Answers
Answer:
See explanation
Step-by-step explanation:
1. Lines l and k are parallel. These lines are cut be transversal n. Angles 2 and 7 are corresponding angles when parallel lines l and k are cut by transversal n. By Corresponding Angles Ttheorem, angles 2 and 7 are congruent.
2. Lines m and n are parallel. These lines are cut be transversal k. Angles 2 and 10 are alternate interior angles when parallel lines m and n are cut by transversal k. By Alternate Interior Angles Theorem, angles 2 and 10 are congruent.
3. Angles 2 and 7 are congruent (see 1)
Angles 2 and 10 are congruent (see 2)
Hence, angles 7 and 10 are congruent by transitive property.
Related Questions
Sharon paid $78 sales tax on a new camera.if the sales tax rate is 6.5%, what was the cost of the camera?
Answers
The cost of the camera if Sharon paid $78 sales tax at a rate of 6.5% is $1200
What was the cost of the camera?
Amount of sales tax = $78
Sales tax rate = 6.5%
Cost of the camera = x
.
Amount of sales tax = Sales tax rate × Cost of the camera
78 = 6.5% × x
78 = 0.065 × x
78 = 0.065x
Divide both sides by 0.065
x = 78/0.065
x = 1200
Therefore, the camera cost $1200
These are for corrections. What is number 15?
Answers
Answer:
[tex]x = 2\sqrt{10}[/tex]
Step-by-step explanation:
We have to solve for x from the logarithmic equation as follows:
[tex]\log x^{2} + \log 25 = 3[/tex]
⇒ [tex]\log 25x^{2} = 3[/tex]
{Since, using logarithmic property [tex]\log A + \log B = \log AB[/tex]}
Now, converting this logarithmic equation above into exponential equation we get,
[tex]25x^{2} = 10^{3}[/tex]
{Since we know that if [tex]\log_{10}a = b[/tex] then, we can write [tex]a = 10^{b}[/tex]}
⇒ [tex]25x^{2} = 1000[/tex]
⇒ [tex]x^{2} = 40[/tex]
⇒ [tex]x = 2\sqrt{10}[/tex] (Answer)
determine all factors of the expression 3x^3+7x^2-18x+8 if one of the factors is x-1
Answers
The factorization of [tex]\(3x^3+7x^2-18x+8\)[/tex] is [tex]\((x-1)(3x^2 + 10x - 8)\)[/tex]. So, the factors are [tex](x-1), (3x^2 + 10x - 8)[/tex], and any additional factors that [tex]\(3x^2 + 10x - 8\)[/tex] may have, which can be further factored if possible.
Given that x-1 is a factor of the expression [tex]\( 3x^3+7x^2-18x+8 \)[/tex], we can use the long division method to find the other factors.
Set up the division as follows:
[tex]3x^2 + 10x - 8[/tex]
______________________
[tex]x - 1 | 3x^3 + 7x^2 - 18x + 8 \\ - (3x^3 - 3x^2)[/tex]
___________________
[tex]10x^2 - 18x + 8 \\ - (10x^2 - 10x)\\[/tex]
______________
-8x + 8
- (-8x + 8)
__________
0
The quotient is [tex]\(3x^2 + 10x - 8\)[/tex], and since there is no remainder, \(x-1\) is indeed a factor.
Therefore, The factorization of [tex]\(3x^3+7x^2-18x+8\)[/tex] is [tex]\((x-1)(3x^2 + 10x - 8)\)[/tex]
So, the factors are [tex](x-1), (3x^2 + 10x - 8)[/tex], and any additional factors that [tex]\(3x^2 + 10x - 8\)[/tex] may have, which can be further factored if possible.
The complete factorization of the original expression [tex]\(3x^3 + 7x^2 - 18x + 8\)[/tex] is:[tex]\[ (x - 1)(x + 4)(3x - 2) \][/tex]
To factorize the expression [tex]\(3x^3 + 7x^2 - 18x + 8\)[/tex] given that one of the factors is [tex]\(x - 1\)[/tex], we can use polynomial division to divide the expression by [tex]\(x - 1\)[/tex] and find the quotient. The factors of the expression will then be [tex]\(x - 1\)[/tex] and the factors of the quotient.
The expression to be factorized is: [tex]\(3x^3 + 7x^2 - 18x + 8\).[/tex]
Let's perform the division step-by-step.
1.Divide the first term of the dividend (3x³) by the first term of the divisor (x):
[tex]\(3x^3 ÷ x = 3x^2\)[/tex].
Write this as the first term of the quotient.
2. Multiply the divisor by this term and subtract the result from the dividend:
Multiply [tex]\(x - 1\)[/tex] by [tex]\(3x^2\)[/tex] to get [tex]\(3x^3 - 3x^2\)[/tex].
Subtract this from the original polynomial: [tex]\(3x^3 + 7x^2\)[/tex]becomes [tex]\(10x^2\)[/tex].
3.Bring down the next term of the original polynomial to form a new dividend:
The new dividend is [tex]\(10x^2 - 18x\)[/tex].
4.Repeat this process for the new dividend**:
Divide [tex]\(10x^2\) by \(x\) to get \(10x\)[/tex].
Multiply [tex]\(x - 1\) by \(10x\)[/tex] to get [tex]\(10x^2 - 10x\)[/tex].
Subtract this from the new dividend:[tex]\(10x^2 - 18x\)[/tex] becomes [tex]\(-8x\)[/tex].
5.Bring down the next term of the original polynomial to form a new dividend:
The new dividend is [tex]\(-8x + 8\)[/tex].
6.Repeat this process for the new dividend**:
Divide [tex]\(-8x\) by \(x\)[/tex] to get [tex]\(-8\)[/tex].
Multiply [tex]\(x - 1\) by \(-8\)[/tex] to get [tex]\(-8x + 8\)[/tex].
Subtract this from the new dividend: [tex]\(-8x + 8\)[/tex] becomes 0.
The quotient we obtain from this division is [tex]\(3x^2 + 10x - 8\)[/tex]. Now, we need to factorize this quadratic expression. Let's proceed with the factorization.
The roots of the quadratic expression [tex]\(3x^2 + 10x - 8\)[/tex] are [tex]\(-4\)[/tex] and[tex]\(\frac{2}{3}\)[/tex]. This means that the quadratic expression can be factored as [tex]\((x + 4)(x - \frac{2}{3})\)[/tex].
However, to express the factors in a more standard form, we'll rewrite the factor [tex]\(x - \frac{2}{3}\) as \(3x - 2\)[/tex], which is obtained by multiplying the numerator and denominator of [tex]\(\frac{2}{3}\)[/tex] by 3.
Therefore, the factorized form of [tex]\(3x^2 + 10x - 8\)[/tex] is [tex]\((x + 4)(3x - 2)\)[/tex].
Combining this with the given factor [tex]\(x - 1\)[/tex], the complete factorization of the original expression [tex]\(3x^3 + 7x^2 - 18x + 8\)[/tex] is:[tex]\[ (x - 1)(x + 4)(3x - 2) \][/tex]
What is the equation in slope-intercept form of the line that passes through the point (2,-2)
and is perpendicular to the line represented by y
A y = 1 / 8x - 7
By=*=>
cx = 3x - 3
0 y = - 3x + 3
Answers
There is no way to determine the rate of change [slope], so it is impossible to answer this question. I apologise.
Please help with number 7
Answers
[tex]\pi[/tex] is a Irrational Number .
[tex]\sqrt{12}[/tex] is a Irrational Number .
3.14 is a Rational Number .
[tex]4 . \overline{123}[/tex] is a Rational Number .
[tex]\sqrt{49}[/tex] is Natural, Whole, Rational Number and Integer .
[tex]-\frac{240}{6}[/tex] is Integer and Rational number.
Explanation:In order to answer this question, we need to know what are Natural Numbers, Whole Numbers, Integer, Rational and Irrational Numbers.
Natural Numbers are those numbers which we use to count on a daily basis, starting from 1, 2, 3, and so on. Whole Numbers are simple the numbers including 0 along with Natural Numbers. Integers are Whole numbers including negative values as well with them. Any number which can be resembled as a fraction of two integers is known as Rational Number. Any number which is not Rational Number is known as Irrational Number, i.e., any number which cannot be represented as a fraction of two integers is known as Irrational Number.We cannot represent [tex]\pi[/tex] as a fraction of two integers and hence is Irrational.
[tex]\sqrt{12}[/tex] can be simplified as [tex]\sqrt{(4 \times 3)}=2 \times \sqrt{3} \times \sqrt{3}[/tex] again cannot represent the same as a fraction of two integers, and [tex]\sqrt{12}[/tex] is irrational.
3.14 can be represented in terms of [tex]\frac{314}{100}=\frac{157}{50}[/tex], and hence it is a Rational Number.
[tex]4 . \overline{123}[/tex] is the case of Repeating decimals, and repeating decimals are always Rational Numbers.
[tex]\sqrt{49}[/tex] is equal to 7 and hence is Natural Number. 7 can also be included in the whole number, rational number and Integer.
[tex]-\frac{240}{6}[/tex] is equal to -40, so it is Integer and Rational Number.
Which property should be used to solve this equation 4+x=13
Answers
Answer:
Step-by-step explanation:
4 + x = 133......to solve this, u would subtract 4 from both sides
so that would be the subtraction property of equality
Answer:
The subtraction property of equalityStep-by-step explanation:
4 + x = 13 subtract 4 from both sides
4 - 4 + x = 13 - 4
x = 9You have 3/6 cup of brown sugar in your cupboard. The recipe for a dessert
calls 1/5 for cup of brown sugar. How much brown sugar would you have left if
you made the dessert?
Answers
need : 1/5
3/6 - 1/5=
15/30 - 6/30=
9/30=
3/10
so you wil have 3/10 of brown sugar left
Which expression is equivalent to Y YY.Z.Z.Z.Z?
Answer : A y exponent 3 z exponent 4
Answers
Answer: the answer is correct
Step-by-step explanation: edge 2020 trust me
Solve the following system of equations by using the elimination method.
x - y = 11
2x + y = 19
(1, 10)
(-1,-1)
(12,2)
(10,-1)
Answers
Answer:
the answer is (6, 1)
Step-by-step explanation:
x² + y² - 12 x - 2 y + 12 = 0
(x²-12x) +(y² -2y) +12 = 0
(x²-2(6)(x)+6²)-6² +(y² -2y+1) -1+12 = 0
(x-6)² +(y-1)² = 5²
the center of a circle is (6, 1)
Sofia wants to place a sticker 2 1/2 inches long in the center of a switch box that 3 3/4 inches wide about how far from the edge of the switch board will you place the sticker
Answers
You will place the sticker [tex]\frac{5}{8}[/tex] inches from the edge of the switch board
Step-by-step explanation:
Given data:
Sticker’s length = [tex]2 \frac{1}{2}[/tex]
Breadth of switch box = [tex]3 \frac{3}{4}[/tex]
Subtracting the above value, we get
[tex]\text { Switch Box's total area }=3 \frac{3}{4}-2 \frac{1}{2}=\frac{15}{4}-\frac{5}{2}=\frac{15-10}{4}=\frac{5}{4}[/tex]
Divided [tex]\frac{5}{4}[/tex] by 2 gives you the distance from the edge if you put the sticker in the centre). Therefore,
[tex]\frac{\left(\frac{5}{4}\right)}{\left(\frac{2}{2}\right)}=\frac{5}{8}[/tex]
So, will place the sticker [tex]\frac{5}{8}[/tex] inches far from the edge of the switch board.
La correa transportadora de una estación automática levanta 500 toneladas de mineral hasta una altura de 90 ft en una hora. ¿Qué potencia en caballos de fuerza se requiere para esto?
Answers
Para levantar 500 toneladas de mineral a una altura de 90 pies en una hora, se requieren aproximadamente 90.91 caballos de fuerza (HP), calculados utilizando la fórmula de trabajo y potencia.
Para calcular la potencia requerida en caballos de fuerza (HP) para levantar 500 toneladas de mineral hasta una altura de 90 pies en una hora, necesitamos utilizar la fórmula de trabajo y la potencia. La potencia se mide en unidades de trabajo por unidad de tiempo.
Primero, convirtamos la altura a pies a la misma unidad que la tonelada, que es la tonelada-pie (ton-ft). 1 tonelada-pie es igual al trabajo necesario para levantar una tonelada a una altura de un pie.
500 toneladas * 90 ft = 45,000 ton-pie
El trabajo total necesario es de 45,000 toneladas-pie.
Dado que el trabajo se realiza en una hora (3600 segundos), podemos usar la siguiente fórmula para calcular la potencia en HP:
[tex]\[Potencia (HP) = \frac{Trabajo (ft-lbf)}{Tiempo (s)} \times \frac{1}{550}.\][/tex]
Donde 1 HP es igual a 550 ft-lbf/s.
Sustituyendo los valores conocidos:
[tex]\[Potencia (HP) = \frac{45,000 \text{ ton-pie} \times 2,000 \text{ lbf/ton} \times 1 \text{ ft}}{3600 \text{ s} \times 550 \text{ ft-lbf/s}} = \frac{180,000,000 \text{ lbf-ft}}{1,980,000 \text{ ft-lbf/s}} \approx 90.91 HP.\][/tex]
Por lo tanto, se requieren aproximadamente 90.91 caballos de fuerza (HP) para realizar este trabajo en una hora.
For more such information on: mineral
https://brainly.com/question/15844293
#SPJ2
HELP PLESE!!!!!! Subtract. State the difference in simplest form.
Answers
Apple produce pays it's employees by the formula P(b)=7/2b+35, where P(b) is the employee's total daily pay and b is the number of bushels of apples picked . According to the formula,what is the rate employees are paid per bushels of apples picked?
Answers
Answer:
Apple Produce pays employees 38.5 for per bushels of apples picked.
Step-by-step explanation:
Given:
Apple produce pays it's employees by the formula;
[tex]P(b) = \frac{7}{2}b+35[/tex]
[tex]P(b)[/tex] ⇒ Employee's Total daily pay
[tex]b[/tex] ⇒ Number of bushels of apples
We need to find the Rate employees are paid per bushels of apples picked.
Rate employees are paid per bushels of apples picked can be calculated by substituting the value of "b = 1" in above formula.
Substituting the value of b = 1 in above formula we get;
[tex]P(1) = \frac{7}{2} \times 1+35\\[/tex]
Now We will take LCM to make the Denominator common.
[tex]P(1) = \frac{7}{2} +\frac{35\times 2}{2} = \frac{7}{2} +\frac{70}{2} = \frac{77}{2}= 38.5[/tex]
Hence Apple Produce pays employees 38.5 for per bushels of apples picked.
Help me solve this problem
Answers
Answer:
The weight of the larger box = 15.75 kg.
The weight of the smaller box = 13.75 kg.
Step-by-step explanation:
We have the two equations based on the scenario.
The equations are:
[tex]$ 7x + 9y = 234 \hspace{20mm} \hdots {(1)} $[/tex]
[tex]$ 5x + 3y = 360 \hspace{20mm} \hdots {(2)} $[/tex]
'x' represents the weight of the larger box.
and 'y' the weight of the smaller box.
Multiplying Equation (2) by 3 throughout, we get:
[tex]$ 15x + 9y = 360 $[/tex]
Subtracting this and Equation (1), we get:
[tex]$ -8x = -126 $[/tex]
[tex]$ \implies x = 15.75 $[/tex] kg.
∴ The weight of the Larger box is 15.75 kg.
Substituting the value of 'x' in either of the equations will give us the value of 'y', the weight of the smaller box.
We substitute in Equation (1).
We get: 9y = 234 - 7(15.75)
⇒ 9y = 123.75
⇒ y = 13.75
∴ The weight of the smaller box is 13.75 kg.
Evaluate the determinant for the following 1 4 4]
5 2 2
1 5 5
Answers
The determinant of given matrix is zero
Step-by-step explanation:
Given matrix is:
[tex]\left[\begin{array}{ccc}1&4&4\\5&2&2\\1&5&5\end{array}\right][/tex]
The determinant of a 3x3 matrix is calculated by selecting a single row.
We are choosing the first row.
So,
[tex]= 1\left|\begin{array}{ccc}2&2\\5&5\\\end{array}\right|-4\left|\begin{array}{ccc}5&2\\1&5\\\end{array}\right|+4\left|\begin{array}{ccc}5&2\\1&5\\\end{array}\right|\\=1(10-10) -4(25-2)+4(25-2)\\=0-4(23)+4(23)\\=-92+92\\=0[/tex]
The determinant of given matrix is zero
Keywords: Matrices, determinant
Learn more about matrices at:
brainly.com/question/9720317brainly.com/question/9621364#LearnwithBrainly
how many solutions does 12=12 have?
Answers
Answer:
There is not solution to that it is just 12 because there is no variable
Step-by-step explanation:
Answer:
I would say one because the solution is 12.
12 = 12.
If cosA = 3/5 and A ∈ (630,720), find sin2A
Answers
Answer:
- [tex]\frac{24}{25}[/tex]
Step-by-step explanation:
Given 630 < A > 720 then A is in the fourth quadrant where
cosA > 0 and sinA < 0
Given
cosA = [tex]\frac{3}{5}[/tex] = [tex]\frac{adjacent}{hypotenuse}[/tex]
Then the triangle is a 3- 4 - 5 with opposite side 4, thus
sinA = - [tex]\frac{opposite}{hypotenuse}[/tex] = - [tex]\frac{4}{5}[/tex]
Using the trigonometric identity
sin2A = 2sinAcosA
= 2 × - [tex]\frac{4}{5}[/tex] × [tex]\frac{3}{5}[/tex]
= [tex]\frac{2(-4)(3)}{5(5)}[/tex] = - [tex]\frac{24}{25}[/tex]
Evaluate the following numerical expression 2+(-3)+7
Answers
Answer:
Step-by-step explanation:
2 + (-3) + 7 = 2 - 3 + 7 = 9 - 3 = 6 <==
a positive multiplied by a negative will be negative
What is the equation of a line that passes through the point (4, 2) and is perpendicular to the line whose equation is y=x3−1 ?
Answers
Answer:
y = -3x + 14
Step-by-step explanation:
13. Identify the y-intercept and the slope for each equation.
a. y=6x-3
b. y=-2 (x + 5)
c. y = 4 (-x + 1)
HELP ASAP
Answers
Answer:
For a ) y = 6x - 3
[tex]slope = m = 6\\y-intercept = c = -3\\[/tex]
For b ) y = -2x - 10
[tex]slope = m = -2\\y-intercept = c = -10\\[/tex]
For c ) y = -4x + 4
[tex]slope = m = -4\\y-intercept = c = 4\\[/tex]
Step-by-step explanation:
Given:
a. y = 6x - 3
b. y = -2 (x + 5)
y = -2x - 10
c. y = 4 (-x + 1)
y = -4x + 4
To Find:
y-intercept and the slope for each equation = ?
Solution:
Slope-intercept Formula is given by
[tex]y=mx+c[/tex]
Where,
m = slope
c = y-intercept
So on comparing the Given equations with the above Equation we get
For a ) y = 6x - 3
[tex]slope = m = 6\\y-intercept = c = -3\\[/tex]
For b ) y = -2x - 10
[tex]slope = m = -2\\y-intercept = c = -10\\[/tex]
For c ) y = -4x + 4
[tex]slope = m = -4\\y-intercept = c = 4\\[/tex]
Justin is considering two websites for downloading music.The costs are detailed here.
Website 1: a yearly fee of $30 and $1.50 for each download
Website 2: $2 for each download
What is a system of equations to represent the costs for one year?
Express your equations in the form of y=mx+b where x is the number of downloads for the year and y is the total cost for the year.
Enter your equations in the boxes.
Answers
Answer:
y = 30 + 1.5x and y = 2x
Step-by-step explanation:
Website 1 has a plan for a yearly fee of $30 and $1.5 for each download.
Therefore, if x is the number of downloads for a year and y is the total cost for the year, then we can model the conditions as
y = 30 + 1.5x ......... (1)
Website 2 has a plan of $2 for each download.
Therefore, we can models the condition as
y = 2x ........ (2)
Therefore, equations (1) and (2) represent the costs for one year. (Answer)
I need help on this it is a fraction subtract another fraction which is negative thx to whoever helps 5/7-(-1/7)
Answers
Answer:
[tex]\frac{5}{7}-(-\frac{1}{7})=\frac{6}{7}[/tex]
Step-by-step explanation:
To evaluate :
[tex]\frac{5}{7}-(-\frac{1}{7})[/tex]
Solution:
Two negatives multiply to become a positive.
Thus, we can remove parenthesis by reversing the signs of the fraction by multiplying the negative outside.
⇒ [tex]\frac{5}{7}+\frac{1}{7}[/tex]
Since the denominators are same for both fractions, so we simply add the numerators.
⇒ [tex]\frac{5+1}{7}[/tex]
⇒ [tex]\frac{6}{7}[/tex] (Answer)
Determine the principal P that must be invested at rate r = 3%, compounded monthly, so that $500,000 will be available for retirement in t = 15 years. (Round your answer to the nearest cent.)
Answers
Answer:
$2,444.95
Step-by-step explanation:
A = P (1 + r)^(nt)
where A is the final amount,
P is the principal,
r is the rate,
n is the compoundings per year,
and t is the number of years.
500,000 = P (1 + 0.03)^(12 × 15)
500,000 = P (1.03)^180
P = 500,00 (1.03)^-180
P ≈ 2,444.95
Final answer:
To determine the principal amount that must be invested at a rate of 3%, compounded monthly, to have $500,000 available for retirement in 15 years, the formula for compound interest can be used. The principal that must be invested is approximately $310,334.84.
Explanation:
To determine the principal amount that must be invested at a rate of 3%, compounded monthly, to have $500,000 available for retirement in 15 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the future value, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
Plugging in the given values, we have:
A = $500,000, r = 0.03 (3%), n = 12 (compounded monthly), and t = 15.
Substituting these values into the formula, we get:
$500,000 = P(1 + 0.03/12)^(12*15)
Solving for P gives:
P = $500,000 / (1 + 0.03/12)^(12*15)
Calculating this expression gives P ≈ $310,334.84. Therefore, the principal that must be invested is approximately $310,334.84.
84.19 take away 49.79 equal
Answers
Answer:
34.4
Step-by-step explanation:
Answer:
34.4
Step-by-step explanation:
USE A CALCULATOR!!!!
Factor completely
25x^2 - 35x + 7y - y^2
Answers
Answer:
5x(5x-7)+y(7-y)
Step-by-step explanation:
25x^2-35x+7y-y^2
5x(5x-7)+y(7-y)
Answer:
(5x-7y) (5x-y)
Step-by-step explanation:
what is exactly half of 14 and 77
Answers
The half of 14 is 7 and the half of 77 is 38.5
Hope this helped! (Plz mark me brainliest)
Dina wants to make 15 3/4 cups of strawberry drink by mixing water and strawberry syrup with a ratio of 2 1/4 cup of water for every 3/4 cup of syrup. how much water and syrup will she need ro use?
Answers
Answer:
The water she need is [tex]7\frac{7}{8} \ cups.[/tex] and strawberry syrup [tex]11\frac{13}{16}\ cups[/tex].
Step-by-step explanation:
Given:
Dina wants to make 15 3/4 cups of strawberry drink by mixing water and strawberry syrup with a ratio of 2 1/4 cup of water for every 3/4 cup of syrup.
Now, to find the quantity of water and syrup she need to use.
As given in question ratio so:
Strawberry syrup = 2 1/4 = 9/4.
Water = 3/4.
Total cups of strawberry drink = 15 3/4 = 63/4.
Let the strawberry syrup be [tex]\frac{9}{4} x[/tex].
And let the water be [tex]\frac{3}{4} x[/tex].
According to question:
[tex]\frac{9x}{4} + \frac{3x}{4}=\frac{63}{4}[/tex].
On adding the fractions:
⇒[tex]\frac{9x+3x}{4} =\frac{63}{4}[/tex]
⇒[tex]\frac{12x}{4} =\frac{63}{4}[/tex]
Multiplying both sides by 4 we get:
⇒[tex]12x=63[/tex]
Dividing both sides by 12 we get:
⇒[tex]x=\frac{63}{12}[/tex]
Dividing numerator and denominator by 3 on R.H.S we get:
⇒[tex]x=\frac{21}{4}[/tex]
Now, putting the value of [tex]x[/tex] on ratios:
Strawberry syrup = [tex]\frac{9}{4}\times x=\frac{9}{4}\times\frac{21}{4}[/tex]
= [tex]\frac{189}{16}[/tex]
= [tex]11\frac{13}{16}\ cups[/tex]
Water = [tex]\frac{3}{4}\times x =\frac{3}{4} \times\frac{21}{4}[/tex]
= [tex]\frac{63}{8}[/tex]
= [tex]7\frac{7}{8} \ cups.[/tex]
Therefore, the water she need is [tex]7\frac{7}{8} \ cups.[/tex] and strawberry syrup [tex]11\frac{13}{16}\ cups[/tex].
solve 4x-3y=-1 and 2x+3y=13 using the elimination method
Answers
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
4x-3y=-1 ...(1)
2x+3y=13..(2)
add (1) and (2) : 4x-3y + 2x+3y = -1 +13
6x =12
x = 12/6 = 2
put x = 6 in (2) : 2(2)+3y = 13
4+3y =13
3y =9
y=3
Evaluate.
52+7⋅3+4
40
50
55
224
Answers
Answer:
77
Step-by-step explanation:
Simplify the following:
52 + 7×3 + 4
7×3 = 21:
52 + 21 + 4
| 5 | 2
| 2 | 1
+ | | 4
| 7 | 7:
Answer: 77
To evaluate the expression 52 + 7 ⋅ 3 + 4, follow the order of operations (PEMDAS). First, multiply 7 by 3 to get 21, then add 52 and 4 to get the final result of 77.
Evaluation of the Expression:
To evaluate the expression 52 + 7 ⋅ 3 + 4, it is important to follow the order of operations (PEMDAS/BODMAS):
ParenthesesExponentsMultiplication and Division (left to right)Addition and Subtraction (left to right)Using these rules, solve the expression step-by-step:
First, handle the multiplication: 7 ⋅ 3 = 21Next, perform the addition: 52 + 21 + 4Simplify further: 73 + 4 = 77Therefore, the correct answer is:
77
Please help me and show steps! I would really appreciate it!
Answers
Answer:
The aircraft has a height of 1000 m at t=2 sec, and at t=8 sec
Step-by-step explanation:
Finding Exact Roots Of Polynomials
A polynomial can be expressed in the general form
[tex]\displaystyle p(x)=a_nx^n+a_{n-1}\ x^{n-1}+...+a_1\ x+a_0}[/tex]
The roots of the polynomial are the values of x for which
[tex]P(x)=0[/tex]
Finding the roots is not an easy task and trying to find a general solution has been discussed for centuries. One of the best possible approaches is trying to factor the polynomial. It requires a good eye and experience, but it gives excellent results.
The function for the trajectory of an aircraft is given by
[tex]\displaystyle h(x)=0.5(-t^4+10t^3-216t^2+2000t-1200)[/tex]
We need to find the values of t that make H=1000, that is
[tex]\displaystyle 0.5(-t^4+10t^3-216t^2+2000t-1200)=1000[/tex]
Dividing by -0.5
[tex]\displaystyle t^4-10t^3+216t^2-2000t+1200=-2000[/tex]
Rearranging, we set up the equation to solve
[tex]\displaystyle t^4-10t^3+216t^2-2000t+3200=0[/tex]
Expanding some terms
[tex]\displaystyle t^4-8t^3-2t^3+200t^2+16t^2-1600t-400t+3200=0[/tex]
Rearranging
[tex]\displaystyle t^4-8t^3+200t^2-1600t-2t^3+16t^2-400t+3200=0[/tex]
Factoring
[tex]\displaystyle t(t^3-8t^2+200t-1600)-2(t^3-8t^2+200t-1600)=0[/tex]
[tex]\displaystyle (t-2)(t^3-8t^2+200t-1600)=0[/tex]
This produces our first root t=2. Now let's factor the remaining polynomial
[tex]\displaystyle t^2(t-8)+200(t-8)=0[/tex]
[tex]\displaystyle (t^2+200)(t-8)=0[/tex]
This gives us the second real root t=8. The other two roots are not real numbers, so we only keep two solutions
[tex]\displaystyle t=2,\ t=8[/tex]