Write a ratio that is equivalent to 13:2, other than 13:2 itself

It took Everly 55 minutes to run a 10-kilometer race last weekend. If you know that 1 kilometer equals 0.621 mile, how many minu

slega [8]

$\bf \cfrac{10km}{55mins}\cdot \cfrac{0.621miles}{1km}\implies \cfrac{62.1miles}{55mins}\approx 1.12909909\approx \boxed{1.13\frac{miles}{mins}}$

5 0

3 years ago

Find the product of the solutions of this equation 2x^2+26x+156=0

NARA [144]

Check the attached file for the answer.

7 0

4 years ago

Theresa Mitsoto invested $3,500 in a 3-year CD that paid 6.5% annual interest. She cashed out the CD at the end of two years wit

Andre45 [30]

Answer:

$56.875

Step-by-step explanation:

Given that :

Amount invested = principal, p = 3500

Interest rate, r = 6.5% = 0.065

Penalty on withdrawal = 3 month simple interest

Simple interest = principal * rate * time

Time = 3 months = 3/12 = 0.25 years

Hence,

Simple interest = 3500 * 0.065 * 0.25

Simple interest = $56.875

Hence, penalty paid = $56.875

7 0

3 years ago

Solve 2 1/2 divided by 5 1/3 = 8/x

ipn [44]

$2\frac { 1 }{ 2 } \quad divided\quad by\quad 5\frac { 1 }{ 3 } \\ \\ 2\frac { 1 }{ 2 } =2+\frac { 1 }{ 2 } =\frac { 5 }{ 2 } \\ \\ 5\frac { 1 }{ 3 } =5+\frac { 1 }{ 3 } =\frac { 15+1 }{ 3 } =\frac { 16 }{ 3 } \\ \\ \\ \frac { \frac { 5 }{ 2 } }{ \frac { 16 }{ 3 } }$

We're dividing fractions, so we will flip the one in the denominator upside down and we will multiply it with the numerator.

$\frac { \frac { 5 }{ 2 } }{ \frac { 16 }{ 3 } } \quad =\quad \frac { 5 }{ 2 } \cdot \frac { 3 }{ 16 } =\frac { 5\cdot 3 }{ 2\cdot 16 } =\frac { 15 }{ 32 }$

Let's equal this too 8/x

$\frac { 15 }{ 32 } =\frac { 8 }{ x }$

Cross multiply.

$8\cdot 32=15\cdot x\\ \\ 256=15x$

Divide both sides by 15.

$\frac { 256 }{ 15 } =\frac { 15x }{ 15 } \\ \\ \frac { 256 }{ 15 } =x$

4 0

3 years ago

I need help on this ! Asap

Gnoma [55]

Answer:

1. Given

2, Exterior sides on opposite rays

3. Definition of supplementary angles

4. If lines are ||, corresponding angles are equal

5. Substitution

Step-by-step explanation:

For the first one, it is given as shown in the problem. Also in the figure you can see that line s is parallel to line t.

2. ∠5 and ∠7 are adjacent, they share a common side. Their non-common side are rays that go in a direction opposite of each other. Also you can see that they form a straight line, which means that they are supplementary.

3. Supplementary angles simply put are angles that sum up to 180°. You know this for sure because of proof 2, specifically the part that they form a straight line. The measure of a straight line is 180°.

4. Corresponding angles are congruent. These are angles that have the same relative position when a line is intersected by parallel lines. You have other example in the figure like ∠2 and ∠6; ∠3 and ∠7.

5. This is substitution because ∠1 substituted ∠5 in this case. Since ∠1 is equal to ∠5, then it can substitute it in the equation given in step 3. This means that ∠1 and ∠7 are supplementary as well.

8 0

3 years ago