≤ 12 ; x ≤ 4
3 + 9 ≤ 12 ; 3 ≤ 4
12 ≤ 12
Therefore, this pair is permitted as long as the total number of widgets and zurls produced each day does not exceed 12.
The factory can only manufacture a maximum of 4 widgets per day, so this combination is not permitted.
(4,12)
x = 4,
y = 12
We can substitute values in equation 1 and 2,
x + y ≤ 12 ; x ≤ 4
4 + 12 ≤ 12 ; 4 ≤ 4
16 ≤ 12
Because the maximum daily production of widgets and zurls is limited to 12, this pair is not permitted.
The factory can only make a maximum of 4 widgets every day, hence this pair is permitted.
Therefore,
The maximum number of widgets the factory can create in a day is 4, therefore x 4. (4,5) and (4,12) are this pair is permissible.
The total number of widgets and zurls produced each day is limited to 12, therefore (11,1) and (3,9) are acceptable. Therefore, x + y 12.
root 18 times root 2
[tex] \sqrt{18} \times \sqrt{2} [/tex]
25 + y = -10 what is the answer of y
Answer: y=-35
Step-by-step explanation:
The question is 25+y=-10
Now, since we want the value of y, we can see that we have to remove the 25 that is added to it. So, we subtract both sides as it an equal side, and -10-25= -35 So, y=-35
25+y=-10
-25 -25
y=-10-25=-35
Hope this helps
-15/x+3=-10/x Thank You For Your Help
Answer:
x=5/3
Step-by-step explanation:
What is the solution set for the inequality,
4 (x − 3) − 7x ≥ 6
The most appropriate choice for linear inequation will be given by
Solution set = {[tex]x \epsilon \mathbb{R}, x \leq 6[/tex]}
What is linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by [tex]>[/tex], [tex]<[/tex], [tex]\geq[/tex], [tex]\leq[/tex] sign
A one degree inequation is known as linear inequation.
Here,
[tex]4(x - 3) - 7x \geq 6\\4x -12 - 7x \geq 6\\-3x -12\geq 6\\-3x \geq 6 + 12\\-3x \geq 18\\x \leq \frac{18}{3}\\x \leq 6[/tex]
Solution set = {[tex]x \epsilon \mathbb{R}, x \leq 6[/tex]}
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the owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. if a sample of 25 fish yields a mean of 3.5 pounds, what is the probability of obtaining a sample mean this large or larger? (round to 2 decimal places)
There is a 0.0228 percent chance of getting a sample mean this big or bigger.
Given that the sample size is 64, the sample size is 3.2, and the standard deviation is 0.8.
The likelihood of a mean of 3.4 is determined as follows:
#First determine the z-value:
[tex]z=\frac{\bar{X}-\mu}{\sigma / \sqrt{n}}$$=\frac{3.4-3.2}{0.8 / \sqrt{64}}$$=2.000$[/tex]
#We then determine the corresponding probability on the z tables:
[tex]Z(X \geq 3.4)=1-P(X < 3.4)$$=1-0.97725$$=0.0228$[/tex]
Hence, the probability of obtaining a sample mean this large or larger is 0.0228.
The sample mean is regularly distributed for samples of any size derived from a population with a normal distribution, with mean X= and standard deviation X=/n, where n is the sample size.
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Find the equation of the line that passes through (-1,-3) and is perpendicular to 2 y = x − 3 . Leave your answer in the form y = m x + c
Answer:
Remember that the slope of perpendicular lines are negative reciprocals of each other.Step-by-step explanation:y = 1 - 2x the slope is -2 the value of the x term.So the slope of the new line using point (- 1, 2) is 1/2.Now use y = mx + b where y = -1, x = 2, and m = 1/2 .y = mx + b-1 = 1/2(2) + b solve for "b", the y-intersect-1 = 1 + b-2 = bThe line that is perpendicular to y = 1 - 2x is y = 1/2x - 2
Step-by-step explanation:
7
John is less than half his mother's age, though the sum of their ages is greater than
sixty. John was born on his mother's twenty-sixth birthday.
By expressing these facts as two inequalities and one equation, find the range of
possible ages for John.
Answer:
Step-by-step explanation:
ans is 7
The expression -7y is a ______.
a. variable
b. constant
c. term
Answer:
a. variable
Step-by-step explanation:
hope this helps
PLEASE HELP ASAP !!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
x = 14
Step-by-step explanation:
First step is to set the opposite sites equal to each other (they are congruent)
13 = 2y + 1
and
x = y + 8
Now solve for y in terms of x so you can substitute it in the other equation
x - 8 = y
Plug into equation
13 = 2(x-8) + 1
13 = 2x - 16 + 1 distribute
13 = 2x - 15 simplify
28 = 2x add 15 to both sides
x = 14
I hope this helps
Please answer the question in the picture
A loan of $50,000 is taken out for six years at 9% interest compounded annually. If the loan is paid off in full at the end of that time period, $50433 must be returned.
What is Compound interest?Compound interest is calculated by multiplying the initial loan amount, or principal, by one plus the annual interest rate multiplied by the number of compound periods multiplied by one. Compound interest is when you earn interest on both your savings and your interest earnings. When you compound interest, you add the interest you've earned back into your principal balance, which earns you even more interest, compounding your returns. Assume you have $1,000 in a savings account earning 5% interest per year. You'd earn $50 in year one, giving you a new balance of $1,050. Compound interest occurs when interest earned on savings begins to earn interest on itself.
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There were three questions on the test
each question was worth 5 marks
Each Question was marked right or wrong(no part marks).
30% of the students got all 3 questions correct
40% of the students got exactly 2 question correct
25% of the students got exactly 1 question correct
5% of the students got no questions correct
Determine The overall clas average(mean)
Answer:
9.75 marks
Step-by-step explanation:
30% of the students got 15 marks (3 questions)
40% of the students got 10 marks (2 questions)
25% of the students got 5 marks (1 question)
5% of the students got 0 marks (0 questions)
0.3(15)+0.4(10)+0.25(5)+0.05(0)/1
the one as denominator represents all students that took the test
4.5+4+1.25+0
9.75
the class average is 9.75
If Victor meets his goal, he will have 264 pages left in his book on Friday. How many pages does Victor need to read by Friday to reach his goal?
Using the subtraction of two amounts, supposing that today is Monday and the book has 764 pages, he needs to read 500 pages to reach his goal.
How many pages does Victor needs to reach by Friday to reach his goal?Considering that Victor has not started to read the book yet, the number of pages that he needs to read is given by the subtraction of the total number of pages of the book by the number of pages that he wants to have remaining on Friday.
In the context of this problem, we have that:
The book has a total of 764 pages.He wants to have only 264 pages remaining on Friday.Then the number of pages that he has to read is given by the subtraction of 764 and 264 as follows:
764 - 264 = 500 pages.
Hence Victor needs to read 500 pages before Friday to reach his goal.
What is the missing information?The problem is incomplete and could not be found on any search engine, hence we suppose that:
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Can someone please give me the solution for x (−2)exponent2 = 4(−2).
Answer:
Step-by-step explanation:
Exponent calculator helps you find the result of any base raised to a positive or negative exponent.
HELP ME ASAP PLEASEE!!
Solve the radical equation AND find the extraneous solutions: √(2x + 3) = x
Answer:
[tex](x+1)(x-3)=0\\x=-1,3\\\sqrt{2(-1)+3}=-1\\ \sqrt{1}=-1\\ \sqrt{2(3)+3}=3\\ \sqrt{9}=3\\[/tex]
There are no extraneous solutions
Step-by-step explanation:
To solve this equation, first we want to cancel out the radical;
[tex](\sqrt{2x+3} )^2=x^2; 2x+3=x^2[/tex]
Now that the equation looks simpler, we can slide 2x+3 to the other side to create a polynomial that we can factor;
[tex]x^2-2x-3=0\\(x+1)(x-3)=0[/tex]
You can check for extraneous solutions by plugging the answers in, which I showed above.
i am in big need for help asap pls help -8 3/4 + -11 1/3 = ____ __ / __
Answer: − 20 1/12
Step-by-step explanation:
5) Zoe paid $1.86 in tip for her dinner. She tipped 20% of the price of her dinner. What was the cost
of her dinner not including the tip?
Step-by-step explanation:
20% = $1.86
1% = 20%/20 = 1.86/20 = $0.093
100% = 1%×100 = 0.093×100 = $9.30
in short : 1.86 × 100/20 = 1.86 × 5 = $9.30
the cost of her dinner without tip was $9.30.
Consider a car with a cash price of $4,000, offered on the installment plan for $146 per month for 36 months.
Calculate (a) the total installment price, (b) the carrying charges, and (c) the number of months needed to save the money at the monthly rate to buy the car for its cash price.
Use commas and decimal points in your answers when appropriate. Round to two decimal places if necessary
The total installment price is 34 and the carrying charges is 34
A sort of contract or arrangement known as an installment loan involves a loan that must be returned over period with a predetermined number of periodic instalments; typically, at least two each payment is required.
The expense related to keeping a financial instrument for a set length of time is known as a carrying charge. This issue is caused by the additional cost of purchasing the bicycle on an instalment plan. This is the additional amount (total) you will pay over cash price since you choose to use an instalment plan.a) Total charge of the Installment price = 146 × 30 = $5256
b) The carrying charges = $5256 - $4000 = $1256
c) Number of months needed to save money = $4000 ÷ 36 = 111.11..
Therefore 11.11 months or 12 months is needed to save money to buy the car.
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