Answer:
[tex]\left(-\frac{1}{2},\frac{\sqrt{3}}{2}\right)[/tex]
Step-by-step explanation:
We know that coordinate of any point on unit circle is given by
[tex]\left(\cos\left(\theta\right),\sin\left(\theta\right)\right)[/tex]
Given that [tex]\theta=-\frac{4\pi}{3}[/tex]
So we just need to plug the value of given angle [tex]\theta=-\frac{4\pi}{3}[/tex] into above formula:
[tex]\left(\cos\left(\theta\right),\sin\left(\theta\right)\right)[/tex]
[tex]=\left(\cos\left(-\frac{4\pi}{3}\right),\sin\left(-\frac{4\pi}{3}\right)\right)[/tex]
[tex]=\left(\cos\left(2\pi-\frac{4\pi}{3}\right),\sin\left(2\pi-\frac{4\pi}{3}\right)\right)[/tex]
[tex]=\left(\cos\left(\frac{2\pi}{3}\right),\sin\left(\frac{2\pi}{3}\right)\right)[/tex]
[tex]=\left(-\frac{1}{2},\frac{\sqrt{3}}{2}\right)[/tex]
Hence choice (3) is correct.
Answer:
-1/2, √3/2
Step-by-step explanation:
in 2004, there were approximately 7100 cinema sites. In 2000, there were 8300.
Write an equation describing this relationship.
The relationship between the year and the number of cinema sites can be expressed with the linear equation y = -300x + 608300, where y is the number of cinema sites and x is the year. This equation was derived by calculating the slope and y-intercept using the points provided.
Explanation:The subject of the question falls into the domain of mathematics, specifically algebra. We are given two points on a line where the x-axis is the year and the y-axis represents the number of cinema sites. The two points are (2000, 8300) and (2004, 7100).
First, we need to calculate the slope, m: m = (y2 - y1) / (x2 - x1) = (7100 - 8300) / (2004 - 2000) = -1200 / 4 = -300.
The slope, -300, is the rate of change suggesting the number of cinemas decreases by 300 each year.
The equation of the line, or the linear equation, will be in the form y = mx + b. We now need to find the y-intercept (b) by substituting one of our points into the equation and solving for b.
If we use the point (2000, 8300): 8300 = -300*2000 + b. Solving for b gives b = 8300 + 600000 = 608300.
Therefore, the equation describing the relationship between the year and the number of cinema sites is y = -300x + 608300.
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Jaz was 43 inches tall. 18 months later she was 52 inches tall. Find the constant rate of change for Jaz's height.
Carlotta drove 72.6 miles on Monday. She drove 84.18 miles on Tuesday. Which gives the best estimate for how many more miles Carlotta drove on Tuesday?
A)84 – 73 = 11 miles
B)73 – 84 = 11 miles
C)85 – 72 = 13 miles
D)84 – 71 = 13 miles
Answer:
A)84 – 73 = 11 miles
Step-by-step explanation:
On Tuesday she drove 84 miles (rounding to the nearest mile)
On Monday she drove 73 miles (rounding to the nearest mile)
Tuesday's mileage - Mondays miles = difference in miles
84-73 = 11 miles
Answer: A. 84 – 73 = 11 mi
Carmen enters a painting in an art contest. The contest rules say that all paintings must be rectangular, with an area no greater that 3,003.04 cm2. Carmen painting is 16 cm wode. What is the greatest lenth the painting can have and still have an area within the contest rules?
Answer:
187.69 cm
Step-by-step explanation:
We have that the maximum area allowed for the painting = 3003.04 [tex]cm^{2}[/tex].
Also, the width of Carmen's painting = 16 cm.
It is required to maximum length of Carmen's painting that will be eligible to take part in the competition.
Let the maximum length of the painting = L cm.
Since, Area of a rectangle = length of the rectangle × width of the rectangle.
i.e. 3003.04 = L × 16
i.e. [tex]L=\frac{3003.04}{16}[/tex]
i.e. L = 187.69 cm
Hence, the length of the painting should not exceed 187.69 cm in order to be eligible to participate in the competition.
Solve by elimination
2x-y=0
3x-2y=-3
To solve a system of equations by elimination, make the coefficients of one variable equal. Subtract one equation from the other to solve for one variable, then substitute this solution into one of the original equations to solve for the other variable. In this case, the solution to the given system of equations is x = 3, y = 6.
Explanation:In mathematics, specifically in algebra, the method of elimination is used to solve a system of simultaneous equations. Your equations are:
2x -y = 03x - 2y = -3To solve this system by elimination, we need to make the coefficients of y in both equations equal by multiplying if necessary. We can obtain this by multiplying the first equation by 2:
4x - 2y = 0
3x - 2y = -3
Next, we subtract one equation from the other to eliminate y:
4x - 3x = 0 - (-3) => x = 3
To find y, substitute x = 3 into the first equation:
2*3 - y = 0 => y = 2*3 = 6
So, the solution to the system of equations is x = 3, y = 6.
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Jayda is cutting a roll of biscuit dough into slices that are 3/4 inches thick if the roll is 10 1/2 inches long how many slices can he cut?
Answer:
Jayda can cut 14 slices of dough that are 3/4 inches thick.
Step-by-step explanation:
In order to solve this problem, we need to take the total amount of dough at 10 1/2 inches and divide it by the thickness of one slide, 3/4 inches, to find the number of slices that can be made from the total amount. You can solve this two different ways. You can either convert your fractions to decimals so that 10 1/2 becomes 10.5 and 3/4 become 0.75 and then divide 10.5/0.75 to get 14. However, you can also keep them as fractions converting 10 1/2 to 21/2 and dividing by 3/4. When we divide with fractions with keep-change-flip, or keep the first fraction-change the sign to multiplication-flip the second fraction. So, we multiply 21/2 x 4/3 and get 84/6, or 14.
Mr robbins earns a commission on each airfare he books. At the end of the day,he had booked $208.60 worth if airfare and earned $31.29. Approximately what is Mr. Robins commision rate.
Answer:
Mr. Robins commision rate is 15%.
Step-by-step explanation:
Formula
[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]
As given
Mr robbins earns a commission on each airfare he books.
At the end of the day,he had booked $208.60 worth if airfare and earned $31.29.
Here
Part value = $31.29
Total value = $208.60
Put in the formula
[tex]Percentage = \frac{31.29\times 100}{208.60}[/tex]
[tex]Percentage = \frac{312900}{20860}[/tex]
Percentage = 15%
Therefore the Mr. Robins commision rate is 15%.
What is the inverse of f(x)=(x-5)^2 for x greater or equal to 5 where function g is the inverse of function f
The inverse function of f(x) = (x - 5)² for x greater or equal to 5 is g(x) = sqrt(x) + 5.
Explanation:The function f(x) = (x - 5)² for x greater or equal to 5 has a specific inverse function denoted as g(x). To find the inverse of a function, one typical solution is to replace f(x) with y, swap x and y, and solve for y. Here, it means writing y = (x - 5)², changing it to x = (y - 5)², and solving for y.
The solved y function is g(x) = √(x) + 5 (where sqrt indicates a square root), ensuring the range for x is greater than or equal to 5 to adhere to the original function constraints.
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A herd of dinosaurs made paintings in the sand with their claws. Each baby dinosaur made 1515 paintings and each adult dinosaur made 77 paintings. The entire herd made 208208 paintings in total, and there were 33 times as many baby dinosaurs as adult dinosaurs. How many baby dinosaurs and adult dinosaurs were there?
Answer:
4 adult dinosaurs and 12 baby dinosaurs.
Step-by-step explanation:
Let the number of adult dinosaurs be x.
Number of baby dinosaurs = 3x
Number of paintings made by each baby dinosaur = 15
Number of paintings made by each adult dinosaur = 7
Total number of paintings made by 3x baby dinosaurs = Number of baby dinosaurs * Number of paintings made by each baby dinosaur
= 3x * 15
= 45x
Total number of paintings made by x adult dinosaurs = Number of adult dinosaurs * Number of paintings made by each adult dinosaur
= x * 7
= 7x
Total number of paintings made by both baby and adult dinosaurs = 45x + 7x
= 52 x
Again the problem says that the total number of paintings made = 208
So, 52x = 208
Dividing both sides by 52
[tex]\frac{52x}{52}[/tex] = [tex]\frac{208}{52}[/tex]
Cancelling out the 52's from the top and bottom on the left
x = 4
So, number of adult dinosaurs = 4
Number of baby dinosaurs = 3x = 3*4 = 12
A system of equations based on the information given can be used to find the number of baby and adult dinosaurs. The two equations are 1515b + 77a = 208208 and b = 33a. Solve these to find the number of each type of dinosaur.
Explanation:This problem can be solved by setting up a system of equations. Let's denote the number of baby dinosaurs as 'b' and the number of adult dinosaurs as 'a'. Then, from the statement, we know two things:
'Each baby dinosaur made 1515 paintings and each adult dinosaur made 77 paintings. The entire herd made 208208 paintings in total, we can set up the equation as 1515b + 77a = 208208.'There were 33 times as many baby dinosaurs as adult dinosaurs', so this can be represented as b = 33a.By substituting the second equation into the first, we can determine the number of adult dinosaurs, and subsequently, the number of baby dinosaurs. Solving this would give us the solution needed.
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Brandy is trying to factor the quadratic $3x^2 - x - 10.$ She starts by assuming that the quadratic factors as \[3x^2 - x - 10 = (x + B)(3x + D),\]for some integers $B$ and $D.$ After some work, Brandy successfully factors the quadratic. Find the ordered pair $(B,D).$
Answer:
(B , D) = (-2,5)
Step-by-step explanation:
The given quadratic expression is
[tex]3x^{2} -x-10[/tex]
compare the given expression with [tex]ax^{2} +bx+c[/tex]
so we have [tex]a = 3 , b = -1 ,c = -10[/tex]
now [tex]ac=3 (-10)=- 30[/tex] and [tex]b= -1[/tex]
we need to find two numbers such that their product is -30 and sum is -1
-6 and 5 are such numbers
so we have
[tex]3x^{2} -6x+5x-10[/tex]
grouping first two terms and last two terms
[tex](3x^{2} -6x)+(5x-10)[/tex]
factor out 3x from first two terms and 5 from last two terms
[tex]3x(x-2) +5(x-2)[/tex]
[tex](x-2)(3x+5)[/tex] ( factor out (x-2))
[tex](x+(-2))(3x+5)[/tex]
hence B =-2 and D= 5
(B,D)= (-2,5)
The price of a pair of jeans was $45 after a 50% markup. What was the price of the jeans before the markup?
Answer:
$30
Step-by-step explanation:
Mark up is the profit on cost. if the pair of jeans was $45 after a 50% markup
Let the price of the jeans before the markup be p then;
p + 50%p = 45
1.5p =45
p = 45/1.5
p = 30
The price before mark up was $30, while the mark up or profit is $15. This shows 50% of the price before mark up.
A triangle has two side of length 10 and 14 what value could the length of the third side be check all that apply
A) 26
B) 16
C) 10
D) 8
E) 5
F) 2
If a, b and c are the lengths of the sides of a triangle then
if a ≤ b ≤ c, then a + b > c.
A) 10, 14, 26
10 + 14 = 24 < 26 INCORRECT :(
B) 10, 14, 16
10 + 14 = 24 > 16 CORRECT :)
C) 10, 10, 14
10 + 10 = 20 > 14 CORRECT :)
D) 8, 10, 14
8 + 10 = 18 > 14 CORRECT :)
E) 5, 10, 14
5 + 10 = 15 > 14 CORRECT :)
F) 2, 10, 14
2 + 10 = 12 < 14 INCORRECT :(
Answer: B) 16, C) 10, D) 8, E) 5Options B, C, D and E are correct answers.
Given that, a triangle has two sides of lengths 10 and 14.
We need to find what value could the length of the third side be and check all that apply.
What is the triangle inequality theorem?Triangle inequality, in Euclidean geometry, theorem that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c. In essence, the theorem states that the shortest distance between two points is a straight line.
Now, from the given options:
A) 10, 14, 26
10 + 14 = 24 < 26 the triangle can not be formed
B) 10, 14, 16
10 + 14 = 24 > 16 the triangle can be formed
C) 10, 10, 14
10 + 10 = 20 > 14 the triangle can be formed
D) 8, 10, 14
8 + 10 = 18 > 14 the triangle can be formed
E) 5, 10, 14
5 + 10 = 15 > 14 the triangle can be formed
F) 2, 10, 14
2 + 10 = 12 < 14 the triangle can not be formed
Therefore, options B, C, D and E are correct answers.
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Janie receives an allowance of \$3$3 per week. In addition, she can earn \$2$2 for each chore she does. This week, she wants to earn enough money to buy a CD for \$13$13. Janie can do fractions of chores. Write an inequality to determine the number of chores, cc, Janie must do this week to earn enough money to buy a CD.
Answer:
Number of chores done by Janie are 5.
Step-by-step explanation:
Janie's allowance per week is $3.
For each chore she earns $2.
Now we assume that number of chores in a week she does = c
Then total earning from chore = $2 × c
So for the purchase of CD total earning this week inequality will be
⇒ 3 + 2c [tex]\geq[/tex]13
⇒ 2c [tex]\geq[/tex] 13-3
⇒ c [tex]\geq[/tex] 10÷2
⇒ c [tex]\geq[/tex] 5
Stock in Ombor Medical Supplies earns a return of 5.3% annually, while bonds issued by Ombor Medical Supplies earns a return of 4.1% annually. If you invest a total of $2,400 in Ombor Medical Supplies, $1,400 of which is in bonds and $1,000 of which is in stocks, which side of the investment will show a greater return after six years, and how much greater will it be?
a. The stocks will earn $55.60 more than the bonds.
b. The stocks will earn $118.60 more than the bonds.
c. The bonds will earn $82.00 more than the stocks.
d. The bonds will earn $26.40 more than the stocks.
Answer:
d. The bonds will earn $26.40 more than the stocks.
Step-by-step explanation:
Assuming, the rates are uniform for 6 years.
Stock in Ombor Medical Supplies earns a return of 5.3% annually, so $1000 will yield annually;
[tex]0.053\times1000=53[/tex] dollars
Total amount in 6 years will become = [tex]53\times6=318[/tex] dollars
Bonds issued by Ombor Medical Supplies earns a return of 4.1% annually, so $1400 will yield annually;
[tex]0.041\times1400=57.40[/tex] dollars
Total amount in 6 years will become = [tex]57.40\times6=344.40[/tex] dollars
We can see that bonds have high yield than stocks.
So, difference amount is = [tex]344.40-318=26.40[/tex] dollars.
Therefore, The bonds will earn $26.40 more than the stocks.
Answer:
it is d
Step-by-step explanation:
i took the edu test :)
(-2/3, sqrt5/3) is a point on a unit circle. Find the cosine, cosecant, and sine of the angle.
Look at the picture.
[tex]\csc\theta=\dfrac{1}{\sin\theta}=\dfrac{1}{\frac{y}{r}}=\dfrac{r}{y}[/tex]
We have the right triangle x, y and r. From the Pythagorean theorem we have:
[tex]r^2=x^2+y^2\to r=\sqrt{x^2+y^2}[/tex]
We have the point
[tex]\left(-\dfrac{2}{3};\ \dfrac{\sqrt5}{3}\right)[/tex]
Substitute:
[tex]r=\sqrt{\left(-\dfrac{2}{3}\right)^2+\left(\dfrac{\sqrt5}{3}\right)^2}\\\\r=\sqrt{\dfrac{4}{9}+\dfrac{5}{9}}\\\\r=\sqrt{\dfrac{9}{9}}\\\\r=1[/tex]
[tex]\csc\theta=\dfrac{1}{\frac{\sqrt5}{3}}=\dfrac{3}{\sqrt5}=\dfrac{3\cdot\sqrt5}{\sqrt5\cdot\sqrt5}=\boxed{\dfrac{3\sqrt5}{5}}[/tex]
The cosine of the angle is -2/3, the sine is √5/3, and the cosecant, being the reciprocal of the sine, is √5/5 after rationalization.
The point (-2/3,√5/3) on a unit circle represents the cosine and sine of a specific angle. Here, the x-coordinate is the cosine of the angle, and the y-coordinate is the sine of the angle.
Therefore, the cosine of the angle is -2/3, and the sine is √5/3.
To find the cosecant of the angle, we take the reciprocal of the sine, which gives us 3/√5 or √5/5 after rationalizing the denominator.
Find the first six terms of the sequence.
a1 = -2, an = 3 • an-1
-6, -18, -54, -162, -486, -1458
-2, -6, -18, -54, -162, -486
-2, -6, -3, 0, 3, 6
0, 3, -6, -3, 0, 3
[tex]a_1=-2\\\\a_n=3\cdot a_{n-1}\\-----------------------------------\\a_1=-2\\\\a_2=3\cdot a_{2-1}=3\cdot a_1\to a_2=3(-2)=-6\\\\a_3=3\cdot a_{3-1}=3\cdot a_2\to a_3=3(-6)=-18\\\\a_4=3\cdot a_{4-1}=3\cdot a_3\to a_4=3(-18)=-54\\\\a_5=3\cdot a_{5-1}=3\cdot a_4\to a_5=3(-54)=-162\\\\a_6=3\cdot a_{6-1}=3\cdot a_5\to a_6=3(-162)=-486\\\\Answer:\ \boxed{-2,\ -6,\ -18,\ -54,\ -162,\ -486}[/tex]
5a + 5b + 5c + 5d
Which expression is another way to write the expression shown here?
A) 5abcd
B) 5a + bcd
C) 5(a + b + c + d)
D) (5a)(5b)(5c)(5d) what the answer
The correct way to rewrite the expression 5a + 5b + 5c + 5d using the distributive property is option C) 5(a + b + c + d).
The expression given is 5a + 5b + 5c + 5d. This is a sum where each term is multiplied by 5. According to the distributive property, also known as the distributive law of multiplication, a common factor can be factored out of a sum. The distributive property is represented as (A + B)C = AC + BC. In this case, the common factor is 5, and the sum of the variables a, b, c, and d is grouped, giving us 5(a + b + c + d).
So, the correct representation of the expression is 5(a + b + c + d), which corresponds to option C).
Please help me out!!!!!!!
Answer: 1%
Explanation:
Add up the frequencies in the bottom row: 350+200+245+125+66+10+4 = 1000
There are 1000 families total. Of this total, 10+4 = 14 families have more than six people. I added up the frequency counts for "7 people" and "8 people" to get 14.
Divide 14 over 1000 and we get 14/1000 = 0.014 = 1.4% which rounds to 1%
BRAINLIEST!!HELPPP!!
Answer:
the answer if am not wrong would be C.n+5
Step-by-step explanation:
Lisa's favorite chocolate candies are wrapped in the shape of a triangular prism with shiny gold paper as shown below. If all sides of the package are covered in the gold paper, what is the surface area of the amount that is wrapped?
Answer:
Surface Area = 150
Step-by-step explanation:
The surface area of this triangular prism is the sum of area of all the sides.
Surface Area = triangle 1 (with base 8 and height 3) + triangle 2 (same as triangle 1) + lateral surface 1 (with length 7 and width 5 (calculation shown below)) + lateral surface 2 (same as lateral surface 1) + bottom (side not shown with length 7 and width 8)
Triangle 1 area: [tex]\frac{1}{2}bh=\frac{1}{2}(8)(3)=12[/tex]Triangle 2 area: [tex]\frac{1}{2}bh=\frac{1}{2}(8)(3)=12[/tex]Lateral surface 1 (rectangle): [tex]l*w=(7)(5)=35[/tex]Lateral surface 2 (rectangle): [tex]l*w=(7)(5)=35[/tex]Bottom surface (rectangle): [tex]l*w=(7)(8)=56[/tex]Summing all these gives us the total surface area.
Total surface area = [tex]12+12+35+35+56=150[/tex]
**** The triangle shown is divided into half by the perpendicular line (3cm) to the base. So the base is divided in half (4 cm and 4 cm).
Now, we have a right triangle with one leg 4 cm and another leg 3 cm. How do we get the hypotenuse? We use Pythagorean Theorem. Which is:
[tex]leg^2+leg^2=hypotenuse^2\\3^2+4^2=hypotenuse^2\\25=hypotenuse^2\\hypotenuse=5[/tex]
Hence, the side length of the hypotenuse is 5 [used above in the calculation]
help me plzzzzzzzzz!
Which values from the given replacement set make up the solution set of the inequality?
2b–4≥2 ; {1,2,3,4}
{1,2}
{3,4}
{1,2,3}
{2,3,4}
Which of the following is described as a line, segment, or ray that bisects a segment at a right angle?
A. Slope
B. Perpendicular bisector
C. Midpoint
D. Angle bisector
Answer:
option B
Step-by-step explanation:
the correct answer is option B
A Line, segment, or ray that bisects a segment at a right angle is Perpendicular bisector.
The slope of the is the rate of change of y-axis w r t to x-axis.
Midpoint is the center of any line segment.
An angle bisector is a line which bisects angle in equal proportion
Suppose a normal distribution has a mean of 98 and a standard deviation of 6. What is P(x< or = to 110)
Answer:
97.8%
Step-by-step explanation:
110 is 2 standard deviations above the mean (6+6 = 12)
12+98 = 110
Looking at the standard deviation curve
P(x< or = to 110) = 1 - P(x>110)
We can find the probability that x>100 by adding anything above 2 standard deviations above the curve.
P(x>110) = 2.1+.1 = 2.2%
P(x< or = to 110) = 1 - P(x>110)
= 1- 2.2%
= 1- .022
= .978
= 97.8 %
Answer:
0.975
Step-by-step explanation:
A P E X
Eric made two investments: Investment Q Q has a value of $ 5 0 0 $500 at the end of the first year and increases by $ 4 5 $45 per year. Investment R R has a value of $ 4 0 0 $400 at the end of the first year and increases by 1 0 % 10% per year. Eric checks the value of his investments once a year, at the end of the year. What is the first year in which Eric sees that investment R R's value exceeded investment Q Q's value?
Answer: After 8 year from the first year Eric will see that investment R's value exceeded investment Q's value.
Step-by-step explanation:
Let after x year from the first year Eric sees that investment R's value exceeded investment Q's value.
Investment Q has a value of $ 500 at the end of the first year and increases by $ 45 per year.
Thus, after x year from the first year the total amount of Investment Q,
500 + 45 x
Similarly, after x year from the first year the total amount of Investment R,
⇒ [tex]400(1+\frac{10}{100} )^x = 400(1.1)^x[/tex]
Thus, [tex]500 + 45 x = 400(1.1)^x[/tex]
By plotting the equations in the graph,
We get, x = -6.178 or 8.069
But year can not be negative,
Therefore, x = 8.069
Thus, Approx after 8 year from the first year Eric will see that investment R's value exceeded investment Q's value.
Answer: it’s 10 I’m 100% sure
select the two binomials that are factors of this trinomial x^2+10x+16
A: x+8
B: x+6
C: x+2
D: X-2
Answer:
The correct options are A: x+8 and C: x+2.
Step-by-step explanation:
We are given the following expression and we are to factorize it:
[tex]x^2+10x+16[/tex]
We are to find such factors that when multiplied they give a result of 16 (1 x 16 = 16) and when added they give a result of 10.
The two such factors of 16 are positive 2 and positive 8.
Factorizing the given expression to get:
[tex]x^2+10+16\\\\x^2+2x+8x+16\\\\x(x+2)+8(x+2)\\\\(x+2)(x+8)[/tex]
Therefore, the two binomial factors of the given expression [tex]x^2+10x+16[/tex] are (x+8) and (x+2).
Answer: x+6 x+2
tell me if I’m wrong because I put x+8 and x+2 and got it wrong it told me it was x+6 and x+2
If l and m are parallel, which pairs of angles are congruent? SELECT ALL THAT APPLY
1 and 3
2 and 4
6 and 7
3 and 6
Answer:
(<1 and <3) (<2 and <4) (<3 and <6)
Step-by-step explanation:
1 and 3 are corresponding equal angles
If one and three are equal, so are 2 and 4 since they are supplementary to equal angles.
6 and 7 are supplementary but not equal.
3 and 6 are equal angles because they are alternate interior angles.
A 1200 sq ft house is advertised for sale at a price of 96000. What is the cost per square foot?
Answer:$80.00
Step-by-step explanation:
APEX
Taylor has $97.23 and her checking account she uses debit card to spend 29 .74 and then deposits 118.08 into her accounts what is Taylor's new balance
Answer:
Taylor's new balance is $ 185.57 .
Step-by-step explanation:
As given
Taylor has $97.23 and her checking account.
she uses debit card to spend $29 .74 .
Than
Balance in the account after uses debit card = $97.23 - $29.74
= $ 67.49
As given
Then deposits $118.08 into her accounts.
Total balance of the account = $118.08 + $67.49
= $ 185.57
Therefore Taylor's new balance is $ 185.57 .
Answer:
$185.57
Step-by-step explanation:
Emma brandy and Damien will cut a rope that is 29.8 feet long into 3 jump ropes. Each of the three jump ropes will be the same length l. Write a division sentence using compatible numbers to estimate the length of each rope.
Answer: Length of each of rope will be 9.93 feet.
Step-by-step explanation:
Since we have given that
Length of rope that Emma brandy and Damien will cut = 29.8
Number of jumps = 3
According to question, each of the three jumps ropes will be the same length l.
Length of rope can be attained by dividing the length of rope with number of jumps.
so, length of each rope will be
[tex]l=\frac{\text{Length of rope}}{\text{Number of jumps cut into }}\\\\=\frac{29.8}{3}\\\\=9.93\ feet[/tex]
Hence, Length of each of rope will be 9.93 feet.
Paws at play made a total of $1,234 grooming 22 dogs. Paws at play charges $43 to groom each small dog and $75 for each large dog. Write a system of equations that can be used to determine the number of small and large dogs that were groomed
Step-by-step explanation:
We are asked to write a system of equations using our given information.
Let x be number of small dogs and y be number of large dogs.
We have been given that paws at play made a total of $1,234 grooming 22 dogs, which means that number of small dogs and large dogs is 22. We can represent this information as:
[tex]x+y=22...(1)[/tex]
We have been given that paws at play charges $43 to groom each small dog and $75 for each large dog. So the total grooming charges for grooming x small and y large dogs will be 43x+75y, that is equal to total charges for grooming $1234.
We can represent this information as:
[tex]43x+75y=1234...(2)[/tex]
Therefore, our desired system of equations is:
[tex]x+y=22...(1)[/tex]
[tex]43x+75y=1234...(2)[/tex]