Answer
Explanation
To know how many solutions this system of linear equations have, we willl need to solve it.
2x + 3y = 6
-8x - 12y = -20
Making x the subject of formula in the first equation
2x + 3y = 6
2x = -3y + 6
Divide through by 2
(2x/2) = (-3y/2) + (6/2)
x = (-3y/2) + 3
Substituting this for x in the second equation
-8x - 12y = -20
x = (-3y/2) + 3
-8 (-3
HELP HELP PLEASE!!!!!!!!!!!!!!!!!!!!
There are 5.65 milliliters of water in a jar. Tess wants only 3.85 milliliters of water in the jar. She calculates that she should remove 1.8 milliliters of water. Which statement shows whether Tess is correct? (1 point)
She is correct. 5.65 + 1.8 = 3.85.
She is correct. 3.85 + 1.8 = 5.65.
She is incorrect. 5.65 + 1.8 = 7.45.
She is incorrect. 3.85 + 1.8 = 4.65.
Answer:
She is incorrect
Step-by-step explanation:
5.65 + 1.8 = 7.45
Answer:
She is correct. 3.85 + 1.8 = 5.65
Step-by-step explanation:
She is correct. 3.85 + 1.8 = 5.65
Classify the equation 6x + 4x - 1 = 2(5x + 4) as having one solution, infinitely many solutions, or no solution. Enter integers or expressions to complete the solution. (Simplify your answers.) Since - 1 = 8, the equation has no solution(s).
Solve;
[tex]\begin{gathered} 6x+4x-1=2(5x+4) \\ \text{Solve the parenthesis,} \\ 10x-1=10x+8 \\ \text{Collect all like terms} \\ 10x-10x=8+1 \\ 0=9 \\ \text{This equation has no solution because 0=9 is not possible} \end{gathered}[/tex]The answer is
No solution
Evaluate the expression y=-4y^2 + 6y+9by th way that's y to the power of 2
we have the following:
[tex]y^2+6y+9[/tex]replacing, y = -4
[tex]\begin{gathered} (-4)^2+6\cdot(-4)+9 \\ 16-24+9=25-24=1 \end{gathered}[/tex]therefore, the answer is 1
What makes the value of X that makes l1 l2?
A. 10
Explanation:From the figure provided:
<(4x)⁰ and <(2x+20)⁰ are alternate interior angles
Note that:
Alternate interior angles are equal
4x = 2x + 20
Collect like terms
4x - 2x = 20
2x = 20
x = 20/2
x = 10
( 5b. A square has an area of 9 cm². What is its side length?
Answer: 2.25
Step-by-step explanation:
9 divided by 4 = 2.25
4 sides on the shape
2.25 cm on one side!
Which decimal equivalent is NOT correct for the given set of numbers
EXPLANATION
Since the value 7/10 is equivalent to 0.7, not to 0.07, the last equivalence is NOT correct.
Consider the following advertisement.Which of the following calculations represents the cost of 2 dozen iris bulbs?
Answer:
C: (6 x $5)+(6 x $4)+(12 x $3)
Explanation:
The total number of bulbs bought = 2 dozens = 2 x 12 = 24
• The cost per bulb for the first half-dozen = $5
[tex]\text{Cost for the first half-dozen=6 x \$5}[/tex]• The cost per bulb for the next half-dozen = $4
[tex]\text{Cost for the next half-dozen=6 x \$}4[/tex]Out of 24 bulbs, we have calculated the cost for 12.
• The number of bulbs left = 24 - 12 = 12.
,• Each additional bulb is $3 per bulb.
The cost for the last 12 will be:
[tex]12\times\$3[/tex]Therefore, the cost for the 2 dozen iris bulbs will be:
[tex](6\times\$5)+(6\times\$4)+(12\times\$3)[/tex]The correct choice is C.
•
•
Which of the following products is irrational?
Answer:
B, C are irrational
Step-by-step explanation:
Not a ratio
Identify the slope and y-intercept of equation y= 3x-10
To answer this question, we need to remember that the slope-intercept form of the line is given by:
[tex]y=mx+b[/tex]Where
• m is the slope of line
,• b is the y-intercept of the line, that is, the point where the line passes through the y-axis. At this point, x = 0.
Since we can see that the given equation is in slope-intercept form:
[tex]y=3x-10[/tex]We can see that the slope of the line is:
[tex]m=3[/tex]And the y-intercept is:
[tex]\begin{gathered} b=-10 \\ (0,-10) \end{gathered}[/tex]In summary, we have that
• The slope of the line is m = 3.
,• The y-intercept of the line is (0, -10)
Two friends drive off in different directions from the same place. one heads north at 25 miles per hour, while the other heads east at 40 miles per hour. complete an equation for the distance between the friends after t hours.
Answer: [tex]5t\sqrt{89}[/tex] miles
=======================================================
Explanation:
Draw a right triangle. The legs of this triangle represent the directions the two friends travel (one going east, the other going north).
The horizontal leg has side length 40t and the vertical leg has length 25t, where t is the number of hours.
I'm using the idea that distance = rate*time.
We'll use the pythagorean theorem to find the hypotenuse in terms of t.
[tex]a = 40t, \ b = 25t\\\\a^2 + b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{(40t)^2+(25t)^2}\\\\c = \sqrt{1600t^2+625t^2}\\\\c = \sqrt{2225t^2}\\\\c = \sqrt{25*89t^2}\\\\c = \sqrt{25t^2}*\sqrt{89}\\\\c = 5t\sqrt{89}\\\\[/tex]
At time t hours, the distance between the two friends is exactly [tex]5t\sqrt{89}[/tex] miles.
the terminal side θ passes through the point (8,-7) what is the exact value of θ in simplified form?
Given:
the terminal side θ passes through the point (8,-7)
so,
[tex](x,y)=(8,-7)[/tex]The point lying in quarter number 4
so,
[tex]\begin{gathered} \tan \theta=\frac{y}{x}=-\frac{7}{8} \\ \\ \theta=\tan ^{-1}(-\frac{7}{8})=-41.186 \\ \\ \theta=360-41.186=318.814 \end{gathered}[/tex]
Multiply 2 2/3 • 1 5/6 Simplify the answer and write as a mixed number.
Answer:18 and 1/3
Step-by-step explanation:22
3
(15)
6
=
55
3
(Decimal: 18.333333) and then as a mixed number is:
A line is drawn on a scatter plot, as shown below:
The line of best fit is the line which closely fits the data points.
Therefore from the look of the graph the statement which best defines the line is that it is the line of best fit because it closely fits the data points. Hence the fourth option is right.
4)PQRS is a rectangle. The length of the diagonal PR is 10cm. If PQ = 8cm, find the perimeter of the
rectangle.
The perimeter of the rectangle PQRS would be 28 cm which is the addition of all lengths of sides.
The given rectangle PQRS that has a length of the diagonal PR is 10 cm and PQ = 8 cm
What is the perimeter of the rectangle?The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.
To determine the perimeter of the rectangle.
Since opposite sides of the rectangle and diagonal are equal.
⇒ PQ = SR = 8 cm
⇒ PR = QS = 10 cm
⇒ PS = QR = x cm (suppose)
In the rectangle, all the angles are right angles
Now in △QRS,
Using Pythagoras' theorem, we have
QS² = QR² + SR²
10² = x² + 8²
x² = 100 - 64
x =√36
x = 6 cm
So length of PS = QR = 6 cm
The perimeter of the rectangle = PQ + SR + PS + QR
The perimeter of the rectangle = 8 + 8 + 6 + 6 = 28 cm
Therefore, the perimeter of the rectangle PQRS would be 28 cm.
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The table below shows a probability density function for a discrete random variable X. What is the probability that X is 2 or 3?
Answer:
Step-by-step explanation:
Santa owed $91 on a bill. By mistake Santa sent a check for $120. What is the balance on Santa's account?
ANSWER
[tex]\$29[/tex]EXPLANATION
To find the balance on Santa's account, we have to subtract the amount he owed from the amount on the check he sent.
Therefore, the balance on Santa's account is:
[tex]\begin{gathered} 120-91 \\ \Rightarrow\$29 \end{gathered}[/tex]That is the answer.
My family has 12 member coming for Christmas dinner. Each person eats an average of 4 lbs of food. How much food should I prepare?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Family
12 members
4 lb food per person
total food = ?
Step 02:
total food
[tex]\begin{gathered} \text{total food = 12 people}\cdot\frac{4lb}{\text{person}} \\ \end{gathered}[/tex]total food = 48 lb
The answer is:
You should prepare 48 lb of food
Plot points between and beyond the Exitir serves in the vertical asymptote evaluate the function at -5, -2,2,5 and 6 Simplify
Step 1: Write out the definition of the function f:
The function f is given by:
[tex]f(x)=\frac{x^2-9}{x}[/tex]Step 2: Calculate the value of the function f at t=-5:
[tex]\begin{gathered} f(-5)=\frac{(-5)^2-9}{(-5)} \\ \text{Hence,} \\ f(-5)=\frac{25-9}{-5}=-\frac{16}{5} \end{gathered}[/tex]Step 3: Calculate the value of the function f at t=-2:
[tex]\begin{gathered} f(-2)=\frac{(-2)^2-9}{(-2)} \\ \text{Hence,} \\ f(-2)=\frac{4-9}{-2}=\frac{-5}{-2}=\frac{5}{2} \end{gathered}[/tex]Step 4: Calculate the value of the function f at t=2:
[tex]\begin{gathered} f(2)=\frac{(2)^2-9}{(2)} \\ \text{Hence,} \\ f(2)=\frac{4-9}{2}=-\frac{5}{2} \end{gathered}[/tex]Step 5: Calculate the value of the function f at t=5:
[tex]\begin{gathered} f(5)=\frac{(5)^2-9}{(5)} \\ \text{Hence,} \\ f(5)=\frac{25-9}{5}=\frac{16}{5} \end{gathered}[/tex]Step 6: Calculate the value of the function f at t=6:
[tex]\begin{gathered} f(6)=\frac{(6)^2-9}{(6)} \\ \text{Hence,} \\ f(6)=\frac{36-9}{6}=\frac{27}{6}=\frac{9}{2} \end{gathered}[/tex]Hence
find the value of x using the kite below (work required)
Since the diagonals in a kite intersect creating a right angle, the angles 2x° and (10x - 6)° are complementary angles. So we have:
[tex]\begin{gathered} 2x+(10x-6)=90 \\ 12x-6=90 \\ 12x=96 \\ x=\frac{96}{12} \\ x=8 \end{gathered}[/tex]So the value of x is 8.
he Hamiltons are paving their driveway. They are paving a rectangular area and an area in the shape of a parallelogram to make it easier to turn around and pull out of the driveway. A sketch of the plan for their driveway uses a scale of 1 in. for every 3 ft. What is the actual area of the entire driveway they want to pave?
If they are paving a rectangular area and an area in the shape of a parallelogram to make it easier to turn around and pull out of the driveway. A sketch of the plan for their driveway uses a scale of 1 in. for every 3 ft. The actual area of the entire driveway they want to pave Is 1350 feet²
Actual areaFirst step is to find the length of both side
Actual length on side
Length = ( 5 + 4) × 3
Length = 9 × 3
Length = 27 feet
Actual length of the other side
Length = 16 2/3 × 3
Length = 16 ×3 +2/3 ×3
Length = 16×3+2
Length = 48 +2
Length = 50 feet
Now let determine the actual area of the whole driveway they want t0 pace
Actual area = 50 feet × 27 feet
Actual area = 1350 feet²
Therefore we can conclude that the actual area is 1350 feet².
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Geometry Angle of Depression and Angle of Elevation. 2. - 3.
2) We can draw this situation as:
We can now find the angle x.
We can use trigonometric ratios as:
[tex]\begin{gathered} \tan(x)=\frac{Opposite}{Adjacent}=\frac{23}{34} \\ x=\arctan(\frac{23}{34}) \\ x\approx34.08\degree \end{gathered}[/tex]3) We can draw this situation as:
We can find x as:
[tex]\begin{gathered} \tan(x)=\frac{Opposite}{Adjacent}=\frac{12}{17} \\ x=\arctan(12/17) \\ x\approx35.22\degree \end{gathered}[/tex]Answer:
2) 34.08°
3) 35.22°
a ____ polynomial is a polynomial with a degree of 3
Let's understand some definitions first:
Polynomial - an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s). (oxford languages)
When we have 1 term, we call it a monomial.
When we have 2 terms, we call it a binomial.
When we have 3 terms, we call it a trinomial.
Now,
• When the power of a variable is 1, we call it a line:
[tex]\begin{gathered} x \\ 2x \\ \text{etc.} \end{gathered}[/tex]• When the highest power is 2, we call it a quadratic polynomial:
[tex]\begin{gathered} x^2 \\ 3x^2 \end{gathered}[/tex]• When the highest power is 3, we call it a cubic polynomial:
[tex]\begin{gathered} x^3 \\ -2x^3 \end{gathered}[/tex]Question
A ____ polynomial is a polynomial with a degree of 3
Answer
A cubic polynomial is a polynomial with a degree of 3
Solve x for the following equation
2^-x =3 * 2^x
in words: 2 to the power of -x = 3 times 2 to the power of x
The solution of x for the exponential equation 2⁻ˣ =3 × 2ˣ would be x = - log 3 / log 2.
What are the properties of logarithms?There are four basic properties of logarithms:
logₐ(xy) = logₐx + logₐy.
logₐ(x/y) = logₐx - logₐy.
logₐ(xⁿ) = n logₐx.
logₐx = logₓa / logₓb.
The given exponential equation below is:
2⁻ˣ = 3 × 2ˣ
Take the logarithm on both sides of the equation,
log 2⁻ˣ = log 3 × 2ˣ
-x log 2 = log 3 + log 2ˣ
-x log 2 = log 3 + x log 2
x log 2 = - log 3
x = - log 3 / log 2
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A mint milk shake contains 1.25 fluid ounces of milk for every 4 ounces of ice cream. A strawberry milk shake contains 1.75 fluid ounces of milk for every 5 ounces of ice cream. Which milk shake is thicker? Explain.?
Both milkshakes have the same thickness.
How to find the thickness of milk?
Given,
A mint milkshake contains 1.25 fluid ounces of milk for every 4 ounces of ice cream.A strawberry milkshake contains 1.75 fluid ounces of milk for every 5 ounces of ice cream.Solution:
Since the mint milkshake contains 1.25 fluid ounces of milk for every 4 ounces of ice cream,One ounce ice equal = 1.25 / 4 = 0.35 ounce of milk.Since the strawberry milkshake contains 1.75 fluid ounces of milk for every 5 ounces of ice cream,One ounce of ice equal = 1.75 / 5 = 0.35ounce of milk.Since both have an equal milk-ice ratio, both milkshakes have the same thickness.To learn more about ratios, refer
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Macy babysits the children in her neighborhood. For each family, she charges a flat fee plus a per hour charge as described by the data in the table.Which equation represents the total amount Macy charges for each family where x represents the number of hours she babysits? A. y = 4x + 71 B. y = 9x + 7 C. y = 4x + 36 D. y = 13x + 117
Answer:
B. y=9x+
Explanation:
To deermine tehe equation, pick two pairs of points from the table.
• The points are (8, 79) and (12, 115)
Substitute these points into the lope-ointercept form of the equation of a line.
[tex]y=mx+b[/tex]At (8,79): x=8 and y=79
[tex]79=8m+b[/tex]At (12, 115): x=12 and y=115
[tex]115=12m+b[/tex]Solve the two equations siultaneously fror m and b.
[tex]\begin{gathered} 79=8m+b \\ 115=12m+b \\ Subtract \\ -36=-4m \\ \implies m=\frac{-36}{-4}=9 \end{gathered}[/tex]Next, substitute m=9 into the first equation to solve for b:
[tex]\begin{gathered} 79=8m+b \\ 79=8(9)+b \\ b=79-72 \\ b=7 \end{gathered}[/tex]Substitute m=9 and b=7 into the slope-intercept form:
[tex]y=9x+7[/tex]The equation that represents the total amount Macy charges for each family where x represents the number of hours she babysits is:
[tex]y=9x+7[/tex]Option B is correct.
6 3/4 ÷ 1 7/8=how do I figure those out?
6The given expression is 6 3/4 ÷ 1 7/8 is :
[tex]6\frac{3}{4}\div1\frac{7}{8}=\text{ }\frac{}{\square}[/tex]Express the mixed frcation in the normal forM :
[tex]\begin{gathered} 6\frac{3}{4}=\frac{6\times4+3}{4} \\ 6\frac{3}{4}=\frac{27}{4} \end{gathered}[/tex]Similarly with the 1 7/8
[tex]\begin{gathered} 1\frac{7}{8}=\frac{1\times8+7}{8} \\ 1\frac{7}{8}=\frac{15}{8} \end{gathered}[/tex]Substitute the value and simplify :
[tex]\begin{gathered} 6\frac{3}{4}\div1\frac{7}{8}=\frac{27}{4}\div\frac{15}{8} \\ 6\frac{3}{4}\div1\frac{7}{8}=\frac{27}{4}\times\frac{8}{15} \\ 6\frac{3}{4}\div1\frac{7}{8}=\frac{9}{1}\times\frac{2}{5} \\ 6\frac{3}{4}\div1\frac{7}{8}=\frac{18}{5} \end{gathered}[/tex]18/5 in the mixed fraction :
18/5 = 3 3/5
Answer : 6 3/4 ÷ 1 7/8 = 18/5 or 3 3/5
The equation below describes a circle. What are the coordinates of the centerof the circle?(x-4)^2 + (y+12)^2 = 17²O A. (4,12)OB. (-4,-12)O C. (-4,12)OD. (4, -12)21
Solution:
The equation is given below as
[tex](x-4)^2+(y+12)^2=17^2[/tex]Concept:
The general equation of a circle is given below as
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ where, \\ (h,k)=center \end{gathered}[/tex]Hence,
By comparing coefficients, we will have the center of the circle be
[tex](h,k)\Rightarrow(4,-12)[/tex]Hence,
The final answer is
[tex]\Rightarrow(4,-12)[/tex]OPTION D is the right answer
Lance had 24 apps on his phone. If the ratio of educational apps to gaming apps is 5:1, how many educational apps are there?
help me with this
PLEASE HELP DUE IN 23 and I’ll be giving 25 points to whoever helps me.Thank you
Answer:
x = 17
Step-by-step explanation:
(6x - 20) and the angle vertically opposite (6x - 4) are same- side interior angles and sum to 180° , that is
6x - 20 + 6x - 4 = 180
12x - 24 = 180 ( add 24 to both sides )
12x = 204 ( divide both sides by 12 )
x = 17
At an after-season sale on winter clothes, I found a bunch of really cute hats and scarves. I decided to buy two hats and two scarves for myself to have for next year. I spent $72. When I told my friends about the sale, they asked me to go back and get something for them. I ended up spending $46 on one hat and two scarves. What was the price of a single hat and a single scarf?Write two integers separated by comma, no spaces, no dollar sign
ANSWER
One hat costs $26 and one scarf costs $10
EXPLANATION
Let the price of one hat be h.
Let the price of one scarf be s.
Two hats and two scarves cost $72. This implies that:
[tex]2h+2s=72[/tex]One hat and two scarves cost $46. This implies that:
[tex]h+2s=46[/tex]From the second equation, make h the subject of the formula:
[tex]h=46-2s[/tex]Substitute that into the first equation and solve for s:
[tex]\begin{gathered} 2(46-2s)+2s=72 \\ 92-4s+2s=72 \\ \Rightarrow92-72=4s-2s \\ 2s=20 \\ \Rightarrow s=\frac{20}{2} \\ s=\$10 \end{gathered}[/tex]Substitute the value of s into the equation for h and solve for h:
[tex]\begin{gathered} h=46-2(10) \\ h=46-20 \\ h=\$26 \end{gathered}[/tex]Hence, one hat costs $26 and one scarf costs $10.
