Lee's family had a garden in the shape of a right triangle. The total area of the garden is 16 square feet. If they expand
the garden to form a triangle with twice the base
and twice the height, by how much will they increase the size of their
garden?
O 16 square feet
• 32 square feet
O
48 square feet
64 square
feet
Answer:
48 square feet
Step-by-step explanation:
Given
Before expansion
[tex]A_1 = \frac{1}{2}bh[/tex] --- area of a triangle
[tex]A_1 = 16ft^2[/tex] --- value of the area
After the base and height were expanded, the area becomes:
[tex]A_2 = \frac{1}{2}BH[/tex]
Where
[tex]B = 2b[/tex]
[tex]H = 2h[/tex]
Substitute 2b for B and 2h for H in [tex]A_2 = \frac{1}{2}BH[/tex]
[tex]A_2 = \frac{1}{2} * 2b * 2h[/tex]
[tex]A_2 = \frac{1}{2} * 2*2*b*h[/tex]
[tex]A_2 = \frac{1}{2} * 4*b*h[/tex]
Rewrite as:
[tex]A_2 = 4 * \frac{1}{2} *b*h[/tex]
[tex]A_2 = 4 * \frac{1}{2}bh[/tex]
Recall that: [tex]A_1 = \frac{1}{2}bh[/tex]
So, we have:
[tex]A_2 = 4 * A_1[/tex]
Substitute 16 for [tex]A_1[/tex]
[tex]A_2 = 4 * 16[/tex]
[tex]A_2 = 64[/tex]
So, the area is [tex]64ft^2[/tex] after the dimensions were expanded
The area increased by:
[tex]Increment = A_2 - A_1[/tex]
[tex]Increment = 64 - 16[/tex]
[tex]Increment = 48[/tex]
It increased by [tex]48ft^2[/tex]
Find mZVUT if IZAUT = 88
and mZVUA = 55°.
T
U
V
9514 1404 393
Answer:
143°
Step-by-step explanation:
Angle VUT is the sum of the angles into which it is divided.
∠VUT = ∠VUA +∠AUT
∠VUT = 55° +88°
∠VUT = 143°
The manufacturer that Russell works for makes
bicycles. The wholesale price for the bikes is
$200; however, they markup the cost by 55%.
What is the retail price for these bikes?
Answer:
$310
Step-by-step explanation:
200 increase 55% =
200 × (1 + 55%) = 200 × (1 + 0.55) = 310
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
What is 2/7 divided by 5/9
Answer:0.006439
Step-by-step explanation:
Answer:
18/35
Step-by-step explanation:
a new shirt costs $14.99. If the shirt is on sale for 1/5 off it price,about how much would you save?
Answer:
about $3.00
Step-by-step explanation:
14.99 x 1/5 = 2.998
round it
3.00
Answer:
you would have 3.00
Step-by-step explanation:
round it up
Line v has a slope of 4/9 Line w is parallel to line v. What is the slope of line v?
Answer:
4/9
Step-by-step explanation:
it is parallel to it ;)
which polynomial represents the difference below? (8x^2+9)-(6x^2+2x+2)
Answer:
The polynomial is 2 x² - 2x + 7
Step-by-step explanation:
Given polynomial
(8 x² + 9 ) - (6x² +2x +2)
= 8 x² +9 - 6x² - 2x -2
= 8x² - 6x² - 2x + 9-2
= 2 x² - 2x + 7
The polynomial is 2 x² - 2x + 7
How do I add 1/8 + 2/6
Answer:
3/24 + 4/24 = 7/24
Step-by-step explanation:
Find a common denominator then multiply the numerator by how many times you multiplied the denominator and add them to get your answer and you may simplify.
Is this a good app for a college student I’m 55 and returning to college after 14years and I’m taking Pre-Med college math 110 and 155
Answer:
Yes it is
Step-by-step explanation:
Its good id say you get a good change of finding your answers here
1. A, D, E
2. A, B, D
3. C, D, E
4. A, B, C
Answer:
4. A,B,C because the dotted line on A B C have the same shape
Q2) A meat pie contains chicken and turkey in the ratio 4 : 1. ( 3 marks)
The pie contains 300 g of chicken.
How much turkey is in the pie?
How much meat is there altogether in the pie?
Plz i begggg
please
1/3g -3 = -9 I need help
Raul used the steps shown below to solve the equation. In which step did Raul make a mistake?
5x-3(2x+7)=2x+9
Step 1: 5x-6x-21=2x+9
Step 2: -11x-21=2x+9
Step 3: -12x=30
Step 4: x=-30/12
A. Step 1
B. Step 2
C. Step 3
D. Step 4
Answer:The answer is B, step two
Step-by-step explanation:5x-6x equals to -1x
2. The complex computation (6+2i)(6-21)-(3-4i)(3+4i) can be simplified to
(1) 15
(3) -10
(2) 39
(4-35
Answer:
the answer is 15
have a good day
how do I make another similar figure
I don't know how to find the slope and y intercept form y=-9x+15
Answer:
Slope=-9, y-intercept=15
Step-by-step explanation:
The slope is always with the x when in slope intercept form, and the y-intercept is the constant (the number with no variable).
Answer:
Slope: 9 y-Intercept Form: 15
Step-by-step explanation:
The formula for slope is y=mx+b. Mx is the slope and b is the y-intercept. Because your equation is written in this form, you can easily find the slope and y-intercept which are 9 and 15. I hope this helps :)
» Round 13.045 to the nearest whole number.
Answer:
13
Step-by-step explanation:
Have a good day
10% of the total time at school out of 360 minutes a day , how much time was spend at lunch ?
Answer:
36 minutes
Step-by-step explanation:
360/10=36 (percent is division of the number)
Please answer all i need help Factor the expression using the GCF. 50x-60 Next one Factor the expression using the GCF. 16m+40 next one Factor the expression using the GCF.27-45c next one Factor the expression using the GCF.
Answer:
10(5x - 6).
8(2m + 5).
9(3 - 5c)
Step-by-step explanation:
Given that
50x-60
16m+40
27-45c
The greatest common factor is a measure of the highest number present inside, or common to all the numbers that were listed. To take this one at a time, we have....
50x - 60. The highest number common to both of them is 10, and thus, we have
50x - 60 = 10(5x - 6), and this is the solved part.
16m + 40. The greatest number that's present inside both numbers is 8, and thus we have
16m + 40 = 8(2m + 5) and this is the solved part.
27 - 45c. The greatest common number is 9, and as a result, we have
27 - 45c = 9(3 - 5c), and this is the solution we were searching for
please give me the right answer i’ve been having trouble for an hour now
Answer:
B
Step-by-step explanation:
(x+4)(3x^2-7)
multiply and get 3x^3 +12x^2 -7x -28 which is anwser choice b
Given (4,1) and slope=2, write the equation in slope-intercept form
Answer:
y = 2x-7
Step-by-step explanation:
Point-slope equation for line of slope m that passes through (x₀,y₀):
y-y₀ = m(x-x₀)
y-1 = 2(x-4)
Put into slope-intercept form:
y = 2(x-4) + 1
y = 2x - 7
A soft-drink manufacturer purchases aluminum cans from an outside vendor. A random sample of 70 cans is selected from a large shipment, and each is tested for strength by applying an increasing load to the side of the can until it punctures. Of the 70 cans, 58 meet the specification for puncture resistance. Find a 95% confidence interval for the proportion of cans in the shipment that meet the specification. Round the answers to three decimal places.
Answer:
The 95% confidence interval for the proportion of cans in the shipment that meet the specification is (0.741, 0.917).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
70 cans, 58 meet the specification for puncture resistance. This means that [tex]n = 50, \pi = \frac{58}{70} = 0.829[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.829 - 1.96\sqrt{\frac{0.829*0.171}{70}} = 0.741[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.829 + 1.96\sqrt{\frac{0.829*0.171}{70}} = 0.917[/tex]
The 95% confidence interval for the proportion of cans in the shipment that meet the specification is (0.741, 0.917).
how to solve an angle in a triangle with two sides given
Step-by-step explanation:
..........................
In triangle ABC, the measure of the exterior angle at point B is 100°. If m∠A is 4 times larger than m∠c, FIND m∠c
pleaseeeeeeeeee!!!!!
Answer:
m<c = 20º
Step-by-step explanation:
We use these following definitions:
The sum of an interior angle with its exterior is of 180º.
The sum of the three interval angles of a triangle is 180º.
The measure of the exterior angle at point B is 100°.
This means that the measure of the interior angle is: 180 - 100 = 80º
m∠A is 4 times larger than m∠c
This means that the measure of angle c is x, and the measure of angle a is 4x. The other angle, B, is 80º. So
[tex]x + 4x + 80 = 180[/tex]
[tex]5x = 100[/tex]
[tex]x = \frac{100}{5}[/tex]
[tex]x = 20[/tex]
The measure of angle C is 20º.
x² - 121
What is a factored form of this expression
Answer:
(x+11)(x-11)
Step-by-step explanation:
(x+11)(x-11)
Answer:
(x+11)(x-11)
Step-by-step explanation:
If you factor it out, it works.
Shane bikes 5 miles to the park in 30 minutes and 3 miles to the library in 45 minutes. What was his average speed?
Step-by-step explanation:
Speed =__distancr covered___
Time taken
=5miles ×3miles÷30 mins×45mins
=15miles÷1350mins
=90 mins
5.Use the slope formula to calculate the slope of the path you selected in question 4. Round
your answer to the nearest hundredth. Show your work. Use the coordinates from question 1
and the pair in question 3 that 1.4.4 math. matches the path you chose. Then use the Compass Tool to
confirm your answer by dragging the point on the line that goes through the boat. (5 points: 3
points for a correctly written equation and work, 2 points for the slope
Answer:
0.96
Step-by-step expla its 0.96 but tell me if wrong. this is only for if u choose the North strait. because 0.959 rounded is 0.96
Answer:
Step-by-step explanation:
I really need help please
Answer:
50°
Step-by-step explanation:
the angles should add up to 180. there is a 90° angle abd a 40° angle which adds up to 130. 180-130 gives you rour missing angle if 50°.
If there are 52 successful outcomes in a sample with a size of 80, what is the
sample proportion?
A. 0.36
B. 0.72
C. 0.52
D. 0.65
Answer:
D. 0.65
Step-by-step explanation:
Do 52/80 to get the answer which is D.