[tex]\bf \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=base\\ h=height\\ \cline{1-1} A=8\\ h=4 \end{cases}\implies 8=\cfrac{1}{2}b(4)\implies 8=2b\implies \cfrac{8}{2}=b\implies 4=b[/tex]
To find the length of the base of a triangle with an area of 8 square feet and a height of 4 feet, you rearrange the formula for the area of a triangle and solve for the base, resulting in a base length of 4 feet.
The question asks for the length of the base of a triangle given that the area is 8 square feet and the height is 4 feet. To find the base of the triangle, we can rearrange the formula for the area of a triangle, which is A = (1/2) * base * height. Substituting in the given values and solving for the base, we get:
Base = (2 * Area) / Height
Next, we replace the values for Area and Height:
Base = (2 * 8 sq ft) / 4 ft
Base = 16 sq ft / 4 ft
Base = 4 feet
Therefore, the length of the base of the triangle is 4 feet.
solve -30+15y/2+2y=-11
Answer:
[tex]\large\boxed{y=\dfrac{8}{37}}[/tex]
Step-by-step explanation:
[tex]Domain:\ 2+2y\neq0\to y\neq-1\\\\\dfrac{-30+15y}{2+2y}=-11\\\\\dfrac{-30+15y}{2+2y}=\dfrac{-11}{1}\qquad\text{cross multiply}\\\\(-30+15y)(1)=(-11)(2+2y)\qquad\text{use the distributive property}\\\\-30+15y=(-11)(2)+(-11)(2y)\\\\-30+15y=-22-22y\qquad\text{add 30 to both sides}\\\\15y=8-22y\qquad\text{add}\ 22y\ \text{to both sides}\\\\37y=8\qquad\text{divide both sides by 37}\\\\y=\dfrac{8}{37}[/tex]
Select the expression that is equivalent to (x+4)^2
Answer:
So for this problem, we can use the formular:
(A + B)² = A² + 2AB + B²
Our orginal expression is: (x + 4)². In this expression, A can be written as x, B represents for 4, that leads to our answer:
(x + 4)² = x² + 2 . 4x + 4² = x² + 8x + 16
The correct answer will be D
Answer: the correct option is (D) [tex]x^2+8x+16.[/tex]
Step-by-step explanation: We are given to select the expression that is equivalent to the following expression :
[tex]E=(x+4)^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We will be using the following formula :
[tex](a+b)^2=a^2+2ab+b^2.[/tex]
Using the above formula, the expression (i) gives
[tex]E\\\\=(x+4)^2\\\\=x^2+2\times x\times4+4^2\\\\=x^2+8x+16.[/tex]
Thus, the required equivalent expression is [tex]x^2+8x+16.[/tex]
Option (D) is CORRECT.
What is the sum of all odd numbers 10 to 55
Answer:
To sum consecutive numbers we use the formula:
n * (n+1) / 2
1 through 55 = (55 * 56) / 2 = 1,540
1 through 9 = (9 * 10) / 2 = 45
10 through 55 = 1,540 -45 = 1,495
********************************************************
EDITED
Gee, it seems I added ALL numbers from 10 through 55
ALL ODD numbers from 10 through 55 sum to
759
Step-by-step explanation:
Write the equation of the graphed function. A. y = 5⁄4x + 3 B. y = 4⁄5x + 3 C. y = 4⁄5x – 3 D. y = 5⁄4x – 3
Is their a picture you can upload to show us?
2. A package of paper towels contains 3 rolls. Each package of paper towels costs $2.79. A function, f(x), is written to represent the cost of purchasing x packages of paper towels. What is the practical domain for the function f(x)?
A. All real numbers
B. All whole numbers
C. All positive numbers
D. All whole numbers that are multiples of 3
Answer:
B
Step-by-step explanation:
Let x be the number of packages of paper towels.
Each package of paper towels costs $2.79.
Then x packages of paper towels cost $2.79x.
Hence, a function f(x) is
[tex]f(x)=2.79x[/tex]
Practically, you can buy 0 packages, 1 package, 2 packages and so on, only whole numbers of packages, so practical domain is all whole numbers.
Which is the image of (-2, -5) reflected across X=2?
(-6, 5)
(-2,9)
(6,-5)
(2,9)
Answer:
(6,-5)
Step-by-step explanation:
As the point is 4 units to the left of X=2, the reflection must be 4 units to the right of X=2
Kia buys 2 Cartons of Vanilla Ice Cream And 6 Cartons of Chocolate Ice Cream. Each carton contains 32 ounces of ice cream. She serves 4 ounces of ice cream in each bowl. What is the greatest number of bowels of ice cream that Kia can serve?
64 bowls because if you Multiply eight times 32. You would get 256 and then you divide that into four and would get 64 which is your answering
the greatest number of bowls of ice cream Kia can serve is 64.
The student wishes to determine the greatest number of bowls of ice cream that can be served given certain quantities of ice cream and serving sizes. To solve this, we first calculate the total amount of ice cream by adding the quantities of vanilla and chocolate ice cream. Kia bought 2 cartons of vanilla and 6 cartons of chocolate, each containing 32 ounces. Thus, the total amount of ice cream is (2 + 6) × 32 ounces. Each bowl served contains 4 ounces of ice cream. To find the number of bowls, we divide the total ounces of ice cream by the ounces per bowl. This yields (8 × 32) ÷ 4, which calculates to 64 bowls. Therefore, the greatest number of bowls of ice cream Kia can serve is 64.
Given: F(x)=x+2 and g(x)=3x+5
(f-g)(x)=
Answer:
- 2x - 3
Step-by-step explanation:
note that (f - g)(x) = f(x) - g(x)
f(x) - g(x) = x + 2 - (3x + 5) = x + 2 - 3x - 5 = - 2x - 3
Two opposite rays
form
a line.
never
sometimes
always
Answer:
always.
Step-by-step explanation:
A ray has a starting point but no end point. Therefore if 2 opposite rays are connected at their endpoints, a line is formed. I cannot think of an exception to this because the definition of a ray is very rigid (the end point is always included).
Find the missing lengths of the sides
Answer: option c
Step-by-step explanation:
You can use these identities:
[tex]sin\alpha=\frac{opposite}{hypotenuse}\\\\tan\alpha=\frac{opposite}{adjacent}[/tex]
Then, using the angle that measures 30 degrees, you know that:
[tex]\alpha=30\°\\opposite=8\\adjacent=b[/tex]
Substituting:
[tex]tan(30\°)=\frac{8}{b}[/tex]
Now you must solve for b:
[tex]b=\frac{8}{tan(30\°)}\\\\b=8\sqrt{3}[/tex]
Using the angle that measures 30 degrees, you know that:
[tex]\alpha=30\°\\opposite=8\\hypotenuse=c[/tex]
Substituting:
[tex]sin(30\°)=\frac{8}{c}[/tex]
Now you must solve for c:
[tex]c=\frac{8}{sin(30\°)}\\\\c=16[/tex]
ANSWER
The correct answer is C
EXPLANATION
The side adjacent to the 60° angle is 8 units.
The hypotenuse is c.
Using the cosine ratio, we have
[tex] \cos(60 \degree) = \frac{adjacent}{hypotenuse} [/tex]
[tex]\cos(60 \degree) = \frac{8}{c} [/tex]
[tex] \frac{1}{2}= \frac{8}{c} [/tex]
Cross multiply
[tex]c = 8 \times 2 = 16[/tex]
Also
[tex]\cos(30 \degree) = \frac{b}{c} [/tex]
[tex]\cos(30 \degree) = \frac{b}{16} [/tex]
[tex] \frac{ \sqrt{3} }{2} = \frac{b}{16} [/tex]
Multiply both sides by 16
[tex]b = 16 \times \frac{ \sqrt{3} }{2} [/tex]
[tex]b = 8 \sqrt{3} [/tex]
The correct answer is C
Victoria read a 160-page historical fiction novel followed by a science fiction novel of the exact same length. Her average reading speed of the science fiction novel was 2 pages per hour more than her average reading speed of the historical fiction novel. Victoria models her novel reading marathon with the following expression, where x represents her average reading speed of the historical fiction novel. What does x + 2 represent in this situation? A. the total time taken to read the novels B. the average reading speed of the historical fiction novel C. the average reading speed of the science fiction novel D. the number of pages of the science fiction novel
The answer is C: the average reading speed of the science fiction novel.
If x is her reading speed for the historical fiction novel, and her reading speed for the sci-fi novel is just two pages more than that of the historical fiction novel, then the equation to find out how fast she reads the science fiction novel would be x + 2, as you’re adding 2 to the reading speed of the historical fiction book (x)
Answer:
The answer to this question is correct but on PLATO the answer choice is actually A.
Step-by-step explanation:
PLATO
What inequality represents the verbal expression? all real numbers less than 70
For this case we have:
Let x be the variable that belongs to the real numbers. Then, all reals less than 70 can be expressed as:
[tex]x <70[/tex]
The tip of the inequality is directed to the real numbers, since they tell us that they are less than 70, for 70 the inequality remains open.
Answer:
[tex]x <70[/tex]
Write the equation of the circle with center (0, 0) and (−1, −3) a point on the circle. A) x2 + y2 = 4 B) x2 + y2 = 5 C) x2 + y2 = 10 D) x2 + y2 = 16
ANSWER
C)
[tex] {x}^{2} + {y}^{2} = 10[/tex]
EXPLANATION
The center of the circle is (0,0).
The circle passes through (-1,-3).
The radius can be obtained using the distance formula:
[tex]r = \sqrt{(0 - 1)^{2} + {(0 - - 3)}^{2} } = \sqrt{10} [/tex]
The equation is given as:
[tex]( {x - h)}^{2} + ( {y - k)}^{2}= {r}^{2} [/tex]
Where (h,k) is the center and r is the radius.
This implies that;
[tex]( {x - 0)}^{2} + ( {y - 0)}^{2}= {( \sqrt{10)} }^{2} [/tex]
[tex] {x}^{2} + {y}^{2} = 10[/tex]
What is the answer? 1000-20000=_
A) -0
B) -1000
C) -19000
D) -200
Answer:
-19000
Step-by-step explanation:
1000-20000=-19000
Answer:
C -19000
Step-by-step explanation:
1,000
- 20,000
----------------------=
-19000
what is the solution to the system of equations ? y=5x+2 3x=-y+10
Answer:
Solution is (1,7).
Step-by-step explanation:
We need to find the solution of the system of following equations.
y= 5x + 2 eq(1)
3x = -y +10 eq(2)
We will solve the equations using Substitution method to find the values of x and y
we put value of y from eq (1) into eq (2), The eq(2) will be:
3x = - (5x + 2) + 10
3x = -5x -2 +10
3x+5x = -2+10
8x = 8
x= 1
Now, putting value of z in eq(1) to find value of y
y = 5x +2
y = 5(1) + 2
y = 5+2
y = 7
So, Solution is (1,7).
In solving an equation with a variable, an operation can be applied to _____ side(s) of the equation.
one
either
both
Answer:
Both.
Step-by-step explanation:
This was so long ago but....
Answer:
both
Step-by-step explanation:
A python curls up to touch the tip of its own tail with its nose, forming the shape of a circle. The python is 2.6 pie meters long. What is the radius r of the circle that the python forms?
Answer:
r = 1.3 meters
Step-by-step explanation:
A python curls up to touch the tip of its own tail with its nose, forming the shape of a circle.
A python curls up to touch the tip of its own tail with its nose, forming the shape of a circle.
The python is 2.6 pi (2.6π) meters long.
What is the radius r of the circle that the python forms?
Now we have: C = π d, or (with d = 2 r): C = 2 π r.
Changing that around: r = C / 2 π
So with our value of C = 2.6π meters, that gives us:
r = 2.6π/2π = 2.6/2, so r = 1.3 meters
Answer:
The answer is 1.3
Step-by-step explanation:
Because it is half of the diameter which was 2.6
Please help, thanks.
Answer:
-109
Step-by-step explanation:
Arithmetic sequence formula:
an = a1 + d(n - 1) where d = -4 and a1 = 19
so
a(33) = 19 - 4(33-1)
a(33) = 19 - 4(32)
a(33) = 19 - 128
a(33) = -109
The missing term : -109
Answer:
-109
Step-by-step explanation:
As x changes from 1 to 2, 2 to 3, and 3 to 4, each change in x is 1. The corresponding changes in y from 19 to 15, from 15 to 11, and from 11 to 7, are each a change of -4 in y. For each change of 1 in x, the corresponding change in y is -4. From 4 to 33 in x, the change is 33 - 4 = 29. The corresponding change in y is 29 * (-4) = -116.
7 + (-116) = -109
Malik
bought two tires for $45 and later sold for $65
Alright. We don't have the question, but Im going to assume it.
2 tires = $45
Later Sold for $65
Revenue is $20
If you mean sold both for each -
Revenue is $85
For this case we can indicate the profits obtained by Malik.
[tex]P = p-c[/tex]
Where:
P: They are the profits
p: It is the sale price
c: It's the cost
We have Malik buy the tires at $ 45, then the cost is $ 45. As he sold them at $ 65 then the sale price is $ 65.
We have:
[tex]P = 65-45\\P = 20[/tex]
So, Malik made a profit of $ 20 $
Answer:
Malik made a profit of $ 20
y=37*1.26^x is rhis a growth or a decay
Answer:
If x is greater than 1 it is growth, if it less than it is decay
Step-by-step explanation:
In 26 years, Peter will be 54 years old. In how many years will he be 75 years old?
Peter will be 75 years old in 47 years.
Answer:
In 47 years Peter will be 75 years old
Step-by-step explanation:
If Peter will be 54 years old in 26 years then subtract 26 from 54
54-26=28
This means that Peter is 28 right now, if you want to double check that work then add 26 to 28 implying that in 26 years Peter with be 54 years old
28+26=54
This shows that your calculations are correct! Now you have to figure out how many years from now will Peter be when he turns 75 years old, so you subtract his current age which is 28 from 75
75-28=47
Now to double check this add 47 to his current age which is 28
28+47= 75
This shows that your calculations are correct and it will take 47 years for Peter to be 75 years old!
The museum has tours every 20
minutes and a video to watch
every 15 minutes. Both the video
and tour start at 10:00 a.m. What
is the next time they will both be
starting at the same time?
Final answer:
The next time a museum tour and video both start at the same time after 10:00 a.m. is at 11:00 a.m., as that is when their intervals (every 20 minutes for tours and every 15 minutes for videos) have their Least Common Multiple.
Explanation:
The question is about finding the next time a museum tour and a video both start at the same time after 10:00 a.m. The tours start every 20 minutes and the videos start every 15 minutes. To find the next common start time, we need to calculate the Least Common Multiple (LCM) of 20 and 15 which is the smallest number that both 20 and 15 can divide into without leaving a remainder.
Multiples of 20 are 20, 40, 60, 80, 100, ...
Multiples of 15 are 15, 30, 45, 60, 75, ...
The first common multiple of the two intervals is 60 minutes. Therefore, since both the tour and the video start at the same time (10:00 a.m.), the next time they will both start together will be 60 minutes later, which is at 11:00 a.m.
(8-(-9))^2 + ((-3)-(-6))^2
Answer:
298
Step-by-step explanation:
Given
(8 - (- 9))² + (-3 - (- 6))² ← evaluate the parenthesis before squaring
= (8 + 9)² + (- 3 + 6)²
= 17² + 3²
= 289 + 9
= 298
Answer: (8+9)^2 + (-3 + 6)^2
= 17^2 + 3^2
= 289 + 9
= 298. ANS.
A line that includes the point (1,10) and has a slope of 7. What is it’s equation in slope intercept form
y = 7x +3 slope is rise over run with would be 7/1 and y intercept is 3
The equation in the slope-intercept form is y=7x+3.
What is the equation in slope-intercept form of point (1,10) and has a slope of 7?Given:
A line that includes the point (1,10) and has a slope of 7.Find:
The equation in slope-intercept form.Solution:
We will use y = mx+b where m = slope and b = y-intercept.
y = mx+b
Now, putting (1,10) in the place of x and y and slope as 7, we get;
10 = 7*1 + b
b = 10-7
b=3
So, the y-intercept is 3.
Now, putting the y-intercept in the slope-intercept equation, we get;
y = 7x+3
Hence, the equation in slope-intercept form is y=7x+3.
To learn more about slope-intercept, refer to:
https://brainly.com/question/1884491
#SPJ2
Kyle’s total sales for the month of January were $10,000, and his total earnings for that month were $1,350.
Kyle’s total sales for the month of February were $15,000, and his total earnings for that month were $1,575.
What is Kyle’s fixed monthly salary in dollars?
Answer:
$900
Step-by-step explanation:
Let the fixed salary be x and the commission be y, then as per given, the earnings:
10000y + x = 135015000y + x = 1575Subtract the first equation from the second:
15000y - 10000y = 1575 -13505000y = 225then
10000y =2*5000y = 2*225 = 450Using the first equation:
x = 1350 - 450 = 900So the fixed salary is $900
what verbal expression best describes the algebraic expression 4x ÷ 6?
A. The sum of four and some number divided by six
B. The product of some number and six divided by four
I think you forgot to put C and D but it is read out
The product of x and four divided by six
(x being some number)
i don't need it but brainliest it is appreciated
Simplify 7a + 2x + 5a - 6x
Answer:
12a - 4x
Step-by-step explanation:
1. 7a + 2x + 5a - 6x
2. 12a + 2 x - 6 x
(2b/3)^4 simplify the expression
Answer:
[tex]\large\boxed{\left(\dfrac{2b}{3}\right)^4=\dfrac{16b^4}{81}}[/tex]
Step-by-step explanation:
[tex]\left(\dfrac{2b}{3}\right)^4\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\ \text{and}\ (ab)^n=a^nb^n\\\\=\dfrac{2^4b^4}{3^4}=\dfrac{16b^4}{81}[/tex]
Answer:
16b^4/81
Step-by-step explanation:
Use the quadratic formula to determine the exact solutions to the equation.
2x2−5x+1=0
Enter your answers in the boxes.
x =
or x =
ANSWER
[tex]x = \frac{5}{4} - \frac{ \sqrt{ 17} }{4} [/tex]
or
[tex]x = \frac{5}{4} + \frac{ \sqrt{ 17} }{4} [/tex]
EXPLANATION
The given equation is:
[tex]2 {x}^{2} - 5x + 1= 0[/tex]
Comparing this to
[tex]a {x}^{2} + bx + c = 0[/tex]
we have a=2, b=-5, c=1
The quadratic formula is given by
[tex]x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
We substitute the values to get,
[tex]x = \frac{ - - 5 \pm \sqrt{ {( - 5)}^{2} - 4(1)(2)} }{2(2)} [/tex]
[tex]x = \frac{ 5 \pm \sqrt{ 17} }{4} [/tex]
[tex]x = \frac{5}{4} - \frac{ \sqrt{ 17} }{4} [/tex]
or
[tex]x = \frac{5}{4} + \frac{ \sqrt{ 17} }{4} [/tex]
pleeeeeeeeaaaseeeeee help meeeeeeee!!!!!!!!!
Answer:
Option D.
[tex]A =96\pi\ cm^2[/tex]
Step-by-step explanation:
The area of the circular bases is:
[tex]A_c = 2\pi(a) ^ 2[/tex]
Where
[tex]a=4\ cm[/tex] is the radius of the circle
Then
[tex]A = 2\pi(4) ^ 2[/tex]
[tex]A = 32\pi\ cm^2[/tex]
The area of the rectangle is:
[tex]A_r=b * 2\pi r[/tex]
Where
[tex]b=8\ cm[/tex]
b is the width of the rectangle and [tex]2\pi r[/tex] is the length
Then the area of the rectangle is:
[tex]A_r=8 * 2\pi (4)[/tex]
[tex]A_r=64\pi\ cm^2[/tex]
Finally the total area is:
[tex]A = A_c + A_r\\\\A = 32\pi\ cm^2 + 64\pi\ cm^2\\\\[/tex]
[tex]A =96\pi\ cm^2[/tex]
Answer:
The correct answer is option B. 96π
Step-by-step explanation:
Points to remember
Surface area of cylinder = 2πr(r + h)
Where r is the radius of cylinder and h is the height of cylinder.
From the figure we get r = 4 cm and h = 8 cm
To find the surface area of cylinder
Surface area = 2πr(r + h)
= 2π * 4(4 + 8)
= 96π
The correct answer is option B. 96π