Answer:
Here, we have used the unit rate i.e. speed of 30 mph to get the distance traveled in 5 number of units i.e. 5 hours.
Step-by-step explanation:
We are asked the way to use a unit rate to solve a rate problem for any number of units.
Let, us assume that a car is moving at a unit rate of 30 miles per hour. And we have to calculate the distance it travels in 5 units of time i.e. 5 hours.
Now, the distance traveled in 5 hours will be given by 30 × 5 = 150 miles.
Since [tex]\textrm {Speed} = \frac{\textrm {Distance}}{\textrm {Time}}[/tex] and here, speed is 30 miles per hour and the time is 5 hours. (Answer)
Grace bought a book for $8 and some pencils that cost $.50 each. She spent a total of $18. Write and solve an equation to determine how many pencils she bought. Let p represent the number of pencils she bought.
Brian sold half of his baseball cards. The next day, he bought 10 more. Now he has a total of 50 cards. Write and solve an equation to determine how many baseball cards he had before he sold any. Let b represent the number of baseball cards he had.
The amount of pencils she bought could be 20p.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. The unitary method is a technique by which we find the value of a single unit from the value of multiple devices and It is a method that we use for most of the calculations in math.
We are given Grace bought a book for $8 and some pencils that cost $.50 each. and spent a total of $18.
when the notebook is $8 and you spend $18 which means bringing 10 worth of pencils.
50c - 1pencil
$1 - 2 pencils
$1.50 is 3
Then we have spent $5 on pencils then have 20p for $10
then $10 + 8 is $18 then spent $18 x
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What is the sum of the series? 4 ∑k=1 (2k^2−4)
The sum of the series [tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)[/tex] is 44.
Step-by-step explanation:
The given series is [tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)=44[/tex]
To find the sum of the series, we need to substitute the values for k in the series.
[tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)=\left[2(1)^{2}-4\right]+\left[2(2)^{2}-4\right]+\left[2(3)^{2}-4\right]+\left[2(4)^{2}-4\right][/tex]
Now, simplifying the square terms, we get,
[tex][2(1)-4]+[2(4)-4]+[2(9)-4]+[2(16)-4][/tex]
Multiplying the terms,
[tex][2-4]+[8-4]+[18-4]+[32-4][/tex]
Subtracting the values within the bracket term, we get,
[tex]-2+4+14+28[/tex]
Now, adding all the terms, we get the sum of the series,
[tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)=44[/tex]
Thus, the sum of the series is [tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)=44[/tex]
Hes right its 44
444444444444444444444
Classify the following triangle. Check all that apply.
A. Scalene
O
B. Obtuse
I
C. Acute
D. Right
E. Equilateral
O
F. Isosceles
Answer:
Right and isosceles
Step-by-step explanation:
Apex
A triangle has a perimeter of 50. If 2 of its
sides are equal and the third side is 5 more
than the equal sides, what is the length of
the third side
Answer:
20 units
Step-by-step explanation:
Let the equal sides of the triangle be x.
Then the third side will be (x+5) units
Since the perimeter is 50, we have:
[tex]x + x + (x + 5) = 50[/tex]
We simplify to get:
[tex]3x + 5 = 50[/tex]
This implies that:
[tex]3x = 50 - 5[/tex]
[tex]3x = 45[/tex]
Divide both sides by 3 to get:
[tex]x = \frac{45}{3} = 15 [/tex]
The length of the third side is:
15+5=20
The smith family went out to dinner. Their bill came to $67.80. If they left a 15% tip and used a $100 gift card to pay for the bill, including the tip, what is the remaining balance on the card?
Answer: $22.03
Step-by-step explanation: 15% 67.8= 10.17. 67.8+10.17=77.97. x=remain balance. x=100.00-77.97=22.03.
4.4% of what number is 66
Answer:
1,500
Step-by-step explanation:
Find x in proportional form.
Answer: 1,500
Step-by-step explanation:
use the is/of = %/100 proportion
An employee working 40 hours per week earns a salary of $600 per week but gets a
second job offer to work 40 hours per week, hourly at $20 an hour. Which position
generates the most income and how much more does that position make? Show
your work or explain how you got your answer.
Answer:
Step-by-step explanation:
40 hours per week*20 dollars per hour=800 dollars per week. This job makes 200 more dollars than the other job.
The amount of generation of the most income in the second job offer will be more which is $800 per week.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
An employee working 40 hours per week earns a salary of $600 per week. Then the rate is given as,
Rate = $600 per week
But gets a second job offer to work 40 hours per week, hourly at $20 an hour. Then the rate is given as,
Rate = $20 x 40
Rate = $800 per week
The amount of generation of the most income in the second job offer will be more which is $800 per week.
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Identify the slope and y-intercept of the
equation:
2x + 2y = -10
Answer:
Step-by-step explanation:
2x + 2y = -10
Making y as subject
2y = -2x - 10
Dividing by 2
y = -2x/2 - 10/2
y = -x - 5
Comparing with y = mx + c
Slope m = -1, y intercept c = -5
The equation is first rewritten in slope-intercept form as y = -x - 5, revealing that the slope is -1 and the y-intercept is -5.
To find the slope and y-intercept of the given equation 2x + 2y = -10, you need to rewrite it in the slope-intercept form, which is y = mx + b, where m represents the slope, and b represents the y-intercept. First, let's separate the y-term on one side by subtracting 2x from both sides of the equation:
2y = -2x - 10
Now divide the entire equation by 2 to solve for y:
y = (-2x/2) - (10/2)
y = -x - 5
Comparing this with the slope-intercept form y = mx + b, we can see that the slope (m) is -1, and the y-intercept (b) is -5.
Jean practices for 19 quarter hour periods each month how many hours does she practice
Solve each system by elimination.
-4x + 8y = -24
7x - 5y = 24
Answer:
The solution is the point (2,-2)
Step-by-step explanation:
we have
[tex]-4x+8y=-24[/tex] -----> equation A
[tex]7x-5y=24[/tex] -----> equation B
step 1
Multiply by 7 equation A both sides
[tex]7(-4x+8y)=7(-24)[/tex]
[tex]-28x+56y=-168[/tex] -----> equation C
step 2
Multiply equation B by 4 both sides
[tex]4(7x-5y)=4(24)[/tex]
[tex]28x-20y=96[/tex] -----> equation D
step 3
Adds equation C and equation D
[tex]-28x+56y=-168\\28x-20y=96\\-----------\\56y-20y=-168+96\\36y=-72\\y=-2[/tex]
Find the value of x
substitute the value of y in any equation
equation A
[tex]-4x+8(-2)=-24\\4x=-16+24\\4x=8\\x=2[/tex]
therefore
The solution is the point (2,-2)
David rides his bike with a constant
speed of 12 miles per hour. How long
will he take to travel a distance of
12 miles?
Answer: 1 hour
Step-by-step explanation: if he travels 12 mph, it will take 1 hour to travel 12 miles.
What is the value of the expression below? Negative 8 + 19 + 8 0 11 19 35
Answer:
The value of the expression is 19
Step-by-step explanation:
We want to find the value of the expression: [tex]-8+19+8[/tex]
We regroup the numbers to make the computation very easy for us.
[tex]-8+8+19[/tex]
Recall that -x+x are zero pairs.
This implies that:
[tex]-8+8+19=0+19[/tex]
Also zero is the identity element of addition of of real numbers
[tex]0+19=19[/tex]
Hence the correct answer is 19
The value of the expression and correct answer is 19
12 yds
How many square yards of cement are needed to create
the walkway around the rectangular pool?
4 yds
12 yds
w
176 square yards
196 square yards
208 square yards
280 square yards
4 yds
4 yds
6 yds
6 yds
Pool
6 yds
yds
12 yds
4 yds
12 yds
Answer:
176 square yards
Step-by-step explanation:
The picture of the question in the attached figure N 1
we know that
The area of the walkway around the rectangular pool, is equal to the area of two trapezoids (#1 and #2), plus the area of two smaller rectangles (#3 and #4)
see the attached figure N 2 to better understand the problem
step 1
Find the area of the two trapezoids (#1 and #2)
[tex]A=2[\frac{1}{2}(b_1+b_2)h][/tex]
simplify
[tex]A=(b_1+b_2)h[/tex]
we have
[tex]b_1=12\ yd\\b_2=4+12+4=20\ yd\\h=4\ yd[/tex]
substitute
[tex]A=(12+20)(4)=128\ yd^2[/tex]
step 2
Find the area of the two smaller rectangles (#3 and #4)
[tex]A=2[LW][/tex]
we have
[tex]L=4\ yd\\W=6\ yd[/tex]
substitute
[tex]A=2[(4)(6)]=48\ yd^2[/tex]
step 3
Find the area of the walkway around the rectangular pool
[tex]128+48=176\ yd^2[/tex]
Answer:
176 sq yards
Step-by-step explanation:
Write an equation of the line through (6,-5) having slope 0. Give the answer in standard form.
0x + 1y = -5 is the standard form of equation
Solution:
Given that we have to write the equation of line passing thorugh (6, -5) and has slope 0
The equation of line in slope intercept form is given as:
y = mx + c ---------- eqn 1
Where, "m" is the slope of line and "c" is the y - intercept
Given that, m = 0
Given point is (6, -5)
To find the y - intercept:
Substitute (x, y) = (6, -5) and m = 0 in eqn 1
-5 = 0(6) + c
c = -5
Substitute c = -5 and m = 0 in eqn 1
y = 0x + (-5)
y = -5
The standard form of equation is given as:
The standard form of an equation is Ax + By = C
In this kind of equation, x and y are variables and A, B, and C are integers
y = -5
0x + 1y = -5 is the standard form of equation
Mr. Lane’s math classes had the pass rates shown. In class 1, 16 out of 24 passed. In class 2, of the class passed. In class 3, 75% of the class passed. In class 4, 0.81 of the class passed. Which class had a pass rate that was exactly 5% greater than another class’s pass rate?
A.Class 1 B. Class 2 C. Class 3
Answer:
Answer 4/5 or class 2
Step-by-step explanation:
4/5=0.80 Class 3 is 70% 75+5=80, or 80%
Final answer:
After converting the pass rates of the classes to percentages, none of the classes have a pass rate that is exactly 5% greater than another class's pass rate.
Explanation:
The student's question pertains to comparing the pass rates of different math classes to determine which class had a pass rate that was exactly 5% greater than another class's pass rate. To answer this, we need to convert the pass rates for each class to a percentage and then compare them.
For class 1, the pass rate is 16 out of 24, which can be converted to a percentage by dividing 16 by 24 and then multiplying by 100, resulting in approximately 66.67%. Class 3 has a pass rate of 75%, as provided. Class 4 has a pass rate of 0.81, which is already in a decimal format comparable to a percentage; it is simply 81% when expressed as a percentage.
By comparing these percentages, we find that Class 3's pass rate is exactly 5% greater than Class 1's pass rate (75% - 66.67% = 8.33%, which is more than 5%). Therefore, none of the classes have a pass rate that is exactly 5% greater than another class's pass rate.
Collin worked at the ice cream parlor over the summer. On his last 7 shifts, he scooped:
8,9,9,7,6,9,8
What was the mean number of scoops?
Answer:
add up the numbers and divide by the counting of the numbers. so the answer will be 56/7 equal to 8
Jake and Mary are both members of a population and a simple random sample is being conducted if the chance of jake being selected is 1/800, what is the chance of Mary being selected
N 4n3 2m 6m 5n 2n
Identify like terms
Final answer:
In the given algebraic expression, 4n³ and 2n³, 2m and 6m, and 5n and 2n are identified as like terms.
Explanation:
The question asks to identify like terms in a given algebraic expression. Like terms in algebra are terms that have the exact same variables raised to the same powers, although they can have different coefficients.
For example, 4n³ and 2n³are like terms because they both contain the variable n to the third power.
On the other hand, 2m and 6m are like terms because they both contain the variable m to the first power.
Lastly, 5n and 2n are like terms because they contain the variable n to the first power.
Using 6 as a denominator, what fraction completes the following equation: 1 − 2/12 = ? a.4/6 c. 3/6 b.5/6 d. 2/6
Answer:
5/6
Step-by-step explanation:
[tex]1-\frac{2}{12}=1-\frac{1}{6}=\frac{1*6}{1*6}-\frac{1}{6}\\\\=\frac{6}{6}-\frac{1}{6}=\frac{6-1}{6}=\frac{5}{6}[/tex]
16. y = -5, x = 5
Determine whether the lines are perpendicular.
Answer:
yes, they are
Step-by-step explanation:
y = -5 is a horizontal line.
x = 5 is a vertical line.
Horizontal and vertical lines are perpendicular to each other. These lines are perpendicular.
:
Which of the following has congruent base angles?
A
all trapezoids
B
all isosceles trapezoids
C
all kites
D
all quadrilaterals
All isosceles trapezoids have congruent base angles.
Option A
Explanation:
An isosceles trapezoid is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides.
Properties of isosceles trapezoid:
Opposite sides of an isosceles trapezoid are the same length (congruent). The angles on either side of the bases are the same size/measure (congruent).The bases (both top and bottom) of an isosceles trapezoid are parallel.Note: Refer the attached file for the image of an isosceles trapezoid.
All isosceles trapezoids come into the category of trapezoids but all trapezoids cannot be marked as isosceles. Clearly, if a trapezoid has congruent legs, it is an isosceles trapezoid.
If a trapezoid has one pair of congruent base angles, then the trapezoid is isosceles. A trapezoid is isosceles if and only if its diagonals are congruent.
In the case of quadrilaterals, if the quadrilateral is an isosceles trapezoid, then each pair of base angles are congruent.
The shape that has congruent base angles is all isosceles trapezoids, as they have two pairs of congruent sides which result in two pairs of congruent base angles due to their geometric properties.
After excluding options such as all trapezoids, all kites, and all quadrilaterals which do not necessarily have congruent base angles, it becomes evident that the correct answer is all isosceles trapezoids.
An isosceles trapezoid is defined as a trapezoid where the non-parallel sides (legs) are congruent. According to geometric properties, these congruent non-parallel sides imply that the base angles are also congruent. So, an isosceles trapezoid always has two pairs of congruent base angles.
To support this, consider the Theorem, in an isosceles triangle the angles opposite the equal sides are equal. Similarly, by applying this to the two triangles that form when dividing an isosceles trapezoid along the line of symmetry, it becomes clear why the base angles are congruent.
WILL GIVE BRAINLIEST
What is X?
Answer:
x = 20
Step-by-step explanation:
2x + 7x = 180
⇔ 9x = 180
⇔ x = 180/9 = 20
Please help asap i will mark branlist
Answer:
B. 3
Step-by-step explanation:
The shape of a box is a square. The volume for a square is lengthxwidthxheight.
For the first box it would be 2x3x6 or 36in.
For the second box, 3x4, which is 12.
Dividing 36 by 12, we get 3.
So 3x4x3 would result in 36in., the same as the first box.
Tower A is 90 feet tall. Tower B is 180 feet tall. Tower C is 5 times as tall as both Towers A and B combined. How tall is Tower C?
Answer:
1350
Step-by-step explanation:
I added tower A and B together (90+180) Which gives me 270. Then I did;
270 * 5= 1350 ft. Hope its correct!
Final answer:
Tower C is 5 times as tall as the combined height of Tower A (90 feet) and Tower B (180 feet), which together are 270 feet tall. Multiplying this by 5 gives us the height of Tower C, which is 1350 feet.
Explanation:
The question asks us to calculate the height of Tower C given the heights of Tower A and Tower B and the relationship between their heights. Tower A is 90 feet tall, and Tower B is 180 feet tall. According to the question, Tower C is 5 times as tall as both Towers A and B combined.
To find the combined height of Towers A and B, we simply add their heights:
Tower A height: 90 feetTower B height: 180 feetCombined height of Tower A and B: 90 + 180 = 270 feetNow, we need to calculate the height of Tower C:
Height of Tower C = 5 × (Height of Tower A + Height of Tower B)Height of Tower C = 5 × 270 feetHeight of Tower C = 1350 feetTherefore, Tower C is 1350 feet tall.
Two species of birds are being compared species a can Fly 18.9 miles in 42Minutes while species be can fly 20.3 miles in 58 minutes which species is slower and at what speed cannot fly. Minutes while species be can fly 20.3 miles in 58 minutes which species is slower and at what speed can it fly.
Answer:
The second species is slower , flying at 21mph
Step-by-step explanation:
18.9/42x60=27mph
20.3/58x60=21mph
The second species is slower , flying at 21mph
The graph of a linear function F is given
Answer:
Step-by-step explanation:
This line goes through the y-axis at 6; therefore, the coordinate at this point is (0, 6).
This line goes through the x-axis at 2; therefore, the coordinate at this point is (2, 0).
The rate of change of a linear function (aka a line) is the slope of the line. We can use the slope formula to solve for the slope:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Filling in with our coordinates:
[tex]m=\frac{0-6}{2-0}=-\frac{6}{2}=-3[/tex]
The rate of change is -3. This means that y decreases 3 with every increase in x of 1.
The solutions to a quadratic equation are -1/3 and 9/2. Which quadratic function is related to this equation?
f(x) = 9x² - 25x -6
f(x) = 6x² -25x -9
f(x) = 9x² + 25x - 6
f(x) = 6x² + 25x - 9
Answer:
f(x) = 6x² -25x -9
Step-by-step explanation:
6x² - 25x -9 = (2x - 9) (3x + 1)
x = (2/9) or (- 1/3)
for elimination what is the 2 ordered pairs
-4x + 3y = -19
-4x - y = -15
Answer:
I would eliminate both of the -4x because they are identical.
Step-by-step explanation:
Cancel out the both of the -4x by eliminating them. Then subtract the 3y - y. Subtract the -19 - 15. You then will be left with 2y = -34. Solve for y. Then plug y back into the equation to solve for the x.
Hope this helped. :^)
Solve for x, 12y+6=6(y+1)
For this case we must solve the following equation:
[tex]12y + 6 = 6 (y + 1)[/tex]
We apply distributive property on the right side of the equation:
[tex]12y + 6 = 6y + 6[/tex]
We subtract 6y on both sides of the equation:
[tex]12y-6y + 6 = 6\\6y + 6 = 6[/tex]
We subtract 6 from both sides of the equation:
[tex]6y = 6-6\\6y = 0[/tex]
Dividing by 6 on both sides of the equation:
[tex]y = 0[/tex]
So, the result is [tex]y = 0[/tex]
Answer:
[tex]y = 0[/tex]
Solve for all missing posts of triangles with the given information. B =53 degrees, a =10, b=17
Answer:
Therefore,
[tex]m\angle A =28\°\\\\m\angle C =99\°\\\\c=21\ units[/tex]
Step-by-step explanation:
Consider a Δ ABC with
m∠ B = 53°
BC = a = 10
AC = b = 17
To Find:
AC = c = ?
m∠ A = ?
m∠ C = ?
Solution:
We know in a Triangle Sine Rule Says that,
In Δ ABC,
[tex]\dfrac{a}{\sin A}= \dfrac{b}{\sin B}= \dfrac{c}{\sin C}[/tex]
substituting the given values we get
[tex]\dfrac{a}{\sin A}= \dfrac{b}{\sin B}[/tex]
[tex]\dfrac{10}{\sin A}= \dfrac{17}{\sin 53}\\\\\sin A=0.469\\A=\sin^{-1}(0.469)=28.02\approx 28\°[/tex]
Therefore m∠A = 28°
Triangle sum property:
In a Triangle sum of the measures of all the angles of a triangle is 180°.
[tex]\angle A+\angle B+\angle C=180\\\\28+53+\angle C=180\\\therefore m\angle C =180-81=99\°[/tex]
Therefore m∠C = 99°
Now From Sine rule we have
[tex]\dfrac{b}{\sin B}= \dfrac{c}{\sin C}[/tex]
Substituting the values we get
[tex]\dfrac{17}{\sin 53}= \dfrac{c}{\sin 99}\\\\c=21.02\approx 21\ unit[/tex]
Therefore,
[tex]m\angle A =28\°\\\\m\angle C =99\°\\\\c=21\ units[/tex]